universe-review.cahtml> universe-review.cahead> universe-review.catitle>Moleculesuniverse-review.ca/title> universe-review.ca/head> universe-review.cabody bgcolor="white" text="black"> universe-review.caa name="table">universe-review.ca/a>universe-review.catable bgcolor="#EBFBFB" border="1" width="95%" align="left" frame="box">universe-review.catr> universe-review.caa href="index.htm" target="default.htm">universe-review.catd width="13%" align="center">universe-review.cab>Home Pageuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="overview.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Overviewuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="F00-contents.htm" target="default.htm">universe-review.catd width="11%" align="center">universe-review.cab>Site Mapuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="F18-index.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Indexuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="F17-glossary.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Appendixuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="option2.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Illustrationuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="FAQ.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>FAQuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="About.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Aboutuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a> universe-review.caa href="form.htm" target="default.htm">universe-review.catd width="10%" align="center">universe-review.cab>Contactuniverse-review.ca/b>universe-review.ca/td>universe-review.ca/a>universe-review.ca/tr>universe-review.ca/table> universe-review.cabr />universe-review.cabr /> universe-review.cah2>universe-review.cafont color="blue">Moleculesuniverse-review.ca/font>universe-review.ca/h2> universe-review.cahr align="left" width="20%" /> universe-review.cah3>Contentsuniverse-review.ca/h3> universe-review.caa href="universe-review.ca#quantum/default.htm#quantum/">Quantum Theory, Blackbody Radiationuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#correspondence/default.htm#correspondence/">Correspondence Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#uncertainty/default.htm#uncertainty/">Uncertainty Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#exclusion/default.htm#exclusion/">Exclusion Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#path/default.htm#path/">Path Integral, Transition to Qunatum Theoryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#quantization/default.htm#quantization/">First Quantization, Schrodinger Equationuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#interpretations/default.htm#interpretations/">Quantum Interpretationsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#hydrogen/default.htm#hydrogen/">Hydrogen Atomuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#covalent/default.htm#covalent/">Covalent Bond, Hydrogen Moleculeuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#ionic/default.htm#ionic/">Ionic Bond, Atomic Shellsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#hydrogenbond/default.htm#hydrogenbond/">Hydrogen Bond, Molecular Orbitaluniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#dipole/default.htm#dipole/">van der Waals Force, Dipole-Dipole Interactionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#physicalchem/default.htm#physicalchem/">Physical Chemistryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#inorganichem/default.htm#inorganichem/">Inorganic Chemistryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#references/default.htm#references/">Referencesuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#Index/default.htm#Index/">Indexuniverse-review.ca/a>universe-review.cabr /> universe-review.cahr align="left" width="20%" /> universe-review.cah3 align="center">universe-review.caa name="quantum">universe-review.ca/a>Quantum Theoryuniverse-review.casup>universe-review.caa href="universe-review.ca#r01/default.htm#r01/">1universe-review.ca/a>,universe-review.caa href="universe-review.ca#r02/default.htm#r02/">2universe-review.ca/a>universe-review.ca/sup>, Blackbody Radiationuniverse-review.ca/h3> universe-review.cap>Molecules are small objects not susceptible of direct observation even under the most powerful microscope. However, their properties can be deduced indirectly from experiments. These objects are different on the conceptual level as well. Classical physics can no longer offer a consistent description. It is replaced by quantum theory, which describes the objects only in term of probability, energy levels, and other quantum numbers. A well-defined orbit such as the path of a planet around the Sun becomes the probability of finding the object at a certain location in the microscopic world. Thus, all the illustrations related to these objects would be just a schematic diagram conveying some ideas, they should never be taken literally as the real thing.universe-review.ca/p> universe-review.catable border="0" width="100%">universe-review.catr> universe-review.catd width="35%">universe-review.caimg src="I12-01-blackbody.gif" name="Blackbody Radiation" alt="Blackbody Radiation" align="left" width="360"/>universe-review.ca/td> universe-review.catd width="65%"> Historically, the quantum theory began with the attempt to account for the discrepancy between the theoretical and observational blackbody radiation. The classical theory of Rayleigh-Jeans failed to fit the observation of the radiation energy distribution from a blackbody at high frequency. In searching for a modification that would reduce the contribution of the high frequencies to the energy, universe-review.caA NAME="Planck">universe-review.ca/A>Planck was led to make an assumption: The energy of the radiation with frequency universe-review.caimg src="I13-15-nu.jpg"> is restricted to integral multiples of a basic unit hv (a quantum), i.e., Euniverse-review.casub>universe-review.caimg src="I13-15-nu.jpg">universe-review.ca/sub> = nhuniverse-review.caimg src="I13-15-nu.jpg"> where h = 6.625x10universe-review.casup>-27universe-review.ca/sup> erg-sec is the Planck constant and n is an integer. With this assumption, Planck obtained an exact fit to the observed distribution of radiation energy. According to classical theory, electromagnetic radiation is a wave phenomenon. The Planck's assumption endows a particle aspect to the same entity. Such universe-review.caA NAME="waveparticle">universe-review.ca/A>wave-particle duality requires radical changes in the fundamental concepts of the properties of matter and energy. An introduction on the subject of "wave" can be found in the appendix: universe-review.caa href="R12-03-wave.htm">Wave, Sound, and Musicuniverse-review.ca/a>. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="35%">universe-review.cah4>Figure 12-01 Blackbody Radiation universe-review.ca/h4> universe-review.ca/td> universe-review.catd width="65%"> universe-review.ca/td> universe-review.ca/tr>universe-review.ca/table> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="correspondence">Correspondence Principleuniverse-review.ca/a>universe-review.ca/h3> universe-review.cap>The first difference is that whereas classical theory always deals with continuously varying quantities, quantum theory must also deal with discontinuous or indivisible processes (e.g., the unit of energy packed in a quantum). The second difference is that whereas classical theory completely determines the relationship between variables at an earlier time and those at a later time, quantum laws determine only probabilities of future events in terms of given conditions in the past.universe-review.ca/p> universe-review.cap>The Correspondence Principle states that the laws of quantum physics must be so chosen that in the classical limit, where many quanta are involved (e.g., n is a large integer in Euniverse-review.casub>universe-review.caimg src="I13-15-nu.jpg">universe-review.ca/sub>=nhuniverse-review.caimg src="I13-15-nu.jpg">), the quantum laws lead to the classical equations as an average. This requirement combined with indivisibility, and incomplete determinism define the quantum theory in an almost unique manner.universe-review.ca/p> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="uncertainty">Uncertainty Principleuniverse-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="60%"> universe-review.caa href="I03-05-uncertainty.jpg">universe-review.caimg src="I03-05-uncertainty.jpg" name="Uncertainty" alt="Uncertainty" align="left" width="480"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="40%">The Uncertainty Principle is derived from three elements: the wave-particle duality, the indivisibility of energy and momentum transfers, and the lack of complete determinism. It states that for a pair of universe-review.caA NAME="conjugate">universe-review.ca/A>conjugate variables such as position/momentum and time/energy (including the rest mass energy mcuniverse-review.casup>2universe-review.ca/sup>), universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="60%">universe-review.cah4>Figure 12-02 Uncertainty Principle universe-review.caa href="I03-05-uncertainty.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="40%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> it is impossible to have a precisely determined value of each member of the pair at the same time. This statement is illustrated with a schematic diagram in Figure 12-02. The corresponding formula is: universe-review.caimg src="I15-19-delta.jpg">x universe-review.caimg src="I15-19-delta.jpg">puniverse-review.casub>xuniverse-review.ca/sub> > universe-review.caimg src="I15-23-h.jpg">, where universe-review.caimg src="I15-19-delta.jpg"> denotes the uncertainty, x is the position of the point mass m along the x-axis, puniverse-review.casub>xuniverse-review.ca/sub> = m vuniverse-review.casub>xuniverse-review.ca/sub> is the momentum along the x-axis, vuniverse-review.casub>xuniverse-review.ca/sub> is the velocity along the x-axis, and universe-review.caimg src="I15-23-h.jpg"> = h/2universe-review.caimg src="I13-15-pi.jpg"> = 1.054x10universe-review.casup>-27universe-review.ca/sup> erg-sec. A similar relation exists for the uncertainty of the time t and energy E, e.g., universe-review.cabr />universe-review.caimg src="I15-19-delta.jpg">t universe-review.caimg src="I15-19-delta.jpg">E > universe-review.caimg src="I15-23-h.jpg">. In case of heavy mass (such as a macroscopic object), the uncertainties and thus the quantum effect becomes very small, classical physics is applicable once more. universe-review.caul>Many quantum phenomena such as superposition, probability density (or wave), vacuum fluctuation, and virtual particles are direct consequence of the uncertainty principle:universe-review.cabr />universe-review.cabr /> universe-review.cali>universe-review.caa name="superposition">universe-review.ca/a>By definition, a state consists of all the information needed to completely describe a system at an instant of time. Since the quantum state is specified by momentum, energy, angular momentum, or spin and there is an uncertainty in determining their value, it implies that a particle can occupy many quantum states (with different probability). This is called superposition. Figure 12-03a illustrates a very simple superposition of two spin states - one parallel and the universe-review.ca/li> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I15-41-superposition.jpg">universe-review.caimg src="I15-41-superposition.jpg" name="Superposition" alt="Superposition" align="left" width="225"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%">other anti-parallel to the direction of a magnetic field, where |universe-review.cab>auniverse-review.ca/b>|universe-review.casup>2universe-review.ca/sup> and |universe-review.cab>buniverse-review.ca/b>|universe-review.casup>2universe-review.ca/sup> are probabilities of finding the particle in the corresponding state. It is only when the state of the particle, e.g. the spin in this case, is measured that it settles into a definite state. But as soon as we stop monitoring its behavior, the particle dissolves into a superposition again.universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-03a Superposition universe-review.cabr />universe-review.caa href="I15-41-superposition.