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Physics 27: Early Quantum Theory and Models of the Atom

Physics 27: Early Quantum Theory and Models of the Atom. Christopher Chui. Properties of the Electron. Cathode ray tube (CRT) was invented. Electrons emit from the cathode, which is negative J.J. Thomson (1897) measured e/m using a CRT

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Physics 27: Early Quantum Theory and Models of the Atom

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  1. Physics 27: Early Quantum Theory and Models of the Atom Christopher Chui Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

  2. Properties of the Electron • Cathode ray tube (CRT) was invented. Electrons emit from the cathode, which is negative • J.J. Thomson (1897) measured e/m using a CRT • Cathode rays are deflected by electric and magnetic fields • F = evB = mv2/r ; eE = evB  e/m = E/[B2r] • Robert Millikan’s oil drop experiment determined the value of e = 1.6 x 10-19 C. Further, m = 9.1x10-31 kg • Planck’s quantum hypothesis: E = nhf, n=1,2,3,… • Wien’s law: lPT = 2.90 x 10-3 m-K Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

  3. Photon Theory of Light • Light is transmitted as tiny particles called photons • Photoelectric effect: when light shines on a metal surface, electrons are emitted from the surface • Increase in intensity of lightmore e will be ejected • Increase in frequency of lightKE increases s.t. • KEmax = hf – Wo • If frequency f is < cutoff frequency fo (hfo=Wo) no e will be ejected, no matter how great the intensity • Vast applications: alarms, door openers, smoke detectors, light meters, film soundtrack, etc Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

  4. Photon Interactions • Compton (1923) scattered short-wavelength light. He found the scattered light had a lower frequency, indicating an energy loss  p= E/c =hf/c = h/l • Wavelength of scattered photons = l +h(1-cos f)/[moc] • The quantity h/[moc] is called the Compton wavelength • The photon may knock an atomic electron to a higher energy state if its energy is not enough to get e out • Pair production: a photon can produce matter, such as the production of an e and a positron • Compton effect has been used to diagnose bone disease such as osteoporosis Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

  5. Wave-Particle Duality • The photoelectric effect, the Compton effect have confirmed the particle theory of light • Young’s experiment on interference and diffraction confirmed the wave theory of light. Therefore, light exists as a wave-particle duality • Bohr’s principle of complementarity: to understand a given experiment, use either the wave or the photon theory, but not both • Wave nature of matter: Louis de Broglie (1923) proposed the wavelength of matter l = h/[mv] • Complementarity also applies to matter Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

  6. Models of the Atom • J.J. Thomson (1897) proposed plum-pudding model • Ernest Rutherford (1911) performed experiments that showed atoms have positive nuclei: e orbit a tiny positive nucleus. The atom is mostly empty space • Atomic spectra: 1/l = R[1/22 – 1/n2], n=3,4,..(Balmer) • R = Rydberg constant = 1.097x107 m-1 • 1/l = R[1/12 – 1/n2], n=2,3,..(Lyman series) UV region • 1/l = R[1/32 – 1/n2], n=4,5,..(Paschen series) IR • Bohr model: e move without radiating energy • Possible orbits are stationary states. Light is emitted when an e jumps from 1 state to a lower state, where hf =Eu – El • Angular momentum, L = mvrn = nh/2p, n = 1,2,3,… Bohr radius Physics 27: Quantum Theory and Models of the Atom - Christopher Chui

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