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{\bf Introduction to Astrophysics II, 29:120\\
     Winter, 2006-2007\\
Sixth Homework Set...March 2, 2007. Due March 8, 2007}\\
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{\bf (1)} Calculate the frequencies of the $J=2 \rightarrow 1$ and 
$J=1 \rightarrow 0$ transitions of the CO molecule.  What kind of telescope would you use to observe these spectral lines? \\

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{\bf (2)} Assume that the temperature in a molecular cloud is 6 K.  Further assume that the intensity of a rotational transition is directly proportional to the population of a state, and that the statistical weights of rotational states are all unity.  What is the ratio of the intensities of the $3 \rightarrow 2$ and $2 \rightarrow 1$ transitions of CO? \\

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{\bf (3)} Using insight from \#2, explain how you would distinguish a cloud with $T=6$ K from one with $T= 15$ K.  You do not need to carry out a calculation, but your explanation should be clear and use equations. \\ 


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{\bf (4)} What is the Jean's Mass for the gas in the Earth's atmosphere?  How does that mass compare with the total mass of the Earth's atmosphere?  A rough estimate for the mass of the Earth's atmosphere will do, jess fine.  
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{\bf (5)} Calculate the time it takes for a free-falling, homologously-contracting cloud to go from its initial radius $r_0$ to $\frac{r_0}{2}$?
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{\bf (6)} A Giant Molecular Cloud (GMC, assumed spherical) has a mass of $5 \times 10^4 M_{\odot}$ and a radius of 10 parsecs.  What is the change in gravitational potential energy as it contracts to $r = 5$ parsecs?  Assuming that it is in virial equilibrium, where does this energy go?
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{\bf (7)} Assuming virial equilibrium, what is the temperature of a GMC with $5 \times 10^4 M_{\odot}$ and $r = 5$ parsecs? The molecular cloud can be assumed to be purely molecular hydrogen. \\

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{\bf (8)} \# 12.9 from book  \\


 
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