Physics 249 Homework 8
Due Nov 9th
1) Five identical non-interacting particles are put in an infinite potential 1D square well
with L=1.0nm. Compare the ground state energy if they are muons (heavy version of the
electron) or pion (pions have symmetric wave functions).
2) Which of the following atoms would you expect to have its ground state split by the
spin orbit interaction. Li, B, Sc, Cu. For the atoms that have ground state splitting how
many split energies are there?
3) For LiCl
a) Calculate the potential energy of attraction at the equilibrium separation
b) Find the disassociation energy neglecting the energy of repulsion.
c) What is the value of the energy of repulsion?
4) Hydrogen can bond covalently with sulfur, tellurium, phosphorus and antimony. Use
the electron configuration tables in appendix C to write the chemical formulas for these
covalent molecules.
5) The equilibrium separation in HF is 0.0917 nm and it’s electric dipole moment is
6.40x10-30 Cm. What percentage of the bonding is ionic
6) The equilibrium potential energy between two atoms in a molecule can be well
described by the formula.
𝑎 12
𝑎 6
𝑈(𝑟) = 𝑈0 [( ) − 2 ( ) ]
𝑟
𝑟
Find r and U at the minimum.
If r = 0.074nm and U= 32.8eV at the minimum graph the potential. On the same graph
include an electrostatic attraction potential energy assuming the H2 molecule acts as ionic
bond with an H+ attracting and H-. How do the two potentials compare at high radius?
What would you conclude about the ionic bonding disassociation energy from this
comparison and is ionic bonding a good model for this system? For the x axis use r/rmin
for the units.