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## Homework Statement

Consider an HI cloud of temperature T ≥ 3 K.

a)

Calculate the energy level difference between the hydrogen atom states leading to 21cm line emission. Show that the ratio of hydrogen atoms in the upper to the lower state of the 21 cm line is approximately 3:1.

b)

Assuming the cloud to be optically thin, find a relation between the total 21 cm Luminosity (in Watts) and the mass of HI (in solar masses). The decay rate is [tex]A_{21} ≈ (1.1 × 10^7 yr)^{−1}[/tex].

## Homework Equations

## The Attempt at a Solution

I have done the first part of a), finding the Energy Difference. I got this to be

[tex] 9.43*10^{-25} [/tex]Joules.

I thought the formula for the second part opf a, showing the ratio is approx. 3, required this formula:

[tex] \frac{n_2}{n_1} = exp(\frac{-(e_2 - E_1)}{kT}) [/tex]

However, this doesn't give me a reasonable value, the value comes a=out to be about 1.

I am also slight uncertain about what to do on part b.

Any ideas would be most appreciated,

TFM