MODERN PHYSICS PHY 320 EXAM 4 (May 13, 2003) (Answer all questions. To get partial credits show all the steps of your calculation clearly. Good luck.) h = 6.626 x 10-34 J.s 1 eV = 1.602 x 10-19 J me = 9.109 x 10-31 kg = 0.5110 MeV/c2 c = 3.0 x 108 m/s 1. Briefly and clearly answer the following questions: (a) What is the definition of central force? Give an example of central force. Is the force conservative or non-conservative? Explain why? (5 pts) (b) Why the energy states of hydrogen-like atoms depend only on one quantum number whereas the energy states of a particle in a threedimensional box depend on all three quantum numbers? (5 pts) (c) What are optical transitions? What is the selection rule that should be obeyed by these transitions? (5 pts) (d) Briefly describe the Stern-Gerlach experiment and explain how this experiment shows that the electrons have spin. (10 pts) (e) State Pauli’s exclusion principle for the electrons. What is Hund’s rule? (5 pts) (f) What is normal Zeeman effect? Show all the optical transitions for the hydrogen atom from n=2 state to n=1 state (consider electrons to be spinless). Find out the frequencies of the emitted photons. How does the Zeeman spectra look like? (10 pts) (g) Considering spin of the electron, show all the optical transitions for the hydrogen atom from n=2 state to n=1 state. Find out the frequencies of the emitted photons. How does the Zeeman spectra look like? (10 pts) Problems: (Points will be taken off for not showing the steps of your calculation and for not getting the right numbers.) 2. A particle of mass m moves in a three-dimensional box with sides L. If the particle is in the third excited level, corresponding to n2=11, find (a) the energy of the particle, (b) the combinations of n1, n2, and n3 that would give this energy, and (c) the wave functions for these different states. (3+3+4=10 pts) Sol: 3. Consider an electron in the 4F state. (a) What are the quantum numbers n, l, and ml for this electron? Calculate the numerical value of (b) the orbital angular momentum and (c) the z component of the orbital angular momentum. Considering the spin of the electron calculate (d) all the possible values of the total angular momentum, and (e) the z component of the total angular momentum. (3+4+3+3+2=15 pts) Sol: 4. Calculate the magnetic energy and Larmor frequency for an electron in the n=2 state of hydrogen, assuming the atom is in a magnetic field of strength B=1.00 T. (10 pts) Sol: 5. (a) Write out the electronic configuration of cobalt (Z=27) and copper (Z=29). (b) Write out the values for the set of quantum numbers n, l, ml, and ms for each of the electrons in cobalt and copper. (15 pts) Sol:

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# MODERN PHYSICS PHY 320 EXAM 4

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