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AKG

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4. The maximum energy of photoelectrons from aluminum is 2.3 eV for radiation of 200 nm and 0.90 eV for radiation of 258 nm. Use these data to calculate Planck's constant and the work function of aluminum

(To give you an idea of where I'm at, I don't know what a photoelectron is, I don't know what it means for the energy of radiation of X wavelength to be Y eV, I have no idea how I would use this to calculate Planck's constant, and I don't know what a work function is ).

5. A 100 MeV photon collides with a proton that is at rest. What is the maximum possible energy loss for the photon?

(My best guess is that 100 MeV tells you the mass of the photon, and you know the speed is c, and you know the initial speed of the proton is 0 and it's mass is some constant - 1g/6.02 x 10²³, and perhaps I should assume conservation of momentum and energy. But I also am not sure which equation applies where. Is the kinetic energy of the proton ½mv² and the momentum mv? What's with the equation E = m²(c²)² + p²c²? Is that the kinetic energy of the photon? Not sure what I should be doing here exactly)

7. An electron of energy 100 MeV collides with a photon of wavelength 3 mm (corresponding to the universal background of blackbody radiation). What is the maximum energy loss suffered by the electron?

(I'm supposed to know what blackbodies are but I have no idea. I'm also supposed to know something about how they radiate, again, no idea. I don't get the stuff in brackets in the question above, and only have a vague idea of the rest of it, similar to my understanding of question 5)

9. A nitrogen nucleus (mass ~ 14 x proton mass) emits a photon of energy 6.2 MeV. If the nucleus is initially at rest, what is the recoil energy of the nucleus in eV?

(Again, this seems like a conservation of momentum/energy question. Let's see if I have any idea: initial energy and momentum are zero. When the photon is fired off, it has some known momentum and energy. We know the mass of the nucleus, and we know that the momentum of the nucleus will be equal in magnitude to that of the photon, and the same goes for it's energy. Do we have two equations with one unknown, the speed of the nucleus? And if so, we can find the speed and thus the energy. And am I right to assume that the classical equations for momentum and energy hold for the nucleus. Actually, I won't even say classical equations, rather, high school equations.)

11. The smallest separation resolvable by a microscope is of the order of magnitude of the wavelength used. What energy electrons would one need in an electron microscope to resolve separations of (a) 15 nm, (b) 0.5 nm?

(I assume that the energy of the electrons is a direct function of their wavelength? So if E = f(λ), I just need to figure out f(15 nm) and that's my answer? And if I'm right, what is that function f(λ)?)

14. Use the Bohr quantization rules to calculate the energy levels for a harmonic oscillator, for which the energy is p²/2m + mw²r²/2; that is, the force is mw²r. Restrict yourself to circular orbits. What is the analog of the Rydberg formula? Show that the correspondence princple is satisfied for all values of the quantum number n used in quantizing the angular momentum.

(???)

16. The classical energy of a plane rotator is given by E = L²/2I where L is the angular momentum and I is the moment of inertia. Apply the Bohr quantization rules to obtain the energy levels of the rotator. If the Bohr frequency condition is assumed for the radiation in transitions from sttes labled by n1 to states labled by n2, show that (a) the correspondence principle holds, and (b) that it implies that only transitions Δn = ±1 should occur.