set2-f7 - in the solar photosphere with a view to properly...

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Astro 405/505, fall semester 2007 Homework, 2nd set, return before Friday, September 14, 4pm. Don’t forget to give your name. Problem 3: Jeans criterion In the absence of energy exchange with the environment a gas is said to evolve adiabatically and the pressure P ρ γ , where γ is the adiabatic index (=5/3 for a monatomic gas). Consider a spherically symmetric gas cloud under adiabatic conditions. Use the ideal gas law to derive a relation between central pressure and the radius of the cloud, that delineates the boundary between gravitationally stable and unstable situations. For simplicity assume the external pressure to be negligible. Gas in star-forming regions in the Galaxy typically has a density n = 10 4 H - atoms / cm 3 and a temperature T 10 K. What is the size of a typical star-forming region? Calculate the mass of unstable gas clouds and compare with the mass of the sun. Problem 4: Sodium in the solar photosphere We are interested in Na and Na
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Unformatted text preview: + in the solar photosphere with a view to properly interpret the lines in the solar emission spectrum. Here you will calculate what fraction of the sodium atoms can we expect to be singly ionized. 1) On account of the high energy of the ±rst excited states you may assume that all sodium atoms and ions are in their ground state. The statistical weights are then g = 2 for Na and g = 1 for Na + . Can you explain why this should be so? (Hint: where do you ±nd Na in the Periodic Table?) 2) Using our treatment of hydrogen in class or the notes, estimate the electron density. 3) In which of the three following states would you expect to ±nd most of the sodium: Na (Na I ), Na + (Na II ),or Na ++ (Na III )? The ionization energies are 5.14 eV for Na and 47.29 eV for Na + ( 1 eV = 1 . 6 · 10-12 erg). You will need to make an estimate for the statistical weight of Na ++ ....
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