5. The CO molecule has a rotational constant of 57.6 GHz (1 GHz = 109 cycles per second. The level degeneracies for CO are typical of diatomic rotational transitions gJ = 2J + 1. (Spreadsheets are your friends.)
a Calculate the rotational partition function for CO at room temperature using the exact formula and the approximate formula. At what J value does the probability peak?
b) For a molecular cloud at 10K, calculate the rotational partition function using the exact formula and the approximate formula. At what J value does the probability peak?