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exam - more than one configuration Do not neglect the g and...

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Physics 780.04 Winter Quarter 2005 Dr. Herbst 16 February MIDTERM EXAMINATION (100 POINTS) IN CLASS 1. (30 points) a) (15 pts) Calculate the half-life against spontaneous emission of radiation for a sample of CO gas in its first excited rotational state ( J =1). The rotational constant B is 57.8975 GHz and the transition dipole is 0.04 Debye. b) (15 pts) Determine a formula for the temperature at which spontaneous and stimulated emission of radiation at a given frequency are equal. Hint: compare A ul and B ul r T ( n ). 2. (40 points) a) (20 pts) Consider phosphorus atoms, which contain 15 electrons. Determine and order the allowed terms that correlate with the ground configuration. Then determine the allowed states including fine structure. Can you predict the order of the fine-structure states? b) (20 pts) Consider the molecular ion O 2 + , which possesses 15 electrons. Determine the term symbols for the three lowest states, which may arise from
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Unformatted text preview: more than one configuration. Do not neglect the g and u symbols. You are given that s u * 2s < s g 2p < p u 2p. If spin-orbit splitting occurs in the lowest energy term, show the states allowed and their order. Are any transitions allowed among your states? 3. (30 points) a) (20 pts) Determine the overall degeneracies (rotational x nuclear spin) of the first 5 rotational levels of 17 O 2 , 18 O 2 , and 17 O 18 O (X 3 S g-), where the nuclear spin of 17 O is 5/2 while that of 18 O is zero. b) (10 pts) Explain briefly why a diatomic molecule that undergoes vibration and rotation can have vibrational transitions in which D v >1. Hint: consider the expansion of the dipole moment function m (R) around R=R e in the integral <v’J’| m (R)|vJ>....
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