Modern
Physics 1
Fall
2007
Test
4
Chapter 8-9. Quantum Mechanics in 3-D
FAX
solutions to 361/593-2184 by Wednesday, 1 pm, Nov. 18, 2009
Questions:
Q1. Particle in a Box
Considering the fact that quantum particles are rarely enclosed in a rectangular box, explain why the particle in a 3-D box is such an important quantum problem.
Q2. Sharp and Fuzzy Variables
What is the difference between sharp and fuzzy variables and which type of variables are the magnitudes and components of the orbital, spin, and total angular momentum quantities.
Q3. Boundary Conditions and Quantum Numbers
Explain why boundary conditions render quantum numbers and
which boundary conditions quantized n, 
, and 
.
Q4. Spin-Orbit Coupling
What is spin-orbit coupling and how does it affect the spectrum of atoms?
Problems:
P1. Degeneracy and Emission Wavelengths
(a) What is the degeneracy of an electron in the first excited state of a cubic box the same size of an atom (i.e. L = 2 a0)? (b) If that electron transitions from its first excited state to its ground state, what is the wavelength of the emitted photon? (c) What is the degeneracy of an electron in the first excited state of a hydrogen atom? (d) If that electron transitions from its first excited state to its ground state, what is the wavelength of the emitted photon?
P2. Hydrogen Wavefunction
An electron is in the 3d
state of the hydrogen atom with
. (a) What is the equation of its complete wave function? (b)
What is its energy in electron volts? (c) What is the magnitude of its orbital
angular momentum?
P3. Spectroscopic Notation
An electron in an atom is in the 5G7/2 state. (a)
Find the values of the quantum numbers n, , and j. (b) What is the magnitude of the electron’s
total angular momentum? (c) What are the possible values for the z component of
the electron’s total angular momentum?
P4. Periodic Table
(a) Write out the electronic configuration for silicon. (b)
Write out the values for the set of quantum numbers n,
, , and 
for each of the outer
six electrons in silicon.