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A blackbody is an object that absorbs all light falling on it. A good 1. Wiens formula gave a good fit to the blackbody radiation data available in , but his theoretical arguments for the formula were considered unsatisfactory. In , measurements of blackbody radiation were extended to lower frequen- cies than previously measured, and the low-frequency data showed significant deviations from Wiens formula. Having proposed this formula, Planck sought a theoretical justification for it.
In December , he presented a theoretical derivation of his equation to the German Physi- cal Society. Planck assumed the radiation emitters and absorbers in the blackbody to be harmonically oscillating electric charges resonators in equilibrium with electromag- netic radiation in a cavity.
He assumed that the total energy of those resonators whose fre- quency is n consisted of N indivisible energy elements, each of magnitude hn, where N is an integer and h Plancks constant was a new constant in physics. Planck distributed these energy elements among the resonators. In effect, this restricted the energy of each resonator to be a whole-number multiple of hv although Planck did not explicitly say this.
Thus the energy of each resonator was quantized, meaning that only certain discrete values were allowed for a resonator energy. Plancks work is usually considered to mark the beginning of quantum mechanics.
However, historians of physics have debated whether Planck in viewed energy quan- tization as a description of physical reality or as merely a mathematical approximation that allowed him to obtain the correct blackbody radiation formula.
Darrigol, Cen- taurus, 43, ; C. Gearhart, Phys.
Brush, Am. Planck was no exception, and the importance ascribed to his work is largely a historical reconstruction H.
Kragh, Physics World, Dec.
The concept of energy quantization is in direct contradiction to all previous ideas of physics. According to Newtonian mechanics, the energy of a material body can vary continuously.
However, only with the hypothesis of quantized energy does one obtain the correct blackbody-radiation curves. The second application of energy quantization was to the photoelectric effect.
In the pho- toelectric effect, light shining on a metal causes emission of electrons. The energy of a wave is proportional to its intensity and is not related to its frequency, so the electromagnetic-wave picture of light leads one to expect that the kinetic energy of an emitted photoelectron would increase as the light intensity increases but would not change as the light frequency changes.
Instead, one observes that the kinetic energy of an emitted electron is independent of the lights intensity but increases as the lights frequency increases.
An increase in the lights frequency n increases the photon energy and hence increases the kinetic energy of the emitted electron. An increase in light intensity at fixed frequency in- creases the rate at which photons strike the metal and hence increases the rate of emission of electrons, but does not change the kinetic energy of each emitted electron.
According to Kragh, a strong case can be made that it was Einstein who first recognized the essence of quantum theory; Kragh, Physics World, Dec. The photoelectric effect shows that light can exhibit particlelike behavior in addition to the wavelike behavior it shows in diffraction experiments.
In , Einstein applied energy quantization to the vibrations of atoms in a solid ele- ment, assuming that each atoms vibrational energy in each direction 1x, y, z2 is restricted to be an integer times hnvib, where the vibrational frequency nvib is characteristic of the element.
Using statistical mechanics, Einstein derived an expression for the constant- volume heat capacity CV of the solid. Einsteins equation agreed fairly well with known CV -versus-temperature data for diamond.
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Now let us consider the structure of matter. In the late nineteenth century, investigations of electric discharge tubes and natu- ral radioactivity showed that atoms and molecules are composed of charged particles. Electrons have a negative charge. The proton has a positive charge equal in magnitude but opposite in sign to the electron charge and is times as heavy as the electron.
The third constituent of atoms, the neutron discovered in , is uncharged and slightly heavier than the proton. Starting in , Rutherford, Geiger, and Marsden repeatedly passed a beam of alpha particles through a thin metal foil and observed the deflections of the particles by allowing them to fall on a fluorescent screen. Alpha particles are positively charged helium nuclei obtained from natural radioactive decay.
Most of the alpha particles passed through the foil essentially undeflected, but, surprisingly, a few underwent large deflections, some be- ing deflected backward.
To get large deflections, one needs a very close approach between the charges, so that the Coulombic repulsive force is great.
If the positive charge were spread throughout the atom as J. Thomson had proposed in , once the high-energy alpha particle penetrated the atom, the repulsive force would fall off, becoming zero at the center of the atom, according to classical electrostatics. Hence Rutherford concluded that such large deflections could occur only if the positive charge were concentrated in a tiny, heavy nucleus.
An atom contains a tiny to cm radius , heavy nucleus consisting of neu- trons and Z protons, where Z is the atomic number. Outside the nucleus there are Z elec- trons. The charged particles interact according to Coulombs law. The nucleons are held together in the nucleus by strong, short-range nuclear forces, which will not concern us.
The radius of an atom is about one angstrom, as shown, for example, by results from the kinetic theory of gases. Molecules have more than one nucleus.
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The chemical properties of atoms and molecules are determined by their electronic structure, and so the question arises as to the nature of the motions and energies of the electrons. Since the nucleus is much more massive than the electron, we expect the motion of the nucleus to be slight compared with the electrons motions.
In , Rutherford proposed his planetary model of the atom in which the elec- trons revolved about the nucleus in various orbits, just as the planets revolve about the sun. However, there is a fundamental difficulty with this model. According to classical 1. An electron circling the nucleus at constant speed is being accelerated, since the direction of its velocity vector is continually changing.
Hence the electrons in the Rutherford model should continually lose energy by radiation and there- fore would spiral toward the nucleus. Thus, according to classical nineteenth-century physics, the Rutherford atom is unstable and would collapse.
A possible way out of this difficulty was proposed by Niels Bohr in , when he ap- plied the concept of quantization of energy to the hydrogen atom.
Bohr assumed that the energy of the electron in a hydrogen atom was quantized, with the electron constrained to move only on one of a number of allowed circles. With the assumption that an electron making a transition from a free ionized state to one of the bound orbits emits a photon whose frequency is an integral multiple of one-half the classical frequency of revolution of the electron in the bound orbit, Bohr used classical mechanics to derive a formula for the hydrogen- atom energy levels.
Using 1. However, attempts to fit the helium spectrum using the Bohr theory failed. Moreover, the theory could not account for chemical bonds in molecules. The failure of the Bohr model arises from the use of classical mechanics to describe the electronic motions in atoms.Most of the alpha particles passed through the foil essentially undeflected, but, surprisingly, a few underwent large deflections, some be- ing deflected backward.
Matei An electron circling the nucleus at constant speed is being accelerated, since the direction of its velocity vector is continually changing. Thomson had proposed in , once the high-energy alpha particle penetrated the atom, the repulsive force would fall off, becoming zero at the center of the atom, according to classical electrostatics. Ira n levine pdf download. By Levine, Ira N. The height of the graph in Fig. PowerPoint slides that can be downloaded and used for presentations For students and to make it easier to partition the reading in for example degree courses It is very rare nowadays for any system to be completely free standing.
Photons must always be treated relativisti- cally, but electrons whose speed is much less than c can be treated nonrelativistically. Organic Chemistry 5th Edition by Janice Smith Preview the Students we're committed to providing you with high value course solutions and study resources Download free ReadAnywhere App for offline access to.