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{\bf Introduction to Astrophysics I, 29:119\\
     Fall, 2008\\
Sixth Homework Set...October 17, 2008.\\ Due October 23, 2008}\\
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For problems (1) - (3), use the energy level diagram for OII given on the page for homework problems.
The fractional numbers next to energy levels are the J quantum number.  The statistical 
weight of a state is 2J+1.\\

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{\bf (1)} At what temperature are 5 \% of the OII ions in the $^2D$ state? Add the two substates and consider it as one state. \\     

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{\bf (2)} For the temperature you obtain, compare $k_B T$ with the energy difference between the $^2D$ and $^4S$ states. What conclusion can you draw from these numbers?   \\

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{\bf (3)}  Consider the emission lines from the $^2P \rightarrow ^4S$ and the 
$^2D \rightarrow ^4S$ transitions.  The $^2S$ state is the ground state.  Assume that the 
intensity of the emission line is equal to a constant times the population of the state, and 
the same constant applies to both transitions. Calculate how the ratio of the line intensities 
depends on temperature over the temperature range 5000 - 50000 K, and make a plot.  {\em Hint:} This is a good use of Mathematica.  Use a linear plot (part of the problem is to intelligently scale the axes) or you will need a lot of decades on your graph.  \\ 

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{\bf (4)} Problem 8.5 from the book.\\

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{\bf (5)} Problem 8.6\\

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{\bf (6)} Problem 8.7\\

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{\bf (7)} Problem 8.9\\

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{\bf (8)} Problem 8.10 \\


 
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