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="75%">Note : Probability = |Probability Amplitude|universe-review.casup>2universe-review.ca/sup>, e.g., universe-review.cab>auniverse-review.ca/b> and universe-review.cab>buniverse-review.ca/b> in Figure 12-03a are the probability amplitudes, the corresponding probabilities are |universe-review.cab>auniverse-review.ca/b>|universe-review.casup>2universe-review.ca/sup> and |universe-review.cab>buniverse-review.ca/b>|universe-review.casup>2universe-review.ca/sup>.universe-review.cabr />universe-review.cabr />universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.cali>universe-review.caa name="pattern">universe-review.ca/a>The uncertainty in space and time is interpreted as the probability of finding the particle at a certain time and place. For example, the electron within the confine of the nucleus exhibits a certain probability pattern. Figure 12-03b shows the probability distribution of an electron in the 3d state (muniverse-review.casub>universe-review.cai>luniverse-review.ca/i>universe-review.ca/sub>=0) of the hydrogen atom. When the electron moves in free space with a certain momentum p, the probability pattern displays a universe-review.caa href="R12-03-wave.htm">wave-like formuniverse-review.ca/a> with the wavelength universe-review.caimg src="I13-15-lambda.jpg"> = h/p, which is known as the universe-review.caa name="deB">universe-review.ca/a>universe-review.cai>de Broglie wavelengthuniverse-review.ca/i>. Since there is a spread of momentum according to the uncertainty principle, the electron wave is described by a wave packet, which is the combination from waves of different wavelengths and universe-review.ca/li> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="15%"> universe-review.caa href="I15-42-probability.jpg">universe-review.caimg src="I15-42-probability.jpg" name="Probability" alt="Probability" align="left" width="150"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="15%"> universe-review.caa href="I15-43-deBroglie.jpg">universe-review.caimg src="I15-43-deBroglie.jpg" name="de Broglie Wave" alt="de Broglie Wave" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="70%">amplitudes (Figure 12-03c). If an object's wavelength is of a similar order to the size of the objects around it, the wave nature comes to the fore. The wavelength of a macroscopic object such as a moving car is something around 10universe-review.casup>-36universe-review.ca/sup> cm; thus it takes some pretty tiny objects to expose the car's wavelike properties. Only microscopic universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="15%">universe-review.cah4>Figure 12-03b Probabilty Pattern universe-review.caa href="I15-42-probability.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="15%">universe-review.cah4>Figure 12-03c de Broglie Wave universe-review.caa href="I15-43-deBroglie.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="70%">objects such as electron has a large enough wavelength to show its wavelike property with objects in manageable size. For example, the de Broglie wavelength for a 75 ev electron is 2 x 10universe-review.casup>-8universe-review.ca/sup> cm, thus the spacing between atoms in a crystal is a good diffraction grating for such electron.universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I03-05-quantumvacuum.jpg">universe-review.caimg src="I03-05-quantumvacuum.jpg" name="vacuum" alt="Quantum Vacuum" align="left" width="230"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%">universe-review.cali>universe-review.caa name="vacuum">universe-review.ca/a>In classical physics, empty space-time is called the universe-review.caA NAME="vacuum">universe-review.ca/A>vacuum. The classical vacuum is utterly featureless. However, in quantum mechanics, the vacuum is a much more complex entity. It is far from featureless and far from empty. The quantum vacuum is just one particular state of a quantum field. It is the quantum mechanical state in which no field quanta are excited, that is, no real particles are present. Hence, it is the "ground state" of the quantum field, the state of minimum energy. Figure 12-03d illustrates the kind of activities going on in a quantum vacuum. It shows virtual particle pairs appear, lead a brief existence, and then annihilate one another in accordance with the Uncertainty Principle.universe-review.ca/li>universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-03d Vacuum Fluctuation universe-review.caa href="I03-05-quantumvacuum.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.cali>There are two kinds of virtual particle. One kind are particles produced out of the vacuum as mentioned above. Many such particles can be produced only in virtual pairs (as shown in Figure 12-03d) in order to preserve the existing balance of properties such as electric charge in the Universe. But particles, which are not constrained by these conservation laws, notably photons, can be produced without any mirror image counterpart (such as in the Casimir effect below).universe-review.cabr />universe-review.cabr /> The particles which join the vertices in a universe-review.caa href="R15-12-QFT.htm#Feynman">Feynman diagramuniverse-review.ca/a > (Figure12-03e) are also virtual particles and can never be detected directly, even though they are of key importance in determining the way "real" particles interact. This kind of virtual particle can be generated in violation of conservation laws, which are obeyed overall during the interaction. All quantum particles can be thought of as being surrounded by a cloud of virtual particles (and pairs) of various kinds, which are being created and (usually) reabsorbed by the parent particle. The lifetime of each of these virtual particles universe-review.ca/li> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%">universe-review.caimg src="I15-23-s7.jpg" name="Virtual Particle" alt="Virtual Particle" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%">(and therefore the distance it can travel from its parent particle) depends on its mass-energy and the leeway allowed by the uncertainty principle. Interactions occur when a real particle come close enough (as in high energy collision) for one or more of the virtual particles in the cloud to be absorbed by the other real particle.universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-03e Feynman Diagram universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-19-Casimir.jpg">universe-review.caimg src="I12-19-Casimir.jpg" name="Casimir Effect" alt="Casimir Effect" align="left" width="225"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%">Since the virtual photons in between two parallel metal plates placed a short distance apart can exist only when they can form a universe-review.caa href="R12-03-wave.htm#standing">standing waveuniverse-review.ca/a>, there are fewer photons in each cubic centimeter of vacuum between the plates than there are in the vacuum outside. So, in effect, there is an excess pressure from outside pushing the plates together. This is known as universe-review.caa name="Casimir">universe-review.ca/a>Casimir effect (see Figure 12-03f). The resulting force is very small, but it has been measured (for plates separated by gaps of a few nanometers), proving that quantum fluctuations of the vacuum are a real phenomenon. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-03f Casimir Effect universe-review.cabr />universe-review.caa href="I12-19-Casimir.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="75%"> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.ca/ul> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="exclusion">Exclusion Principleuniverse-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="45%"> universe-review.caimg src="I12-02-exclusion.jpg" name="Exclusion Principle" alt="Exclusion Principle" align="left" width="325"/>universe-review.ca/td> universe-review.catd width="55%"> The Pauli Exclusion Principle states that identical universe-review.caA NAME="fermions">universe-review.ca/A>fermions -- one type of fundamental matter with 1/2 integer spin quantum number -- cannot be in the same place at the same time and with the same orientation (i.e., cannot have the same quantum state). It is this Exclusion Principle that requires the electrons in an atom to occupy different energy levels instead of all congregating in the lowest energy level. Chemistry would be very different without this rule. The exclusion principle is also responsible for the degenerate pressure, which prevents the White Dwarf from complete collapse. The other type of matter, universe-review.caA NAME="bosons">universe-review.ca/A>bosons (particles with integer spin quantum number), do not have this property. The boson gas can form universe-review.caA NAME="condensate">universe-review.ca/A>Bose-Einstein condensate near absolution zero temperature. They are all in the same quantum state, and behave like a single entity. Figure 12-04 shows the bosons bunch together, while the fermions keep their distance at temperature a few hundreds billionths of a degree above absolution zero (nanoKelvin=nK). Superfluidity refers to frictionless universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="45%">universe-review.cah4>Figure 12-04 Fermions and Bosonsuniverse-review.ca/h4>universe-review.ca/td> universe-review.catd width="55%">flow of spin 0 boson, e.g., helium-4 at low temperature. universe-review.cabr />universe-review.cabr /> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="path">Path Integraluniverse-review.casup>universe-review.caa href="universe-review.ca#r03/default.htm#r03/">3universe-review.ca/a>universe-review.ca/sup>, Transition to Quantum Theoryuniverse-review.ca/a>universe-review.ca/h3> The transition from classical to quantum in theoretical physics is most elegantly prescribed by path integral. According to classical physics the movement from "here" at time tuniverse-review.casub>1universe-review.ca/sub> to "there" at time tuniverse-review.casub>2universe-review.ca/sub> in Figure 12-05 is through the shortest path (the dash line) in evaluating the universe-review.caa href="I12-15-action.jpg">Actionuniverse-review.ca/a>. In quantum theory all paths are possible. Each possible route corresponds to a "history". Each universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-03-pathintegral.jpg">universe-review.caimg src="I12-03-pathintegral.jpg" name="Path Integral" alt="Path Integral" align="left" width="230"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%"> history has associated with it a number, called the amplitude (do not confuse this transition amplitude with the state vector amplitude in universe-review.caa href="universe-review.ca#superposition/default.htm#superposition/">superpositionuniverse-review.ca/a>), which defines the probability of that particular path being followed. While the classical path (the dash line) occurs with higher probability, the probability for the other paths vary according to a weighting factor. The probability of going from "here" to "there" is the sum of the probability for all paths. This formulism was originally devised by universe-review.caa href="I15-16-Feynman.jpg">Richard Feynmanuniverse-review.ca/a> for his PhD thesis in early 1940s. Twenty years earlier the transition from classical to quantum had to be formulated with a postulation which can be shown to be equivalent to the method of path integral. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-05 Path Integral universe-review.cabr />universe-review.caa href="I12-03-pathintegral.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td>universe-review.catd width="75%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="quantization">First Quantization, Schrodinger Equationuniverse-review.casup>universe-review.caa href="universe-review.ca#r04/default.htm#r04/">4universe-review.ca/a>universe-review.ca/sup>universe-review.ca/a>universe-review.ca/h3> universe-review.cap>It was postulated that the momentum p and position q are no longer mere numbers but are operators satisfying the commutative relation:universe-review.cabr />universe-review.cabr /> (qp - pq)universe-review.caimg src="I15-23-psi.jpg"> = universe-review.cai>iuniverse-review.ca/i>universe-review.caimg src="I15-23-h.jpg">universe-review.caimg src="I15-23-psi.jpg">. universe-review.cabr />universe-review.cabr /> This is called the first quantization, which endows wave property to a particle. Actually only p is treated as an operator - a differential operator acting on the wave function universe-review.caimg src="I15-23-psi.jpg">(q), q remains to be a number. The commutative relation can be viewed as a mathematical statement for the Uncertainty Principle. Since it implies that p cannot be a function of q (because it would mean p and q can be determined precisely at the same time), p can be related to q only in the form of an operator such asuniverse-review.cabr /> - universe-review.cai>iuniverse-review.ca/i> universe-review.caimg src="I15-23-h.jpg"> d/dq. The commutative relation is the direct result of such interpretation. Application of this rule for p and q to the equation relating the total energy E to the kinetic energy puniverse-review.casup>2universe-review.ca/sup>/2m and the potential energy V(q), e.g., E = puniverse-review.casup>2universe-review.ca/sup>/2m + V(q), yields the time-independent Schrodinger Equation for one particle with mass m and interaction V: universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd> universe-review.caa name="Schrodinger">universe-review.ca/a>universe-review.caimg src="I12-04-SchrodingerEq.jpg" name="Schrodinger Equation" alt="Schrodinger Equation" align="left" width="400"/>universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> For a given interaction V the problem is to find the Energy E and the corresponding universe-review.caA NAME="wave">universe-review.ca/A>wave function universe-review.caimg src="I15-23-psi.jpg">. The wave function is the probability amplitude of finding the particle at certain position (again do not confuse this amplitude with the state vector amplitude in universe-review.caa href="universe-review.ca#superposition/default.htm#superposition/">superpositionuniverse-review.ca/a>). The absolute