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\hw{07}

\problem{Problem 1 (5 points)}
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Read extra carefully part 9.2 of  the book, pay attention to the definition
of  the Rossseland  mean  opacity. What  are the  mechanisms  due to  which
opacity grows steeply with increase of temperature and then drops (refer to
figure 9.10)?


\problem{Problem 2 (5 points)}
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Solve problem 9.1 from the text book.




\problem{Bonus Problem 3 (5 points)}
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Solve problem 9.6 from the text book.


\problem{Problem 4 (5 points)}
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If we compare  Hydrogen and Nitrogen atoms spectra of  the Solar radiation.
What is the ratio of their Doppler broaden linewidths? Assume that relevant
temperature of the Sun is 5800~K.


\problem{Problem 5 (5 points)}
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If a particular spectral line is only  naturally broadened (i.e. no
pressure or Doppler broadening) then its shape is given by Lorentz profile.
In this case the  optical depth is given by
\begin{equation}
	\tau(\rho, \Delta \lambda) = \frac{\rho}{\rho_0} \frac{1}{1+(\Delta \lambda/\gamma)^2} 
\end{equation}
where $\Delta \lambda = \lambda-\lambda_0$ detuning from the center of the
absorption line and $\gamma$ is the natural linewidth of this line.

Plot transmission Voigt profiles 
\begin{equation}
	T=e^{-\tau(\rho, \Delta \lambda)}
\end{equation}
as a function of a relative detuning $x= \Delta \lambda / \gamma$ for
different density ratios ($\rho/\rho_0$).  

Make sure that you catch a behavior of the growing absorption with increase
of density and then broadening of the absorption line once it hits the zero
of transmission.  Essentially you  should recreate  figure 9.20.  Though it
might  look different  for large  $\rho$, since  we disregard  the pressure
broadening.

Note: feel free to use some software. But I will not accept plots made with
MS Office Excel or OpenOffice or LibreOffice (essentially anything which is
made with Office like products).

\problem{Bonus problem 6 (5 points)}
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Based on problem 5  try to recreate the curve of  growth depicted at figure
9.21.



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