Changed the way we look at things. Classical Physics. Classical Physics. Classical Physics. Classical Physics. Blackbody Radia on 11/29/11

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1 Changed the way we look at things. Late 19 th century inves gate the next decimal point. For example: Newton s mechanics had been brought to a high degree of both prac cal and theore cal sophis ca on by the work of Lagrange and Hamilton resul ng in the theory of elas city and thermodynamics. The equivalence of heat and mechanical work had been demonstrated by the experiments of Rumford and Joule. Carnot had formulated the 2 nd law of thermodynamics (heat and mechanical energy). Gibb s had developed thermodynamics which is presented essen ally in unchanged form in every P Chem book today. The kine c theory of gases were to great refinement by Maxwell, Boltzmann and Gibbs giving us the MB distribu on of molecular speeds and its consequences in chemical kine cs. First half of 19 th century was very ac ve because of the discovery of electric and magne c effects exemplified by Faraday. Maxwell s predic on of the electromagne c nature of light unified the fields of op cs and electricity and magne sm. Hertz work was the final blow to the corpuscular theory of light and solidified the wave theory of light. Blackbody Radia on J. J. Thomson ( ) Nobel Prize Physics Succeeded Lord Rayleigh as director of the Cavendish Laboratory He trained 7 Nobel prize winners (son too). Calc. Z (off by 50%) and mass of e -. Discovery of e - showed that the atom was more complex than previously thought. Resigned his posi on as director of the Cavendish lab at Cambridge in favor of Ernest Rutherford because he did not like the new physics of Niels Bohr. Unable to be explained by classical physics. The Rayleigh- Jeans Law worked at high wavelengths (low frequencies such as the IR) but diverged at low wavelengths (high frequencies such as the UV). Spectral energy density (ρ) infinite value. Called the ultraviolet catastrophe. 1

2 Blackbody Radia on 2 8pVf df hf r ( f, T ) df =. 3 hf / kt c e - 1 Observa ons of radia on from a blackbody and its radia on (measured by spectroscopic lines) provided the first experimental evidence for quantum theory. Every me one sees a neon or sodium light, one is seeing quantum theory in prac ce. The light from a neon or sodium source is a spectroscopic line. An electric field excites atoms of the neon or sodium atom to a discrete quantum state; the atom then makes a transi on by emi ng light that is characteris c of the atom, and yields the par cular color of light that one sees. Furthermore, semiconductors and electronic chips in general exist due to quantum theory. Electronic devices, from computers, television, to mobile phones are all based on the semiconductor, and aeroplanes, ships, cars all use semiconductors in an essen al manner. More complex technologies such as MRI (Magne c Resonance Imaging), lasers, physical chemistry, fabrica on of new drugs, modern materials science and so on all draw on the principles of quantum theory. It is no exaggera on to predict that twenty first century technology will largely be based on the principles of quantum physics. A black body which is maintained at a constant temperature T steadily loses energy from its surface in the form of electromagne c radia on. Since the atoms composing the blackbody are in contact with a heat bath at temperature, each atom has approximately an amount of energy, where k = Boltzmann's constant. Since the atoms are jiggling around due to thermal mo on, classical electromagne c theory then predicts that all wavelength's of radia on, in par cular up to infinitely short wavelengths, should be emi ed by a blackbody. 2

3 This classical predic on for the spectrum of radia on that is emi ed by such a blackbody is contradicted by experiment. Max Planck, a German physicist, correctly explained the experimentally measured black- body spectrum by making the epoch- making conjecture in 1900 that electromagne c waves are the macroscopic manifesta ons of packets of wave- energy called photons. Planck further made the quantum hypothesis that the energy of photons is quan zed in the sense that the energy of the photons only comes in discrete packets, the smallest packet called a quantum. Photons can have wavelength from zero to infinity. For a wave of frequency ν, or equivalently, of wavelength, the quanta of energy are given by (c is the velocity of light): E = hν = N hc/λ, with N = 1, 2 h = X J. s Albert Einstein showed that light was a stream of par cles (which would later be named photons). This phenomenon is called the photoelectric effect. When you shine a light upon certain metals, a stream of par cles (later found to be electrons) is emi ed from that metal. The emission has been found to have certain proper es. The number of electrons emi ed by the metal depends on the intensity of the light beam applied on the metal; more intense the beam, higher the number of electrons emi ed. The emi ed electrons move with greater speed if the applied light has a higher frequency. No electron is emi ed un l the light has a threshold frequency, no ma er how intense the light is. 3