square of the amplitude is the probability density. The Schrodinger Equation can be expanded to a system of many particles and more than one source of interaction. However, it becomes rapidly un-manageable beyond one particle and one interacting source located at the center (of the coordinate frame). universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="interpretations">Quantum Interpretationsuniverse-review.ca/a>universe-review.ca/h3> universe-review.caul> universe-review.cali>Copenhagen Interpretation - The quantum system usually exists in the universe-review.caa href="universe-review.ca#superposition/default.htm#superposition/">superposition of statesuniverse-review.ca/a>. It is only through the measurement that a certain state reveals its identity (according to the associated probability). Such situation does not bother practical physicists, who just carry out routine calculations or experiments, as long as the rules of quantum theory yield consistent results. It is the pure theorists and philosophers, who are very un-comfortable with such interpretation. universe-review.caa name="cat">universe-review.ca/a>Schrodinger himself was particularly distressed about two things -- the idea that a quantum system could be in a superposition of states, and the requirement of an intelligent observer to "collapse the wave function" and force a quantum system to take up an unique state. He used a "thought experiment" to demonstrate the absurdity of such an interpretation, which could result in a cat half alive and half dead. This is known as the "Schrodinger's cat paradox". According to the idea of superposition of states, a radioactive nucleus could be half decayed and half not decayed, unless its state is measured. Schrodinger pointed out that the radioactive substance could be sealed in a box with a universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-21-cat.jpg">universe-review.caimg src="I12-21-cat.jpg" name="Schrodinger's Cat" alt="Schrodinger's Cat" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> detector to monitor it. The detector is wired up to release a cloud of poison gas if the radioactive material decays; while the famous cat is kept inside. If the box is sealed and nobody looks into it, then the radioactive nucleus is in a fifty-fifty superposition of states, so are the poison gas (has and has not been released) and the cat (has and has not been killed, see Figure 12-06a). Thus, everything remains in limbo until an intelligent observer looks into the box. At this point, the superposition collapses and the cat becomes either dead or alive. But in spite of such nonsense as this paradox, the Copenhagen interpretation is still enshrined in most textbooks as the standard interpretation, and no cat has ever been put through such indignities.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06a Schrodinger's Cat universe-review.caa href="I12-21-cat.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-21-decoherence.jpg">universe-review.caimg src="I12-21-decoherence.jpg" name="Decoherence" alt="Decoherence" align="left" width="240"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> universe-review.cali>universe-review.caa name="decoherence">universe-review.ca/a>Decoherence - It is suggested that coupling between a quantum system in a superposition and the environment in which it is embedded leads the system to 'collapse' or decay over time into one state or another. The rate of decoherence depends on the size of the quantum system. Physicists can now create and maintain quantum particles such as atoms or photons in superpositions for significant periods of time, if the coupling to the environment is weak. For a system as big as a cat, however, comprised of billions upon billions of atoms, decoherence happens almost instantaneously, so that the cat can never be both alive and dead for any measurable instant (Figure 12-06b). The obvious flaw with this argument is that nobody knows where to draw the line. Thus, the boundary between the two extremes, where a quantum system have enough contact with the outside world to start behaving like a classical object, is currently a subject of active researches.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06b Decoherence universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="30%"> universe-review.caa href="I13-22-MatterWave.jpg">universe-review.caimg src="I13-22-MatterWave.jpg" name="Matter Wave" alt="Matter Wave" align="left" width="300"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="70%"> universe-review.caa name="MatterWave">universe-review.ca/a>Recently in 2004, half-a-dozen experiments have been designed to determine the boundary between the classical and quantum world. One experiment shown in Figure 12-06c fires Cuniverse-review.casub>70universe-review.ca/sub> (70 carbon atoms in the soccerball-like crystal of about 1 nm across) universe-review.caa href="I13-21-fullerene.jpg">fullerene ballsuniverse-review.ca/a> at 190 m/sec toward two diffraction gratings. The first grating creates the matter wave from the fullerenes. The wave is then diffracted by the second grating and the interference pattern is formed on the detecting screen demonstrating the wave property universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="30%">universe-review.cah4>Figure 12-06c Matter-Wave Experiment universe-review.caa href="I13-22-MatterWave.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="70%">of the fullerenes. However, the interference pattern fades away if the fullerenes are heated by a laser heater (to about 2700universe-review.casup>ouniverse-review.ca/sup>C) or collide with gas (leaking into the vacuum chamber of the universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> experiment). No one has a definitive answer for how the striking photons or molecules switch between quantum and classical behavior. One explanation is that the interaction causes an uncertainty in the position of the fullerenes, blurring the interference pattern. Another idea asserts that the disappearance of the quantum property is caused by entanglement between the photons/molecules, the fullerenes, and the rest of the world (via the wall of the chamber). It goes on further to speculate that if an apertures can be created on the scale of a person's de Broglie wavelngth (~ 10universe-review.casup>-33universe-review.ca/sup> cm) and an isolated environment can be set up, then that person can turn quantum as described in the section of "universe-review.caa href="universe-review.ca#manyworlds/default.htm#manyworlds/">many worlduniverse-review.ca/a>". universe-review.cabr />universe-review.cabr />universe-review.cali>universe-review.caa name="hidden">universe-review.ca/a>Hidden Variables - This interpretation is based on the assumption that all the usual versions of quantum mechanics are incomplete, and that there is an underlying layer of reality which contains additional information about the world. This additional information is in the form of the hidden variables. If physicists knew the values of these hidden variables, the arguments goes, they could predict the precise outcomes of particular measurements, not just the probabilities of getting particular results. A helpful analogy can be made with a pack of playing cards prepared by a cheating card dealer universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-21-dealer.jpg">universe-review.caimg src="I12-21-dealer.jpg" name="Card Dealer" alt="Card Dealer" align="left" width="240"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> (Figure 12-06d). He knows precisely the sequence in the deck; only the ignorant gamblers insist that the chance of picking a particular card is 1 in 52. Thus, it seems that the hidden variables idea is much more sensible than the Copenhagen interpretation. However, it was ignored by most physicists largely because the mathematician John von Neumann had devised a proof that they could not work in the quantum world. Eventually, it is shown that the whole argument against hidden variables was based on an unfounded assumption. The key feature of hidden variables theory, which still disturbs many people is that they are essentially non-local. It is shown lately that non-locality is an integral part of the quantum world. Finally, the idea of hidden variables is taken more seriously by more scientists in the last ten years.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06d Hidden Variables, aka Card Dealer universe-review.caa href="I12-21-dealer.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-21-twoslits.jpg">universe-review.caimg src="I12-21-twoslits.jpg" name="Double-Slit Experiment" alt="Double-Slit Experiment" align="left" width="228"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> universe-review.cali>universe-review.caa name="manyworlds">universe-review.ca/a>Many Worlds - This interpretation states that whenever the world is faced with a choice at the quantum level, the universe divides into many, so that all possible options are followed, i.e., all the states are realized. Originally, it was suggested that we might think of the experiment with two slits in terms of two different realities, in one of which the electron goes thought slit 1 while in the other it goes through slit 2. Our world is a recombination of the two possibilities (the two worlds merge to become one again, see double slit pattern in Figure universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06e Double-Slit Experiment universe-review.caa href="I12-21-twoslits.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">12-06e), producing interference between the two worlds. When we look to see which slit the electron goes through, we make one world real while the other disappears, so there is no interference (see single slit pattern in Figure 12-06e).universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I02-26-quantumworlds.jpg">universe-review.caimg src="I02-26-quantumworlds.jpg" name="Quantum Worlds" alt="Qunatum Worlds" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> The idea has been expanded further to treat each outcome of every possible quantum event as existing in a real world. It has been shown that such interpretation leads to exactly the same predictions for the outcome of experiments as the other interpretations. The only problem is that there is no way to test, and it is difficult to imagine the mind-boggling idea of 10universe-review.casup>100universe-review.ca/sup> slightly imperfect copies of oneself all constantly splitting into further copies (see Figure 12-06f). However, some cosmologists find it useful to get around the puzzle, which is insurmountable in the Copenhagen interpretation (it requires an outer observer to work), of explaining what observation can collapse the wave function of the entire Universe and bring it into reality. universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06f Quantum Worlds universe-review.caa href="I02-26-quantumworlds.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-21-Penrose.jpg">universe-review.caimg src="I12-21-Penrose.jpg" name="Penrose Interpretation" alt="Penrose Interpretation" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> universe-review.cali>universe-review.caa name="Penrose">universe-review.ca/a>Penrose Interpretation - Recently in 2005, Roger Penrose comes up with a new quantum interpretation. According to his theory each quantum event would create its own distortions in space-time, which requires energy to sustain. Since the stability of a system depends on the amount of energy involved (the lesser the easier to maintain), a macroscopic object tends to settle down in only one location (producing only one distorted space-time). For microscopic objects such as electrons, atoms, and molecules the distortion is negligible; they can persist with the many quantum states (superposition) essentially forever as standard quantum theory predicts. There is an on-going experiment to verify this theory. It directs a laser beam (separated by universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-06g Penrose Inter- pretation universe-review.caa href="I12-21-Penrose.