YOUR NAME: PHY 491 - 2013 Midterm Exam

YOUR NAME:
PHY 491 - 2013
Midterm Exam
1. In the intergalactic medium, oxygen (Z = 8) can be highly ionized. This has been seen in
far-ultraviolet spectroscopy. Consider an oxygen ion where only one electron is left. What
is the energy of a photon that it would emit in a transition from the first excited to the
ground state, given that the electron binding energy in a hydrogen atom is Ry≈ 13.6 eV; an
approximate value is sufficient (10 pt)
2. Consider an atom with the ground-state electron configuration 1s2 2s2 2p2 . What is the
ground-state term and what is the value of the total momentum J in the ground state, according to Hund’s rule? (10 pt) Do you expect the atom to show diamagnetic or paramagnetic
response to a magnetic field - provide arguments (3 pt)
3. Consider a diatomic molecule with nuclear masses ∼ M and the typical electron binding
energy Ee . Consider the quartic term in the expansion of the potential energy in the relative
displacement ∆R of the nuclei from the equilibrium position ∆U = K1 (∆R)4 . Estimate K1
in terms of Ee and the electron mass me . (10 pt) Using the first-order perturbation theory,
estimate the shift of the lowest vibrational energy level ∝ K1 (5 pt).
You need 30 pt
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