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# Quantum Theory

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1. Quantum Theory AP Physics B Chapter 27 Notes

2. First A Little Digression to EM Waves • Any form of radiation is an EM wave, and they all behave similarly • Many are incredibly useful and many are incredibly dangerous • Understanding them requires applying what we learned about electric and magnetic fields

3. Electromagnetic Waves Maxwell’s equations are key to describing all electric and magnetic phenomena Beyond the scope of this class, but a key hypothesis of Maxwell is a changing Ewill produce B

4. Producing Electromagnetic Waves Two straight wires connected to an ac generator can create an EM wave Electric part of the wave: The red arrow represents E produced at point P by oscillating charges on the antenna. The black arrows are the E produced by earlier oscillations. The portion of the wave going right is shown.

5. Producing Electromagnetic Waves Magnetic portion of wave: The current used to create E causes a magnetic field. Using RHR we can determine B is perpendicular to E since E is parallel to I

6. Producing Electromagnetic Waves Far from the source, the wave propagates itself by the changing E-field producing a B-field and the changing B-field producing an E-field. E&M wave is transverse and can travel in a vacuum since it is a field wave

7. Electromagnetic Waves Maxwell was able to calculate the speed of EM radiation and determine that is was the same for all types of EM waves and the same in all directions He found: v= c= E/B or: Later this was confirmed experimentally

8. Electromagnetic Waves Like all waves, EM waves have a frequency and wavelength related by:

9. Electromagnetic Waves You will be expected to know the relative position of different wave types in the EM spectrum (f and λ)

10. What is Quantum? Quantum mechanics is the study of processes which occur at the atomic scale. Derived from Latin meaning “how much”. Quantum theory is based on wave-particle duality and is used to explain a variety of phenomenon classical mechanics cannot explain

11. Quantum Theory Several phenomenon were unexplainable using Newtonian mechanics: • Presence of “cathode rays” • Blackbody radiation • Photoelectric effect • Compton Scattering

12. Cathode Rays A discharge tube was found to make the far end of a tube glow when a large voltage was applied across electrodes—called “cathode rays”

13. Cathode Rays It was found that these rays could be deflected by electric or magnetic fields—made to go in circular paths: Fmag=evB=mv2/r e/m= v/Br = E/B2r (when Felec=Fmag) e/m = 1.76 x1011 C/kg

14. Fundamental Charge e Cathode rays soon became known as electrons and Millikan determined the charge e Felec = Fg qE=mg  q=mg/E q=e=1.6 x10-19 C

15. Blackbody Radiation All objects emit thermal radiation (IαT4); a blackbody is one that emits thermal radiation only. Frequency of peak increases with T. Max Planck explained: Energy of the atomic oscillation varies with frequency

16. Blackbody Radiation Planck postulated that energy came in integer multiples of E = hf h is Planck’s constant h = 6.626 x 10-34 foundby fitting radiation curves

17. Photoelectric Effect Einstein expanded Planck’s theory to suggest that light is emitted in small packets of energy--photons E = hf Electrons Light This explains the photoelectric effect—if light strikes a metal, electrons are emitted…only if the frequency of light is high enough!

18. Photoelectric Effect Energy levels of photons are typically very small, so a new energy unit is often used. Recall: W = qV Where W is in J. If q is one electron and V is one V, then: 1J = 1.6 x 10-19 eV The electron volt (eV) is a measure of energy and used quite often in atomic energy level calculations

19. Photoelectric Effect—EM Spectrum Recall the EM spectrum—now knowing that E increases as f increases  more dangerous!

20. Photoelectric Effect Photoelectric effect cannot be explained by wave theory which suggests: • Number of electrons and their energy should increase with intensity of light • Frequency would not matter In fact, intensity of light does not affect energy of electrons, a minimum frequency is required to emit electrons and KE of electrons increases linearly with frequency

21. Photoelectric Effect Photoelectric effect cannot be explained by wave theory which suggests: • Number of electrons and their energy should increase with intensity of light • Frequency would not matter In fact, intensity of light does not affect energy of electrons, a minimum frequency is required to emit electrons and KE of electrons increases linearly with frequency

22. Photoelectric Effect When plotting E of electrons vs. f, you see there is no emission, and no KE, below a threshold frequency. Above this f, electron KE increases linearly, with slope of h (E=hf). Minimum frequency required to free an electron

23. Photoelectric Effect As light energy hits the cathode (also known as emitter), work must be done to free the electron from its atom—this is called the work function, f, or W0. The least tightly bound e leaves first and has the most KE, given by: KEmax=hf - f Collector Emitter Photocell Schematic—creates a circuit

24. Photoelectric Effect—Stopping Potential Connect a battery to a photocell, with the voltage potential applied against the direction of electron flow—if the voltage is increased enough, e flow stops. This is the stopping potential. Since W=qV, we can find: qVs=KEmax=hf- f - + Reverse Battery Polarity

25. Photoelectric Effect—Stopping Potential Graphing Vs versus f gives a straight line with slope of h/e Vs= (h/e)(f-f0) Where f0 is the work function frequency

26. Photon Mass, Energy and Momentum A photon’s energy is all kinetic: KE= E=hf Since it travels at the speed of light, we cannot use mv for momentum and must use relativistic formula: p= E/c=hf/c=h/λ Single photon energy relates only to f, but the number of photons produced depends on intensity.

27. Compton Effect Compton scattered x-rays from various metals, and found the scattered frequency was less than the original frequency—meaning that energy was “lost”. It was explained using quantum theory and noting an electron was freed from the material.

28. Wave-Particle Duality So what is light—wave or particle? Yes Wave Particle Diffraction Photoelectric effect Interference Compton effect Refraction Electron energy state

29. De Broglie Wavelength De Broglie proposed that the wavelength of a material particle is related to its momentum, symmetric with the photon: λ=h/p = h/mv Wave-particle duality applies to material objects as well as light For small masses (e) the λ is large enough to visualize—electron microscope

30. Atom Models Rutherford’swork confirmed the atom had a dense nucleus, but was mostly empty space.

31. Atom Models Atomic spectra led Bohr to postulate that electrons move in orbits without radiating energy. If the electron changes orbits, it either emits or absorbs a packet of energy (photon).

32. Energy Levels The energy levels can be thought of as rungs on a ladder—moving farther away from the nucleus is a higher (excited) energy level and absorbs energy. Moving closer to the nucleus is a lower (relaxed) energy level and releases energy.

33. Energy Levels The energy of the photon emitted (or absorbed) is equal to the difference in energy or the orbitals: hf = ΔE = EU - EL

34. Energy Levels The lowest energy level is the ground state—all others are excited states and all have negative values (PE = 0 at ∞)

35. Energy Levels The lowest energy level is the ground state—all others are excited states and all have negative values (PE = 0 at ∞)

36. Energy Levels--Example An experiment is performed on a sample of atoms known to have a ground state of ‑5.0 eV. The gas is illuminated with "white light" (400 ‑ 700 nm). A spectrometer capable of analyzing radiation in this range is used to measure the radiation. The sample is observed to absorb light at only 400 nm. After the "white light" is turned off, the sample is observed to emit visible radiation of 400 nm and 600 nm. 1. Draw the energy level diagram 2. What is the wavelength of any other radiation, if any, that might have been emitted in the experiment? Why was it not observed?