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/td>universe-review.catd width="80%">a beam splitter) toward a very tiny mirror to check if it can be in two states at the same time. Until now, the experiment is running with a significantly smaller mirror (an object called fullerene ball) than needed to test Penrose's theory. universe-review.ca/li>universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.ca/ul> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="hydrogen">Hydrogen Atomuniverse-review.ca/a>universe-review.casup>universe-review.caa href="universe-review.ca#r05/default.htm#r05/">5universe-review.ca/a>,universe-review.caa href="universe-review.ca#r06/default.htm#r06/">6universe-review.ca/a>universe-review.ca/sup>universe-review.ca/h3> Beside some idealized cases, analytical solution of the Schrodinger equation can be obtained only for hydrogen atom which has one electron moving about an atomic nucleus. The energy levels are shown in Figure 12-07a while the universe-review.caA NAME="probability">universe-review.ca/A>probability density corresponding to different quantum states are shown in Figure 12-07b where n, universe-review.cai>luniverse-review.ca/i>, and m are the total, orbital, and magnetic universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-05-energy.jpg">universe-review.caimg src="I12-05-energy.jpg" name="Energy Levels" alt="Energy Levels" align="left" width="210"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="25%"> universe-review.caa href="I12-06-wave.jpg">universe-review.caimg src="I12-06-wave.jpg" name="Probability Density" alt="Probability Density" align="left" width="230"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="50%">quantum number respectively; the probability densities have either spherical symmetry or rotational symmetry about the z axis. When the electron jumps from a higher energy level Euniverse-review.casub>n+1universe-review.ca/sub> to a lower one Euniverse-review.casub>nuniverse-review.ca/sub>, a photon with frequency universe-review.caimg src="I13-15-nu.jpg"> = (Euniverse-review.casub>n+1universe-review.ca/sub> - Euniverse-review.casub>nuniverse-review.ca/sub>)/h is released. Excitation is the reversed process when the electron in energy level Euniverse-review.casub>nuniverse-review.ca/sub> absorbs a photon with frequency universe-review.caimg src="I13-15-nu.jpg">. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-07a Energy Levels universe-review.cabr />universe-review.caa href="I12-05-energy.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="25%">universe-review.cah4>Figure 12-07b Probability Density universe-review.caa href="I12-06-wave.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="50%"> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> The state of the electron in an atom is specified by four quantum numbers. The universe-review.caA NAME="number">universe-review.ca/A>principal quantum number n determines the energy level; its value runs from 1, 2, 3, ... For each n, the orbital quantum number universe-review.cai>luniverse-review.ca/i> = 0, 1, 2, ... (n-1); it is related to the magnitude of angular momentum. Then for each universe-review.cai>luniverse-review.ca/i>, the magnetic quantum number m can be universe-review.cai>-luniverse-review.ca/i>, universe-review.cai>-luniverse-review.ca/i>+1, ...universe-review.cai>luniverse-review.ca/i>-1, universe-review.cai>luniverse-review.ca/i>; it is related to the z component of the angular momentum (see Figure 12-07a). The spin quantum number s is either +1/2 or -1/2. For n = 1, universe-review.cai>luniverse-review.ca/i> = 0, m = 0, there is only 2 possible quantum states for the electron, with s = +1/2 and -1/2 respectively. For n = 2, universe-review.cai>luniverse-review.ca/i> = 0, m = 0 and universe-review.cai>luniverse-review.ca/i> =1, m = -1, 0, +1; there is a total of 2 + 6 = 8 possible quantum states. Therefore, it requires 2 electrons to complete the shell for n = 1, and 8 electrons to complete the shell for n = 2, ...and so on (see more in universe-review.caa href="F13-atom.htm#Table1301">Table 13-01universe-review.ca/a>, topic Atom). The orbital quantum number universe-review.cai>luniverse-review.ca/i> is often designated by a letter, s for universe-review.cai>luniverse-review.ca/i> = 0, p for universe-review.cai>luniverse-review.ca/i> = 1, d for universe-review.cai>luniverse-review.ca/i> = 2, and f for universe-review.cai>luniverse-review.ca/i> = 3 ... The quantum number universe-review.cai>luniverse-review.ca/i> is non-additive while m is additive and relates to an universe-review.caa href="R15-10-groups.htm">Abelian groupuniverse-review.ca/a> (e.g., the two dimensional rotation about the z-axis). universe-review.caA NAME="multiplet">universe-review.ca/A>Particles having the same non-additive quantum numbers but differing from each other by their additive quantum numbers are said to belong to the same multiplet. The number of members of a multiplet is called its multiplicity. For a given multiplet universe-review.cai>luniverse-review.ca/i> the multiplictiy is equal to 2universe-review.cai>luniverse-review.ca/i>+1. universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="covalent">Covalent Bond, Hydrogen Moleculeuniverse-review.casup>universe-review.caa href="universe-review.ca#r07/default.htm#r07/">7universe-review.ca/a>universe-review.ca/sup>universe-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-07-H2wave.jpg">universe-review.caimg src="I12-07-H2wave.jpg" name="H2 Wave Function" alt="H2 Wave Function" align="left" width="280"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="25%"> universe-review.caa href="I12-08-H2energy.gif">universe-review.caimg src="I12-08-H2energy.gif" name="H2 Potential Curve" alt="Potential Curve" align="left" width="170"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="50%">When two hydrogen atoms approach each other, the final configuration depends on the spin of the two electrons (a consequence of the Exclusion Principle). If the spin of the two electrons is parallel as shown in the right side of Figure 12-08, the two atoms remain separated. However, if the spin of the two electrons is antiparallel as shown in the left side of Figure 12-08, the two atoms combine to form a hydrogen molecule. There is a high probability universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-08 Huniverse-review.casub>2universe-review.ca/sub> Wave Function universe-review.cabr />universe-review.caa href="I12-07-H2wave.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="25%">universe-review.cah4>Figure 12-09 Huniverse-review.casub>2universe-review.ca/sub> Potential Curve universe-review.caa href="I12-08-H2energy.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="50%">of finding the electrons in between the atomic nuclei and this "electron cloud" tends to keep them from breaking up. This kind of binding is universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> called covalent bond, and is purely a quantum effect. Figure 12-09 shows the electronic energy as a function of inter-nuclear separation. It is usually referred to as universe-review.caA NAME="potential">universe-review.ca/A>potential curve. The potential curve can be derived either theoretically from the numerical solution of the Schrodinger equation or experimentally by analyzing the spectroscopic data. The potential curve Uuniverse-review.casub>Auniverse-review.ca/sub> is repulsive while Uuniverse-review.casub>Suniverse-review.ca/sub> forms a potential well to keep the atomic nuclei within unless they absorb a quantum of light with energy more than the dissociation energy of 4.52 ev. universe-review.cabr />universe-review.cabr /> In presenting the potential curve for a diatomic molecule, one of the atomic nucleus is usually fixed at the origin of the coordinate frame. The other nucleus is then portrayed as vibrating and rotating inside the potential well as shown in Figure 12-10a. The vibration is restricted to discrete energy levels. Each of the vibrational energy level universe-review.cab>vuniverse-review.ca/b> is further split into a series of rotational energy levels universe-review.cab>Juniverse-review.ca/b> called vibrational band. Wave functions are shown in two vibrational energy levels in Figure 12-10b. According to classical physics, particle cannot penetrate the potential wall; however, in quantum there is a certain probability of infiltration (tunneling) outside the wall (see Figure 12-10b). In general, transitions are favored by superimposing an initial universe-review.catable border="0" width="100%">universe-review.catr> universe-review.catd width="25%"> universe-review.caa href="I12-09-rotation.jpg">universe-review.caimg src="I12-09-rotation.jpg" name="Energy Levels" alt="Energy Levels" align="left" width="285" />universe-review.ca/a>universe-review.ca/td> universe-review.catd width="20%">universe-review.caa href="I12-09-vtransition.jpg">universe-review.caimg src="I12-09-vtransition.jpg" name="Transition" alt="Transition" align="left" width="170" />universe-review.ca/a>universe-review.ca/td> universe-review.catd width="55%">configuration of high probability with a final one of high probability as shown by the green line in Figure 12-10b. Transitions are also governed by selection rules, which usually allow transitions to occur only between change of the rotational or vibrational quantum number by an amount universe-review.caimg src="I15-31-plusminu.jpg">1. The former is related to the initial and final states of the molecule, which favors the one step change in the rotational configuration. While the latter is linked to the oscillating state of the molecule, which occurs only at certain resonant energy so that the emitting or absorbing photon can carry only universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-10a Vibrational and Rotational Energy Levels universe-review.caa href="I12-09-rotation.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="20%">universe-review.cah4>Figure 12-10b Transition universe-review.caa href="I12-09-vtransition.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="55%">that amount - one step at a time.universe-review.cabr />universe-review.cabr />universe-review.cabr />universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="ionic">Ionic Bonduniverse-review.casup>universe-review.caa href="universe-review.ca#r08/default.htm#r08/">8universe-review.ca/a>universe-review.ca/sup>, Atomic Shellsuniverse-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="30%"> universe-review.caa href="I12-12-shells.gif">universe-review.caimg src="I12-12-shells.gif" name="Atomic Shells" alt="Atomic Shells" align="left" width="350" />universe-review.ca/a>universe-review.ca/td> universe-review.catd width="70%">The most stable electron configuration of an atom consists of closed shells -- 2 for the n =1 shell; 8 for the n = 2 shell; ... (See Figure 12-11.) Thus He with 2 electrons and Ne with 10 electrons are among the most stable chemical elements. Atoms with incomplete outer shells tend to gain or lose electrons in order to attain stable configuration, becoming negative or positive ions in the process. For example, it requires 5.1 ev to ionize (remove) the outer shell electron from the sodium (Na); while adding an electron to the incomplete shell of chlorine (Cl) releases 3.8 ev. Thus the formation of a Nauniverse-review.casup>+universe-review.ca/sup> ion and a Cluniverse-review.casup>-universe-review.ca/sup> ion by the donation of one electron of Na to Cl requires just 5.1 - 3.8 = 1.3 ev. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="30%">universe-review.cah4> Figure 12-11 Atomic Shells universe-review.caa href="I12-12-shells.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="70%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="30%"> universe-review.caa href="I12-10-ionic.jpg">universe-review.caimg src="I12-10-ionic.jpg" name="Ionic Bond" alt="Ionic Bond" align="left" width="290" />universe-review.ca/a>universe-review.ca/td> universe-review.catd width="70%"> Figure 12-12 shows the decrease in potential energy as the Nauniverse-review.casup>+universe-review.ca/sup> and Cluniverse-review.casup>-universe-review.ca/sup> ions approaching each other. For very small separation of the ions, however, there is a strong repulsion due to the Exclusion Principle. The minimum in the potential curve occurs at r = 0.24 nm. At this separation the mutually attractive and repulsive forces on the ions exactly balance, and the system is in equilibrium with the creation of an ionic bond. To dissociate a NaCl molecule into Na and Cl atoms requires an energy of 4.2 ev, breaking it up into Nauniverse-review.casup>+universe-review.ca/sup> and Cluniverse-review.casup>-universe-review.ca/sup> ions requires an additional energy of 1.3 ev. universe-review.cabr />universe-review.cabr /> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="30%">universe-review.cah4> Figure 12-12 Ionic Bond universe-review.caa href="I12-10-ionic.