PROBLEMS
1. What speed must an electron have in order for it's wavelength to be 100 pm?
2. What is the wavelength of a 1500 kg car traveling down 17th street at 20 m/s?
3. What effect does going faster have on wavelength?
4. What is meant by "wave-particle duality"?
5. Describe briefly the experimental setup used to show interference in carbon-60 molecules.
6. Why do macroscopic objects never show interference patterns?
7. Cite a limitation of the WS quantization condition.
8. Using the WS quantization condition, derive the energy states possible in a system of an electron confined to a linear region of length .
9. What is the frequency and wavelength of a photon required to excite the system in the problem above from n=2 to n=3?
10. What is the probability of finding the system in problem 8 in the second excited state at room temperature?
11. Using the same probability function, consider the atmosphere as particles that have probabilities of having enough energy to reach "excited states" corresponding to higher potential energies associated with a greater gravitational potential energy U=mgh. Assume the atmosphere is made entirely of diatomic nitrogen (it is not) and find the altitude (h) where the atmospheric density should be half of that at sea level. (HINT: The density is proportional to the probability of particles having energy to reach those altitudes.) Use T=300K. Make sure your units are compatible!
12. Find the radius of the first and second excited states of hydrogen.
13. The transitions from excited states downward to n=2 are the ones that lead to visible light in hydrogen. These lines that end in n=2 make up the Balmer series. Find the wavelengths of the four visible lines in the Balmer series.
14. The sun is largely made of hydrogen. The temperature of the surface of the sun is 5777K. What is the probability of finding hydrogen in the three states that will lead to the Balmer series which is clearly visible from earth? Feel free to use
Answers
1.
2.
3. It gets shorter
4. The notion that all things are waves and due to wave quanta, they deliver discrete amounts of energy and momentum that we perceive as particle interactions.
5. See article.
6. Wavelengths are too short.
7. It doesn't apply to non-periodic systems.
8. Follow along with that section of text.
9. ; 6.6 nm
10. So small that the calculator thinks zero.
11. 6298m if using g=9.8m/s2
12. ,
13. 657nm, 487nm, 434nm
14.