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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\hw{06}

\problem{Problem 1 (5 points)}
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Recreate plots depicted at figures 8.8 and 8.9. First do it 
for the $P_e = 20~\mathrm{N/m}^2$  (as in the book), second do it for 
the electronic pressure depicting the sun photosphere $n_e =
2\times10^{23}$~m$^{-3}$.


\problem{Problem 2 (5 points)}
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Assuming that the Earth has albedo of $\alpha = 0.36$, find the equilibrium
temperature for the Earth.




\problem{Bonus Problem 3 (5 points)}
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Now assume that we have a lot of green house gases, which does not let the
radiation with wavelength higher than 1~$\mu$m escape the Earth. Find how
high will be the equilibrium temperature to compensate  via the allowed emission
with wavelength below 1~$\mu$m. Here we neglect the fact that the Earth
atmosphere efficiently screen short wavelength radiation in UV and below.
Why do we neglect this fact?

You will have to do some numerical integrals.


\problem{Problem 4 (5 points)}
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Ratio of probabilities to occupy high energy level with respect to the
ground level (n=1) for Hydrogen atom is
given by Boltzmann distribution.
\begin{equation}
	\frac{p(n)}{p(1)} = \frac{g(n)}{g(1)} \frac{\exp{(-E_n/kT)}}{\exp{(-E_1/kT)}}
\end{equation}
given that $g(n) = 2 n^2$ it seems that this ration goes to $\infty$ for a
fixed temperature with growing $n$. Yet, we use in our approximations that
hydrogen is mostly in the ground state. What is wrong with the above
equation?
Hint: it might be connected to the size of the atom.


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