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="70%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> Table 12-01 below shows the differences between ionic and covalent compounds.universe-review.cabr />universe-review.cabr /> universe-review.catable bgcolor="#EBFBFB" border="1" width="80%" align="center"> universe-review.catr> universe-review.cath>Propertyuniverse-review.ca/th> universe-review.cath>Ionic Compoundsuniverse-review.ca/th> universe-review.cath>Covalent Compoundsuniverse-review.ca/th> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Elementsuniverse-review.ca/td> universe-review.catd align="center">metal - nonmetaluniverse-review.ca/td> universe-review.catd align="center">nonmetal - nonmetaluniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Phase (at STP)universe-review.ca/td> universe-review.catd align="center">solid (in universe-review.caa href="I01-04-crystal.gif">crystal latticeuniverse-review.ca/a>)universe-review.ca/td> universe-review.catd align="center">solid, liquid or gasuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Hardnessuniverse-review.ca/td> universe-review.catd align="center">hard and brittle (salt)universe-review.ca/td> universe-review.catd align="center">brittle and weak (sugar) universe-review.cabr />or soft and waxy (butter)universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Melting/Boiling Pointsuniverse-review.ca/td> universe-review.catd align="center">highuniverse-review.ca/td> universe-review.catd align="center">lowuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Solubilityuniverse-review.ca/td> universe-review.catd align="center">mostly soluble in wateruniverse-review.ca/td> universe-review.catd align="center">solubility varies widelyuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Electrical Conductivityuniverse-review.ca/td> universe-review.catd align="center">solid - nonconductor, universe-review.cabr />liquid or aqueous solution - conductoruniverse-review.ca/td> universe-review.catd align="center">insulatorsuniverse-review.ca/td> universe-review.ca/tr> universe-review.ca/table> universe-review.cah4 align="center">Table 12-01 Properties of Ionic and Covalent Compoundsuniverse-review.ca/h4> Note: STP - standard conditions of 0universe-review.casup>ouniverse-review.ca/sup>C temperature and 1 atmospheric pressure (= 14.7 lb/sq-in = 101 kpa).universe-review.cabr />universe-review.cabr /> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="hydrogenbond">universe-review.ca/a>Hydrogen Bonduniverse-review.casup>universe-review.caa href="universe-review.ca#r09/default.htm#r09/">9universe-review.ca/a>universe-review.ca/sup>, Molecular Orbitaluniverse-review.casup>universe-review.caa href="universe-review.ca#r10/default.htm#r10/">10universe-review.ca/a>universe-review.ca/sup>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="15%"> universe-review.caa href="R12-01-orbitalwave.htm">universe-review.caimg src="I12-11-orbitalwave.jpg" name="Orbitals" alt="Orbitals" align="left" width="148"/>universe-review.ca/td> universe-review.catd width="20%">universe-review.caa href="I12-11-orbitalenergy.gif">universe-review.caimg src="I12-11-orbitalenergy.gif" name="Orbital Energy Levels" alt="Orbital Energy Levels" align="left" width="198"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="65%">It becomes very difficult to solve the Schrodinger equation numerically for molecule with many electrons. An approximate method called universe-review.caA NAME="MO">universe-review.ca/A>Molecular Orbital Theory (MO for short) has been developed for constructing reasonably accurate molecular structure (the wave functions and energy levels) with reasonably computational time. The MO starts with a linear combination of the wave functions for the electrons of each atom as shown in the left side of Figure 12-13a. The energy of the system is minimized with respect to the coefficients of the linear combination at different inter-atomic separation. The final result yields the wave functions (probability amplitude) for the molecule as shown in the universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="15%">universe-review.cah4>Figure 12-13a Orbitals universe-review.cabr />universe-review.caa href="R12-01-orbitalwave.htm">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="20%">universe-review.cah4>Figure 12-13b Orbital Energy Levels universe-review.caa href="I12-11-orbitalenergy.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="65%">right side of Figure 12-13a as well as the molecular energy levels as shown in Figure 12-13b. The isosurface shown in Figure 12-13a is called atomic or molecular universe-review.caA NAME="orbitals">universe-review.ca/A> orbitals. It is defined as the universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> surface within which the probability of finding the electron has some definite value, say 90%. The molecular orbital designated with an * is the unstable antibonding state, otherwise, it is the stable bonding state. The + or - sign signifies a positive or negative value for the wave function. Each orbital can accommodate two electrons with opposite spin direction. universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="15%">universe-review.caa href="I12-12-N2img.jpg">universe-review.caimg src="I12-12-N2img.jpg" name="Nuniverse-review.casub>2universe-review.ca/sub> Orbital Image" alt="Nuniverse-review.casub>2universe-review.ca/sub> Orbital Image" align="left" width="165"/>universe-review.ca/td> universe-review.catd width="15%">universe-review.caa href="I12-12-N2cal.jpg">universe-review.caimg src="I12-12-N2cal.jpg" name="Nuniverse-review.casub>2universe-review.ca/sub> Orbital Calculated" alt="Nuniverse-review.casub>2universe-review.ca/sub> Orbital Calculated" align="left" width="160"/>universe-review.ca/td> universe-review.catd width="70%">universe-review.caa name="N2orbital">universe-review.ca/a>Recently (in 2005), a method has been developed to take image of a molecule by using a short laser pulse lasting just 3 x 10universe-review.casup>-14universe-review.ca/sup> second. Figure 12-14a shows a electron orbital of a nitrogen molecule as imaged by such technique. It agrees quite well with the orbital as calculated from theoretical models (Figure 12-14b). The colours represent the amplitude of the wave function - the electron is most likely to be found at the red and dark blue areas. Producing a three-dimensional image requires repeating the process at different angles, like a hospital CT scanner.universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="15%">universe-review.cah4>Figure 12-14a Nuniverse-review.casub>2universe-review.ca/sub> Image universe-review.caa href="I12-12-N2img.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="15%">universe-review.cah4>Figure 12-14b Nuniverse-review.casub>2universe-review.ca/sub> Model universe-review.caa href="I12-12-N2cal/default.htm">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="70%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-13-Hbondenergy.gif">universe-review.caimg src="I12-13-Hbondenergy.gif" name="H2O Energy Levels" alt="H2O Energy Levels" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="25%"> universe-review.caa href="I12-13-Hbondorbital.gif">universe-review.caimg src="I12-13-Hbondorbital.gif" name="Hydrogen Bond" alt="Hydrogen Bond" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="50%">In the Huniverse-review.casub>2universe-review.ca/sub>O molecule, the electric field around the oxygen atom is stronger than that around the hydrogen. The electrons from the hydrogen atoms are drawn close to the oxygen. This leaves the hydrogen atoms positively charged at one end. The four pairs of valence electrons around the oxygen atom (six contributed by the O atom -- 2 in the 2s, 4 in the 2p states; and one each by the H atoms in the 1s state) occupy four spuniverse-review.casup>3universe-review.ca/sup> orbitals that form a tetrahedral pattern. The energy levels for these four pairs of electrons are lower than the original levels in universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-15 Huniverse-review.casub>2universe-review.ca/sub>O Energy Levels universe-review.caa href="I12-13-Hbondenergy.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="25%">universe-review.cah4>Figure 12-16 Hydrogen Bond universe-review.caa href="I12-13-Hbondorbital.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="50%">separated atoms as shown in Figure 12-15 (MO1 - MO4). Since the positively charged atomic nucleus for the hydrogen is partially exposed, it often attracts to universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> other negatively charged orbitals such as the electron pairs of the oxygen atom in another Huniverse-review.casub>2universe-review.ca/sub>O molecule (See Figure 12-16). This is called hydrogen bond. It is different from the covalent bond since there is no orbital overlap; it is not an ionic bond since there is no charge transfer from one atom to another. The strength of the hydrogen bond is about 10 times weaker than the covalent and ionic bonds. Hydrogen bonds are important in fixing properties such as solubilities, melting points, and boiling points, and in determining the form and stability of crystalline structures. Molecules such as water carrying hydrogen bonds are called polar molecules. They play a crucial role in biological systems. universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="dipole">van der Waals Forceuniverse-review.casup>universe-review.caa href="universe-review.ca#r11/default.htm#r11/">11universe-review.ca/a>universe-review.ca/sup>, Dipole-Dipole Interactionuniverse-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-14-vanderwaals1.jpg">universe-review.caimg src="I12-14-vanderwaals1.jpg" name="Van der Waals Interaction" alt="Van der Waals Interaction" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="25%"> universe-review.caa href="I12-14-vanderwaals2.gif">universe-review.caimg src="I12-14-vanderwaals2.gif" name="Van der Waals, Nonpolar" alt="Van der Waals, Nonpolar" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="50%">All atoms and molecules -- even inert-gas such as those of helium and argon -- exhibit weak, short-range attractions for one another due to van der Waals forces. These forces are responsible for the condensation of gases into liquids and the freezing of liquids into solids. Such familiar aspects of the behavior of matter in bulk as friction, surface tension, viscosity, adhesion, cohesion, and so on also arise from van der Waals forces. The interaction is between dipole-dipole. It can be the interaction between a permanent and an induced dipole as shown in Figure 12-17 or between a universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-17 van der Waals Interaction universe-review.caa href="I12-14-vanderwaals1.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="25%">universe-review.cah4>Figure 12-18 van der Waals, Nonpolar universe-review.caa href="I12-14-vanderwaals2.gif">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="50%">time average dipole (due to fluctuations of charge) and an induced dipole as shown in Figure 12-18. The van der Waals interaction is about 10 times weaker than hydrogen bond. The stronger hydrogen bond can be considered as interaction between permanent dipoles.universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="physicalchem">Physical Chemistryuniverse-review.ca/a>universe-review.ca/h3> Before the development of high energy physics, it has been found convenient to divide natural phenomena into two broad classes: one consists of changes of an apparently permanent nature involving the transformation of one form of matter into another, while in the second are included temporary changes, general resulting from an alteration of external conditions. It is the study of the phenomena in these two categories, which constitute the sciences of chemistry and physics, respectively. The distinction between these aspects of the study of nature may be indicated in another way: chemistry may be said to deal with matter and its transformations, whereas physics is concerned with energy and its transformations. It is clearly not possible to draw a sharp distinction between the two points of view, for many problems in both physics and chemistry are concerned with interactions between energy and matter; it is these problems which constitute the fundamental basis of the subject of physical chemistry.universe-review.cabr />universe-review.cabr /> Followings are some selected topics in physical chemistry. Most of the phenomena were described originally from the macroscopic point of view. The microscopic interpretation is available only after the discovery of atomic structure. The modern subjects in physical chemistry such as universe-review.caa href="universe-review.ca#hydrogenbond/default.htm#hydrogenbond/">quantum chemistryuniverse-review.ca/a>, and universe-review.caa href="R13-09-thermodynamics.htm#connection">statistical mechanicsuniverse-review.ca/a> take the microscopic point of view. They are presented elsewhere in this website (click the underlined subject above to see more). universe-review.caul> universe-review.cali>universe-review.caa name="thermochem">universe-review.ca/a>Thermochemistry - It is the application of the universe-review.caa href="R13-09-thermodynamics.htm#laws">first law of thermodynamicsuniverse-review.ca/a> (conservation of energy) to processes such as: chemical reactions, phase changes, e.g., boiling and melting, and the formation of solutions. The first thermochemistry universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-20-thermochem.jpg">universe-review.caimg src="I12-20-thermochem.jpg" name="Thermochemistry" alt="Thermochemistry" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%">law (proposed in 1780) states that: universe-review.cai>the quantity of heat required to decompose a compound into its elements is equal to the heat evolved when that compound is formed from its elements.universe-review.ca/i> The second law of thermochemistry (discovered experimentally in 1840, also known as Hess law). It states that universe-review.cai>the heat change in universe-review.ca/i> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-19 Hess Law universe-review.cabr />universe-review.caa href="I12-20-thermochem.