ISM Astronomy heating rate due to photoionization question?

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Jennifer

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Hi everyone! Can someone please help me with the following problem...I have been stuck for a few days and still don't have much clue...Thank you! : )

-Show that, in equilibrium, the heating rate due to photoionization of atom X is
Alpha * n(e)n(X+) *E, where alpha is the recombination rate coefficient for X+ e- -> X+ hv
and E is the excess energy released in the photoionization.

-Show that at T = 15K (approximately) the heating and cooling due to C+ balance in any cloud.
 
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