QUANTUM MECHANICS Chapter 12

Transcription

1 QUANTUM MECHANICS Chapter 12 Colours which appear through the Prism are to be derived from the Light of the white one Sir Issac Newton, 1704 Electromagnetic Radiation (prelude) FIG Electromagnetic Radiation standing waves, traveling waves wave properties of light (matter) classical: Maxwell νλ = c interference constructive destructive diffraction debroglie hypothesis: pλ = h particle properties blackbody radiation photoelectric effect electric and magnetic fields are the wavefunctions resulting from Maxwell s equations FIG Electromagnetic Spectrum 100 MHz EX 1. What is the frequency of 520 nm photons of green light? watch units! νλ = c Energy Increases infrared Latin infra - below ultraviolet Latin ultra - beyond

2 -2- Prelude to Modern Quantum Theory (quantitization and wave-particle duality, 12.2) 1900 blackbody radiation - Planck quantized energy of matter 1905 photoelectric effect - Einstein quantized electromagnetic radiation 1913 stability of atoms - Bohr quantized matter (old quantum theory) 1914 Franck-Hertz experiment - energy in atoms in discrete levels 1923 Compton scattering of x-rays - particle characteristics of light 1924 de Broglie matter waves: pλ = h (where p = mv) 1927 Davisson-Germer electron diffraction experiment - wave nature of electrons Problems that classical physics could not explain blackbody radiation (12.3) (Planck quantized energy of matter) radiation emitted by oscillating dipoles in the hot solid EX 2. What is the energy of 520 nm photons of green light? classically E osc = kt and intensity of emitted light, I, 1) T/λ 4 - blows up for small λ 2) continuously increases with decreasing λ experimentally a peak is observed Planck found agreement between theory and experiment if the radiated energy were quantized (E = nhν) and he found the energy of the oscillator to be given by E osc = hν/(e hν/kt -1), which has the high T limit of E osc = kt h is Planck s constant = J s E = nhν = nhc/λ FIG Blackbody radiation: light emitted by a heated object T = 7000 K ultraviolet catastrophe classical: I T / λ 4 T = 5000

3 photoelectric effect (12.4) (Einstein quantized electromagnetic radiation) E electron = E light E binding of electron in solid = hν φ (φ is the work function) -3- (intense) FIG Photoelectric effect (weak) The light must provide enough energy to the electron in the metal to overcome its binding energy φ. Any additional energy becomes kinetic energy of the ejected electron EX 3. The longest wavelength of light which can ionize metallic cesium is 600 nm. What is the binding energy of these electrons (has symbol φ in our text)? electron appears immediately classically E depends on I not ν kinetic energy = hν hν 0 => collision with light particles stability of atoms and emission spectra (12.7) (Bohr quantized matter) (Orbiting electron accelerates in the direction of the nucleus.) Classically, an accelerating electron emits radiation, loses energy, radius of orbit decreases, spirals into nucleus => unstable FIG Emission spectra of H, Hg, Ne

4 -4- Why did H atom emission spectra (Balmer, Lyman, Paschen, Brackett, Pfund series) all follow: Rydberg Equation Bohr explained the emission spectra with a model of a hydrogenic atom (atom or ion with only one electron: H, He +, Li 2+, etc) with quantized energy: Z is the atomic number (number of protons) Ry is the Rydberg constant FIG Energy levels of hydrogen atom

5 -5- EX 4. Calculate the ionization energy of hydrogen. What is the ionization energy of He +? absorb a photon energy increases emit a photon energy decreases Triangulum Galaxy - a large region of ionized hydrogen Balmer Paschen Lyman

6 -6- De Broglie Relation (12.5) Louis de Broglie (PhD thesis): pλ = h Diffraction (12.6) diffraction from a CD diffraction from clouds waves interfere constructively and destructively FIG - Diffraction size of slit similar to wavelength of wave single slit experiment double (multiple) slit experiment