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">universe-review.cai>a chemical reaction is the same whether it takes place in one or several stages.universe-review.ca/i> That is, the heat change depends on the initial and final states only (Figure 12-19).universe-review.ca/li>universe-review.cabr />universe-review.cabr /> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-20-reactionrate.jpg">universe-review.caimg src="I12-20-reactionrate.jpg" name="Reaction Rate" alt="Reaction Rate" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%">universe-review.cali>universe-review.caa name="reactionrate">universe-review.ca/a>Chemical Kinetics - Chemical kinetics study reaction rates in a chemical reaction. It is measured by the amount of reactant used up, or the amount of product formed, in a certain period of time. Reactions with low activation energies go faster than reactions with high activation energies. The rate of a reaction can be affected by the temperature, the amounts of reactants in the container, and catalysts (Figure 12-20). Reactions almost always go faster at higher temperatures, because the increase in kinetic energy makes the reactants move faster and collide more often. The rate of a reaction also increases when reactants are added (resulting in higher concentration) universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-20 Reaction Rate universe-review.caa href="I12-20-reactionrate.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">since there are more collisions between the reactants. Another way to speed up a reaction is to lower the energy of activation. This can be done by adding a catalyst, which speeds up the reaction but is not itself changed or used up.universe-review.ca/li>universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table>universe-review.cabr />universe-review.cabr /> universe-review.cali>Solution - universe-review.caa name="solution">universe-review.ca/a>A solution is a mixture in which one substance called the solute (the component that changes state upon dissolving or in smaller amount) is uniformly dispersed in another substance called the solvent. Because the solute and the solvent do not react with each other, they can be mixed in varying proportions (see Figure 12-21). Solutes and solvents may be solids, liquids, or gases (see Figure 12-22). Gases form solutions easily because their particles are universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-18-solution.jpg">universe-review.caimg src="I12-18-solution.jpg" name="Solution" alt="Solution" align="left" width="150"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="20%"> universe-review.caa href="I12-18-types.jpg">universe-review.caimg src="I12-18-types.jpg" name="Types of Solution" alt="Types of Solution" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="60%">moving so rapidly that they are far apart and attractions to the other gas particles are not important. When solids or liquids form solutions, there must be an attraction between the solute particles and the solvent particles. Otherwise, the particles do not mix and no solution forms. Compounds containing nonpolar molecules such as iodine, oil, or grease do not dissolve in water because water is polar. The polarities of a solute and a solvent must be similar in order to form a solution. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-21 Solution universe-review.caa href="I12-18-solution.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="20%">universe-review.cah4>Figure 12-22 Types of Solution universe-review.caa href="I12-18-types.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="60%">It is found as early as the 1800s that whenever a substance is dissolved in a liquid the vapor pressure (the pressure at which the rate of evaporation is equal to the universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> rate of condensation) of the latter is lowered. Such behaviour has the effect of rising the boiling point and lowering the freezing point of the solution. It also produces osmosis, which is the flow of a solvent, usually water, through a semipermeable membrane into a solution of higher solute concentration, i.e., diluting the solution.universe-review.ca/li>universe-review.cabr />universe-review.cabr /> universe-review.cali>universe-review.caa name="electrolyte">universe-review.ca/a>Electrochemistry - For the subject of physical chemistry the most important conductors are those of the electrolytes; they are distinguished from electronic conductors, such as metals, by the fact that the passage of an electric current is accompanied by the transfer of matter. There are two main groups of electrolytic conductors; the first consists of pure universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="15%"> universe-review.caa href="I12-20-electrolyte.jpg">universe-review.caimg src="I12-20-electrolyte.jpg" name="Electrolyte" alt="Electrolyte" align="left" width="150"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="20%"> universe-review.caa href="I12-20-battery.jpg">universe-review.caimg src="I12-20-battery.jpg" name="Battery" alt="Battery" align="left" width="180"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="65%">substances, e.g., fused salts, and the second of solutions. The most thoroughly studied examples of the latter are solutions of acids, bases and salts in water. Sodium chloride (NaCl) is a strong electrolyte, which dissociates in water into hydrated ions of Nauniverse-review.casup>+universe-review.ca/sup>(aq) and Cluniverse-review.casup>-universe-review.ca/sup>(aq). As shown in Figure 12-23a, the light bulb glows as these ions provide a path for current flow in a circuit of : light bulb - battery - electrolytic solution - light bulb. HF is a weak electrolyte only generates a dim light. While nonelectrolytic substances such as sugar block the universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="15%">universe-review.cah4>Figure 12-23a Electro- lyte universe-review.caa href="I12-20-electrolyte.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="20%">universe-review.cah4>Figure 12-23b Battery universe-review.cabr />universe-review.caa href="I12-20-battery.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="65%">passage of electricity altogether. Figure 12-23b shows the essential parts of a lead storage battery. When the switch in the battery circuit is closed, reactions take place at the anode universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> and the cathode as shown in the diagram. The battery can store energy because the system of lead, lead dioxide, and sulfuric acid is in a higher energy state than those of the chemical substances they can react to form, namely, lead sulfate and water. When fully charged, the voltage between the terminals of a lead storage battery is 2.0 volts. Most automobile starters require either 6 or 12 volts to function, so the car batteries consists of 3 or 6 individual lead cells connected together to provide the proper voltage. By connecting the terminals of the battery to a source of direct current which, flows in the direction opposite to that of normal battery current flow, the battery can be recharged. universe-review.cabr />universe-review.cabr /> universe-review.cali>universe-review.caa name="phasechange">universe-review.ca/a>Phase Change - The term phase as used here relates to the fact that matter exists either as a solid, liquid, or gas such as ice, water, and steam for Huniverse-review.casub>2universe-review.ca/sub>O. Transitions from one phase to another are accompanied by the absorption or liberation of heat and usually by a change in volume. Figure 12-24 uses Huniverse-review.casub>2universe-review.ca/sub>O as an example to illustrate the process of phase change. The experiment puts ice (at -25universe-review.casup>ouniverse-review.ca/sup>C) into a container, which is surrounded by a heating coil (generating an uniform heating rate). Temperature of the ice rises from a to b until it reaches 0universe-review.casup>ouniverse-review.ca/sup>C - the melting point. Ice turns into water from b to c. The heat spent for the phase change (per unit mass) is called the heat of fusion. The temperature universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-20-phasechange.jpg">universe-review.caimg src="I12-20-phasechange.jpg" name="Phase Change" alt="Phase Change" align="left" width="225"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%">remains constant during the change of phase. Once the conversion is complete, the temperature of the water starts to rise again from c to d with a different rate since the specific heat (capacity to absorb heat) of water is greater than that of ice. Similar phase change occurs from d to e for water changing into steam. It takes longer time for the phase change from d to e, because the heat of vaporization (~ 540 cal/gm) is about 7 times higher than the heat of fusion. If the heating process continues from e to f, the gas would be called "superheated steam". The process reversed when heat is removed from the container.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-24 Phase Change universe-review.cabr />universe-review.caa href="I12-20-phasechange.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-20-surfacetension.jpg">universe-review.caimg src="I12-20-surfacetension.jpg" name="Surface Tension" alt="Surface Tension" align="left" width="195"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%">universe-review.cali>universe-review.caa name="surfacetension">universe-review.ca/a>Surface Tension - A molecule in the interior of a liquid is completely surrounded by other molecules, and so, on the average, it is attracted equally in all directions. On a molecule in the surface, however, there is a resultant attraction inwards, because the number of molecules is greater in the bulk of the liquid than in the vapor. As a consequence of this inward pull the surface of a liquid always tends to contract to the smallest possible area; it is for this reason that drops of liquid and bubbles of gas in a liquid become spherical, a needle floats on the top of water, certain water bugs can travel across the surface of a pond or lake (see Figure 12-25). When compounds called surfactants are added to water, they disrupt the hydrogen bonding between the water molecules. As a result, the surface tensions decreased and the water spreads universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-25 Surface Tensionuniverse-review.cabr />universe-review.caa href="I12-20-surfacetension.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">out rather than forming drops. Soap, detergents, shampoos, and fabric softeners, are example of surfactants we use every day.universe-review.ca/li>universe-review.cabr />universe-review.cabr />universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.ca/ul> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3 align="center">universe-review.caa name="inorganichem">Inorganic Chemistryuniverse-review.ca/a>universe-review.casup>universe-review.caa href="universe-review.ca#r12/default.htm#r12/">12universe-review.ca/a>universe-review.ca/sup>universe-review.ca/h3> Inorganic chemistry is the branch of chemistry concerned with the properties and reactions of inorganic compounds. This includes all chemical compounds without the chains or rings of carbon atoms, which are termed organic compounds and are studied elsewhere in this website under the topic of "universe-review.caa href="F11-monocell.htm#organic">Unicellular Organismsuniverse-review.ca/a>". Followings are some basic concepts of inorganic chemistry: universe-review.caul> universe-review.cali>Periodic Table - A molecule is a compound composed of a group of two or more atoms held together by chemical bonds. A molecular formula is a symbolic representation of the composition of a compound in terms of its constituent elements (e.g., Huniverse-review.casub>2universe-review.ca/sub>O, CHuniverse-review.casub>4universe-review.ca/sub>, Cuniverse-review.casub>6universe-review.ca/sub>Huniverse-review.casub>12universe-review.ca/sub>Ouniverse-review.casub>6universe-review.ca/sub>, ... etc. where the integers represent the number of the particular element in the molecule). The periodic table (see Figure 12-26) is a structured list of all known elements, arranged in order of their universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="R12-02-periodictable.htm">universe-review.caimg src="I12-16-periodictable.jpg" name="Periodic Table" alt="Periodic Table" align="left" width="210"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%"> atomic numbers. The horizontal rows are called periods. All elements in a period have the same number of shells of electrons. Each element across the row has an increment of one outer electron from left to right. The vertical columns are called groups. Elements within the same group all have the same number of electrons in their outer shell. They therefore tend to have similar chemical properties. Elements in the table can be classified as metals, non-metals, or metalloids. Metals have certain properties, which distinguish them from non-metals. These include generally high melting points, a shiny appearance, and good malleability (flatten into sheets), ductility (drawn into wires) and conductivity of electricity and heat. Some elements have both metallic and non-metallic properties. They are known as metalloids. universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-26 Periodic Table, Traditional universe-review.caa href="R12-02-periodictable.htm">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="75%"> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table>universe-review.ca/li> universe-review.cali>Valence - The concept of universe-review.caa name="valence">valenceuniverse-review.ca/a> is very important in determining if a chemical reaction can proceed or not. The valence numbers (oxidation numbers or states) for all the elements are listed on the top right of the symbol name in universe-review.caa href="F13-atom.htm#periodic">Figure 13-01auniverse-review.ca/a>. The valence of a free atom is zero, but in a chemical compound, the value has some positive or negative value. For example, when carbon burns, the reaction is universe-review.cabr /> C + Ouniverse-review.casub>2universe-review.ca/sub> ==> COuniverse-review.casub>2universe-review.ca/sub> universe-review.cabr /> the carbon atom starts with zero valence and becomes +4 in COuniverse-review.casub>2universe-review.ca/sub>; the valence of each oxygen atom is -2, so that the net valence of COuniverse-review.casub>2universe-review.ca/sub> is zero - a requirement for the chemical reaction to proceed. The increase in valence number from 0 to +4 (for the carbon atom in COuniverse-review.casub>2universe-review.ca/sub>) is referred to as universe-review.caa name="oxidation">oxidationuniverse-review.ca/a> reaction.universe-review.cabr /> Another example is the universe-review.caa name="reduction">reductionuniverse-review.ca/a> reaction:universe-review.cabr /> CuO + Huniverse-review.casub>2universe-review.ca/sub> ==> Cu + Huniverse-review.casub>2universe-review.ca/sub>Ouniverse-review.cabr /> where the valence of Cu changes from +2 (in CuO) to zero, i.e., there is a decrease in the valence of Cu in this reaction. Thus, the rule for classifying reactions is: an element is oxidized when its valence number (oxidation number) increases; universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="20%"> universe-review.caa href="I12-20-valence.jpg">universe-review.caimg src="I12-20-valence.jpg" name="Valence" alt="Valence" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="80%"> and is reduced when its valence number decreases. Figure 12-27 shows the valence for some common chemical elements. The value for electronegativity is a number that indicates the relative ability of an element to attract electrons. The rule for forming chemical compounds is to complete the shell by either accepting electrons or to denote depending on which way is easier to achieve. In Figure 12-27 the universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="20%">universe-review.cah4>Figure 12-27 Valence universe-review.cabr />universe-review.caa href="I12-20-valence.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="80%">number of electrons to form a complete shell is two for hydrogen, and eight for carbon and oxygen. Thus oxygen tends to accept two more electrons and has a higher value for electronegativity. Further detail can be found in the topic on universe-review.caa href="F13-atom.htm#periodic">Atomuniverse-review.ca/a>.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table>universe-review.cabr />universe-review.cabr /> universe-review.cali>Classification - Inorganic compounds are classified into acids, bases, salts, and oxides as shown in Table 12-02 below:universe-review.cabr />universe-review.cabr /> universe-review.catable bgcolor="#EBFBFB" border="1" width="100%" align="center"> universe-review.catr> universe-review.cath width="10%">Substanceuniverse-review.ca/th> universe-review.cath width="40%">Propertiesuniverse-review.ca/th> universe-review.cath width="50%">Classificationuniverse-review.ca/th> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">universe-review.caa href="I12-20-acid.jpg">Acidsuniverse-review.ca/a>universe-review.ca/td> universe-review.catd align="left">Dissolve in water and produce Huniverse-review.casup>+universe-review.ca/sup>. universe-review.cabr />Taste - sour, feel - may sting.universe-review.ca/td> universe-review.catd align="left">Oxygenless: HCluniverse-review.cabr />Oxoacids: Huniverse-review.casub>2universe-review.ca/sub>SOuniverse-review.casub>4universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">universe-review.caa href="I12-20-base.jpg">Basesuniverse-review.ca/a>universe-review.ca/td> universe-review.catd align="left">Accept acids' Huniverse-review.casup>+universe-review.ca/sup> such as NaOH and MgO. universe-review.cabr />Taste - bitter, feel - slippery.universe-review.ca/td> universe-review.catd align="left">Alkalis: soluble such as NaOHuniverse-review.cabr />Insouble Base: Cu(OH)universe-review.casub>2universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">universe-review.caa href="I12-20-salt.jpg">Saltsuniverse-review.ca/a>universe-review.ca/td> universe-review.catd align="left">Ionic compounds consist of metal and nonmetal ions. universe-review.cabr />universe-review.cabr />universe-review.cabr />Form crystal, universe-review.cabr />universe-review.cabr />hard and brittle, universe-review.cabr />universe-review.cabr />hight melting/boiling points, universe-review.cabr />universe-review.cabr />conduct electricity when dissolved or melted, universe-review.cabr />universe-review.cabr />may react with water to form neutral, acid or basic solution.universe-review.ca/td> universe-review.catd align="left">Insoluble: attraction between ions > with water - PbCluniverse-review.casub>2universe-review.ca/sub>universe-review.cabr /> Neutral: dissolves into hydrated ions -universe-review.cabr /> (Huniverse-review.casub>2universe-review.ca/sub>O)(Nauniverse-review.casup>+universe-review.ca/sup>)(Huniverse-review.casub>2universe-review.ca/sub>O)(Huniverse-review.casub>2universe-review.ca/sub>O)(Cluniverse-review.casup>-universe-review.ca/sup>)(Huniverse-review.casub>2universe-review.ca/sub>O)universe-review.cabr /> Medium: dissolves into metal cations and anions of acid radical - (Nauniverse-review.casup>+universe-review.ca/sup>)universe-review.casub>2universe-review.ca/sub>(SOuniverse-review.casub>4universe-review.ca/sub>universe-review.casup>2-universe-review.ca/sup>)universe-review.cabr /> Acid: dissolves into metal cations, hydrogen and acid radical anions - (Nauniverse-review.casup>+universe-review.ca/sup>)(Huniverse-review.casup>+universe-review.ca/sup>)(COuniverse-review.casub>3universe-review.ca/sub>universe-review.casup>2-universe-review.ca/sup>)universe-review.cabr /> Basic: dissolves into metal cations, hydroxyl and acid radical anions - (Znuniverse-review.casup>2+universe-review.ca/sup>)(OHuniverse-review.casup>-universe-review.ca/sup>)(Cluniverse-review.casup>-universe-review.ca/sup>)universe-review.cabr /> Double: dissolves into two cations and one anion - universe-review.cabr /> ( Kuniverse-review.casup>+universe-review.ca/sup>)(Aluniverse-review.casup>3+universe-review.ca/sup>)(SOuniverse-review.casub>4universe-review.ca/sub>universe-review.casup>2-universe-review.ca/sup>)universe-review.casub>2universe-review.ca/sub>universe-review.cabr /> Mixed: dissolves into one cations and two anion - universe-review.cabr />( Cauniverse-review.casup>2+universe-review.ca/sup>)(Cluniverse-review.casup>-universe-review.ca/sup>)(OCluniverse-review.casup>-universe-review.ca/sup>)universe-review.cabr /> Complex: dissolves into complex cations or anions - universe-review.cabr />[Ag(NHuniverse-review.casub>3universe-review.ca/sub>)universe-review.casub>2universe-review.ca/sub>universe-review.casup>+universe-review.ca/sup>](Bruniverse-review.casup>-universe-review.ca/sup>), (Nauniverse-review.casup>+universe-review.ca/sup>)[Ag(CN)universe-review.casub>2universe-review.ca/sub>universe-review.casup>-universe-review.ca/sup>] universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">universe-review.caa href="I12-20-oxides.jpg">Oxidesuniverse-review.ca/a>universe-review.ca/td> universe-review.catd align="left">Consist of two elements, one of which is universe-review.cabr />oxygen. The oxide group contains the greatest variations of physical properties. Some are hard, some soft. Some have a metallic luster; others are clear and transparent. universe-review.ca/td> universe-review.catd align="left">Non-salts: CO, NO, Nuniverse-review.casub>2universe-review.ca/sub>O (see universe-review.caa href="I12-20-oxidetypes.jpg">general rulesuniverse-review.ca/a>)universe-review.cabr /> Basic: salts with metal oxidation number +1, to +3 - MgOuniverse-review.cabr /> Amphoteric: salts with oxidation # +2, to +4 - Aluniverse-review.casub>2universe-review.ca/sub>Ouniverse-review.casub>3universe-review.ca/sub>universe-review.cabr /> Acid: salts with metal oxidation number +3, to +7 - SiOuniverse-review.casub>2universe-review.ca/sub> universe-review.ca/li>universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.cah4 align="center">Table 12-02 Classification of Inorganic Compoundsuniverse-review.ca/h4> universe-review.cali>Chemical Reactions - Table 12-03 is a list of the reactions between different classes of inorganic compounds :universe-review.cabr />universe-review.cabr /> universe-review.catable bgcolor="#EBFBFB" border="1" width="80%" align="center"> universe-review.catr> universe-review.cath width="30%">Reactantsuniverse-review.ca/th> universe-review.cath width="20%">Productsuniverse-review.ca/th> universe-review.cath width="50%">Exampleuniverse-review.ca/th> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">metal + non-metaluniverse-review.ca/td> universe-review.catd align="center">saltuniverse-review.ca/td> universe-review.catd align="left">Hg + S ==> HgSuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">basic oxide + acid oxideuniverse-review.ca/td> universe-review.catd align="center">saltuniverse-review.ca/td> universe-review.catd align="left">MgO + COuniverse-review.casub>2universe-review.ca/sub> ==> Mg COuniverse-review.casub>3universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">base + aciduniverse-review.ca/td> universe-review.catd align="center">saltuniverse-review.ca/td> universe-review.catd align="left">Ca(OH)universe-review.casub>2universe-review.ca/sub> + 2HCl ==> CaCluniverse-review.casub>2universe-review.ca/sub> + 2Huniverse-review.casub>2universe-review.ca/sub>Ouniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">metal + oxygenuniverse-review.ca/td> universe-review.catd align="center">basic oxideuniverse-review.ca/td> universe-review.catd align="left">2Mg + Ouniverse-review.casub>2universe-review.ca/sub> ==> 2MgOuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">non-metal + oxygenuniverse-review.ca/td> universe-review.catd align="center">acid oxideuniverse-review.ca/td> universe-review.catd align="left">4P + 5Ouniverse-review.casub>2universe-review.ca/sub> ==> 2Puniverse-review.casub>2universe-review.ca/sub>Ouniverse-review.casub>5universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">basic oxide + wateruniverse-review.ca/td> universe-review.catd align="center">baseuniverse-review.ca/td> universe-review.catd align="left">Nauniverse-review.casub>2universe-review.ca/sub>O + Huniverse-review.casub>2universe-review.ca/sub>O ==> 2NaOHuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">acid oxide + wateruniverse-review.ca/td> universe-review.catd align="center">aciduniverse-review.ca/td> universe-review.catd align="left">SOuniverse-review.casub>3universe-review.ca/sub> + Huniverse-review.casub>2universe-review.ca/sub>O ==> Huniverse-review.casub>2universe-review.ca/sub>SOuniverse-review.casub>4universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">acid + saltuniverse-review.ca/td> universe-review.catd align="center">salt + aciduniverse-review.ca/td> universe-review.catd align="left">Huniverse-review.casub>2universe-review.ca/sub>SOuniverse-review.casub>4universe-review.ca/sub> + BaCluniverse-review.casub>2universe-review.ca/sub> ==> BaSOuniverse-review.casub>4universe-review.ca/sub> + 2HCluniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">acid + metaluniverse-review.ca/td> universe-review.catd align="center">saltuniverse-review.ca/td> universe-review.catd align="left">6HCl + 2Al ==> 2AlCluniverse-review.casub>3universe-review.ca/sub> + 3Huniverse-review.casub>2universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">base + saltuniverse-review.ca/td> universe-review.catd align="center">salt + baseuniverse-review.ca/td> universe-review.catd align="left">Ba(OH)universe-review.casub>2universe-review.ca/sub> + Kuniverse-review.casub>2universe-review.ca/sub>SOuniverse-review.casub>4universe-review.ca/sub> ==> BaSOuniverse-review.casub>4universe-review.ca/sub> + 2KOHuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">base + acid oxideuniverse-review.ca/td> universe-review.catd align="center">acid saltuniverse-review.ca/td> universe-review.catd align="left">KOH + COuniverse-review.casub>2universe-review.ca/sub> ==> KHCOuniverse-review.casub>3universe-review.ca/sub>universe-review.ca/td> universe-review.ca/tr> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.cah4 align="center">Table 12-03 Reactions of Inorganic Compoundsuniverse-review.ca/h4> universe-review.catable border="0" width="100%">universe-review.catr>universe-review.catd width="25%"> universe-review.caa href="I12-17-reactive.jpg">universe-review.caimg src="I12-17-reactive.jpg" name="Reactivity Series" alt="Reactivity Series" align="left" width="200"/>universe-review.ca/a>universe-review.ca/td> universe-review.catd width="75%"> Many of the most commonly used metals, such as iron and silver, belong to a group called