Due to the presence everywhere of the cosmic background radiation, the minimum p

Question

Due to the presence everywhere of the cosmic background radiation, the minimum possible temperature of a gas in interstellar or intergalactic space is not 0 K but 2.7 K. This implies that a significant fraction of the molecules in space that can be in a low-level excited state may, in fact, be so. Subsequent de-excitation would lead to the emission of radiation that could be detected. Consider a (hypothetical) molecule with just one possible excited state. (a) What would the excitation energy (in terms of

Explanation / Answer

a)
Using given equation:

31 = 100 e- [ Ex - Eo] / kT

0.31 = e- [ Ex - Eo] / kT

-1.17 =  -[ Ex - Eo] / kT

1.17 x 1.38 x 10-23 x 2.7 =  Ex - Eo

4.36 x 10-23 = Ex - Eo

delta E = 4.36 x 10-23 J = 272.74

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