4 These observa ons baffled physicists for many decades, since they cannot be explained if light is thought of only as a wave. If light were to be a wave, both the energy and the number of the electrons emi ed from the metal should increase with an increase in the intensity of light. Observa ons contradicted this predic on; only the number, and not the energy, of the electrons increased with the increase of the intensity of the light. What Einstein showed was that the photoelectric effect as it had been observed could be explained if individual par cles (or quanta) of light were penetra ng the metal and knocking electrons loose from atoms. According to Einstein's classic 1905 paper, increasing the intensity of the light increased the number of photons, while the energy of each individual photon remained the same, as long as the frequency of the light remained the same. Therefore the number of electrons emi ed would increase, but the energy transmi ed to them by the par cles of light would remain the same. In one stroke Einstein showed that light is a stream of par cles, and also that there was solid evidence for the existence of quanta. His theory could sa sfactorily explain all the known proper es of the photoelectric effect, and was the first result derived from quantum theory of the interac on between radia on and ma er. Problem #1 The minimum energy needed to remove an electron from potassium metal is 3.7 X J. Will photons of frequencies 4.3 X s - 1 (red light) and 7.5 X s - 1 (blue light) trigger the photoelectric effect? If so, how fast will the ejected electrons move? Problem #2 A sodium vapor street lamp emits bright- yellow light at λ = 589 nm. What is the energy change for a sodium atom involved in this emission? How much energy is emi ed per mole of sodium atoms? In 1913 Niels Bohr came to work in the laboratory of Ernest Rutherford. Rutherford, who had a few years earlier, discovered the planetary model of the atom asked Bohr to work on it because there were some problems with the model: According to the physics of the me, Rutherford's planetary atom should have an extremely short life me. Bohr thought about the problem and knew of the emission spectrum of hydrogen. He quickly realized that the two problems were connected and a er some thought came up with the Bohr model of the atom. Bohr's model of the atom revolu onized atomic physics. 4

5 The Bohr model consists of four principles: 1) Electrons assume only certain orbits around the nucleus. These orbits are stable and called "sta onary" orbits. 2) Each orbit has an energy associated with it. For example the orbit closest to the nucleus has an energy E1, the next closest E2 and so on. 3) Light is emi ed when an electron jumps from a higher orbit to a lower orbit and absorbed when it jumps from a lower to higher orbit. 4) The energy and frequency of light emi ed or absorbed is given by the difference between the two orbit energies, e.g., Electron Transi ons The Bohr model for an electron transition in hydrogen between quantized energy levels with different quantum numbers n yields a photon by emission with quantum energy. Hydrogen Energy Levels Hydrogen Energy Levels The basic structure of the hydrogen energy levels can be calculated from the Schrodinger equation. The energy levels agree with the earlier Bohr model, and agree with experiment within a small fraction of an electron volt. Hydrogen Energy Levels Hydrogen Spectrum 5

6 Hydrogen Spectrum At left is a hydrogen spectral tube excited by a 5000 volt transformer. The three prominent hydrogen lines are shown at the right of the image through a 600 lines/mm diffraction grating. An approximate classification of spectral colors: Violet ( nm) Blue( nm) Cyan ( nm) Green ( nm) Yellow ( nm) Orange ( nm) Red ( nm) E(light) = E f E i where "f" and "i" represent final and ini al orbits. E = hν = N hc/λ, with N = 1, 2 h = X J. s With these condi ons Bohr was able to explain the stability of atoms as well as the emission spectrum of hydrogen. According to Bohr's model only certain orbits were allowed which means only certain energies are possible. These energies naturally lead to the explana on of the hydrogen atom spectrum. Bohr's model was so successful that he immediately received world- wide fame. Unfortunately, Bohr's model worked only for hydrogen. Thus, the final atomic model was yet to be developed. An electron in a given sta onary state of a hydrogen atom, characterized by the quantum numbers, n, l and m l, and, should, in principle, remain in that state indefinitely. In prac ce, if the state is slightly perturbed- - e.g., by interac ng with a photon- - then the electron can make a transi on to another sta onary state with different quantum numbers. Bohr found that the allowed E s of the electron are restricted by n according to: E = - (1/n 2 ) X J, n = 1, 2, 3, R = X J or Rydberg s constant For n = 1, E = X J. Suppose that an electron in a hydrogen atom makes a transi on from an ini al state whose radial quantum number is n i to a final state whose radial quantum number is n f. The energy of the electron will change by ΔE = E f - E i = X J (1/n 2 f - 1/n i2 ). E photon = hν and ν = E photon / h; λ = c / ν 6

7 Problem Calculate the wavelength of the spectral line when the electron in the hydrogen atom undergoes a transi on from 4 th energy level to 2 nd energy level. What is the color of the radia on? 7