transition metals, found in the middle of the periodic table. They have more than one valence. The compounds that they form are often brightly coloured. Many metals react with water, with dilute acids and with the oxygen in the air. They can be listed in order of how reactive they are. This is known as the reactivity series and is shown in Figure 12-28 with the most reactive on top and the least reactive on the bottom.universe-review.ca/li> universe-review.ca/td>universe-review.ca/tr> universe-review.catr>universe-review.catd width="25%">universe-review.cah4>Figure 12-28 Reactivity Series universe-review.caa href="I12-17-reactive.jpg">[view large image]universe-review.ca/a>universe-review.ca/h4>universe-review.ca/td> universe-review.catd width="75%"> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> Chemical reactions can also be classified by the process involved in the reaction such as combustion, decompostition, photoreduction, etc. There is a very good website in universe-review.caa href="universe-review.ca#r13/default.htm#r13/">Ref. 13universe-review.ca/a>, where it offers plenty of demonstrations for the various types of process in chemical reactions.universe-review.ca/li>universe-review.cabr />universe-review.cabr /> universe-review.cali>Comparison between Inorganic and Organic Compounds - Inorganic compounds differ from organic compounds in many aspects, Table 12-04 summarizes the major differences. The subject of Organic Chemistry and some of the Organic Compounds in living cell can be found in universe-review.caa href="F11-monocell.htm#organic">Topic-11universe-review.ca/a>.universe-review.cabr />universe-review.cabr /> universe-review.catable bgcolor="#EBFBFB" border="1" width="100%" align="center"> universe-review.catr> universe-review.cath width="48%">universe-review.caa href="universe-review.ca#chemistry/default.htm#chemistry/">Inorganic Compoundsuniverse-review.ca/a>universe-review.ca/th> universe-review.cath width="52%">Organic Compoundsuniverse-review.ca/th> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">A few compounds with carbon atom, e.g., COuniverse-review.casub>2universe-review.ca/sub>, CCluniverse-review.casub>4universe-review.ca/sub>.universe-review.ca/td> universe-review.catd align="center">All organic compounds are carbon base.universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Elements joined by ionic or covalent bondsuniverse-review.ca/td> universe-review.catd align="center">Elements never joined by ionic bondsuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Dissolve in water, may produce ionsuniverse-review.ca/td> universe-review.catd align="center">Do not dissolve in water, but in other organic liquids such as alcohol, ...universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">High melting and boiling pointsuniverse-review.ca/td> universe-review.catd align="center">Low melting and boiling pointsuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Vaporize at high temperatureuniverse-review.ca/td> universe-review.catd align="center">Decompose by heat more easilyuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Flammability highuniverse-review.ca/td> universe-review.catd align="center">Flammability lowuniverse-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Reaction proceed quicker as solutions of the reactants are brought togetheruniverse-review.ca/td> universe-review.catd align="center">Reaction proceed at much slower rates in hours or days (except in living cell with enzymes)universe-review.ca/td> universe-review.ca/tr> universe-review.catr> universe-review.catd align="center">Do not exhibit isomerism universe-review.ca/td> universe-review.catd align="center">May exist as isomersuniverse-review.ca/td> universe-review.ca/tr>universe-review.ca/li> universe-review.ca/table> universe-review.cah4 align="center">Table 12-04 Difference Between Inorganic and Organic Compoundsuniverse-review.ca/h4> Note: Isomers are chemical compounds with identical molecular formula but different arrangements of elements.universe-review.ca/ul>universe-review.cabr /> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.caol>universe-review.cah3>universe-review.caa name="references">References:universe-review.ca/a>universe-review.ca/h3> universe-review.cali>universe-review.caa name="r01">universe-review.ca/a>Quantum Theory, Overview -- universe-review.caa href="http://www.levity.com/mavericks/quantum.htm">http://www.levity.com/mavericks/quantum.htmuniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r02">universe-review.ca/a>Quantum Theory, more detail -- universe-review.caa href="http://www.srikant.org/core/node12.html">http://www.srikant.org/core/node12.htmluniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r03">universe-review.ca/a>Path Integral -- universe-review.caa href="http://www.chem.unc.edu/lectures/2003Hermans/notes3/pathintegral.pdf">http://www.chem.unc.edu/lectures/2003Hermans/notes3/pathintegral.pdfuniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r04">universe-review.ca/a>Schrodinger Equation -- universe-review.caa href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c1">http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c1universe-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r05">universe-review.ca/a>Hydrogen Atom, Schrodinger Equation -- universe-review.caa href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2">http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2universe-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r06">universe-review.ca/a>Hydrogen Atom, Energy and Wave Functions -- universe-review.caa href="http://www.kw.igs.net/~jackord/bp/i6.html">http://www.kw.igs.net/~jackord/bp/i6.htmluniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r07">universe-review.ca/a>Covalent Bond, Hydrogen Molecule -- universe-review.caa href="http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/hmol.html">http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/hmol.htmluniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r08">universe-review.ca/a>Ionic Bond -- universe-review.caa href="http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/ionic_bonds.htm">http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/ionic_bonds.htmuniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r09">universe-review.ca/a>Hydrogen Bond -- universe-review.caa href="http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/hydrogen_bonds.htm">http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/hydrogen_bonds.htmuniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r10">universe-review.ca/a>Molecular Orbitals -- universe-review.caa href="http://www.chm.davidson.edu/ChemistryApplets/MolecularOrbitals/">http://www.chm.davidson.edu/ChemistryApplets/MolecularOrbitals/universe-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r11">universe-review.ca/a>van der Waals Force -- universe-review.caa href="http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/van_der_waals_forces.htm">http://207.10.97.102/chemzone/lessons/03bonding/mleebonding/van_der_waals_forces.htmuniverse-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r12">universe-review.ca/a>Inorganic Compounds -- universe-review.caa href="http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/compound.html#c2">http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/compound.html#c2universe-review.ca/a>universe-review.ca/li> universe-review.cali>universe-review.caa name="r13">universe-review.ca/a>Chemical Reactions -- universe-review.caa href="http://boyles.sdsmt.edu/subhead/types_of_reactions.htm">http://boyles.sdsmt.edu/subhead/types_of_reactions.htmuniverse-review.ca/a>universe-review.ca/li> universe-review.ca/ol> universe-review.caa href="default.htm#top/">universe-review.cah4>[Top]universe-review.ca/h4>universe-review.ca/a> universe-review.cahr align="center" width="15%" /> universe-review.cah3>universe-review.caa name="Index">Indexuniverse-review.ca/a>universe-review.ca/h3> universe-review.catable border="0" width="100%"> universe-review.catr> universe-review.catd width="49%"> universe-review.caa href="universe-review.ca#electrolyte/default.htm#electrolyte/">Batteryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#condensate/default.htm#condensate/">Bose-Einstein condensateuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#bosons/default.htm#bosons/">Bosonsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#Casimir/default.htm#Casimir/">Casimir effectuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#conjugate/default.htm#conjugate/">Conjugate variablesuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#interpretations/default.htm#interpretations/">Copenhagen interpretationsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#correspondence/default.htm#correspondence/">Correspondence Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#covalent/default.htm#covalent/">Covalent bond, hydrogen moleculeuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#deB/default.htm#deB/">de Broglie wavelengthuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#decoherence/default.htm#decoherence/">Decoherenceuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#electrolyte/default.htm#electrolyte/">Electrolyteuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#exclusion/default.htm#exclusion/">Exclusion Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#fermions/default.htm#fermions/">Fermionsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#quantization/default.htm#quantization/">First quantization, Schrodinger Equationuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#hidden/default.htm#hidden/">Hidden variablesuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#hydrogen/default.htm#hydrogen/">Hydrogen atomuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#hydrogenbond/default.htm#hydrogenbond/">Hydrogen bond, molecular orbitaluniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#inorganichem/default.htm#inorganichem/">Inorganic chemistryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#ionic/default.htm#ionic/">Ionic bond, atomic shellsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#manyworlds/default.htm#manyworlds/">Many worldsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#MO/default.htm#MO/">Molecular Orbital theoryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#orbitals/default.htm#orbitals/">Orbitalsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#oxidation/default.htm#oxidation/">Oxidationuniverse-review.ca/a>universe-review.cabr /> universe-review.ca/td>universe-review.catd width="2%"> universe-review.ca/td>universe-review.catd width="49%"> universe-review.caa href="universe-review.ca#path/default.htm#path/">Path integral, transition to Qunatum Theoryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#phasechange/default.htm#phasechange/">Phase changeuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#physicalchem/default.htm#physicalchem/">Physical chemistryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#Planck/default.htm#Planck/">Planckuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#potential/default.htm#potential/">Potential curveuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#probability/default.htm#probability/">Probability densityuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#interpretations/default.htm#interpretations/">Quantum interpretationsuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#number/default.htm#number/">Quantum numbersuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#quantum/default.htm#quantum/">Quantum Theory, blackbody radiationuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#reactionrate/default.htm#reactionrate/">Reaction rateuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#reduction/default.htm#reduction/">Reductionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#cat/default.htm#cat/">Schrodinger's catuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#surfacetension/default.htm#surfacetension/">Surface tensionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#solution/default.htm#solution/">Solutionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#thermochem/default.htm#thermochem/">Thermochemistryuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#uncertainty/default.htm#uncertainty/">Uncertainty Principleuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#vacuum/default.htm#vacuum/">Vacuumuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#valence/default.htm#valence/">Valenceuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#dipole/default.htm#dipole/">van der Waals force, dipole-dipole interactionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="R12-03-wave.htm#wave">Waveuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#wave/default.htm#wave/">Wave functionuniverse-review.ca/a>universe-review.cabr /> universe-review.caa href="universe-review.ca#waveparticle/default.htm#waveparticle/">Wave-particle dualityuniverse-review.ca/a>universe-review.cabr />universe-review.cabr /> universe-review.ca/td>universe-review.ca/tr>universe-review.ca/table> universe-review.cahr align="center" width="15%" /> universe-review.cah4>universe-review.caa href="index.htm">[Home Page]universe-review.ca/a>universe-review.ca/h4> universe-review.ca/body> universe-review.ca/html>