## Question

###### For each of the following questions on optical spectra and spectroscopy, please provide answers no longer...

For each of the following questions on optical spectra and spectroscopy, please provide answers no longer than 3 lines. (a) (2 marks) Describe how emission lines can be used as a diagnostic for gas temperature. (b) (2 marks) Describe how a continuum spectrum can be used as a temperature diagnostic (c) (2 marks) If a continuum spectrum peaks at 100 ?m wavelength, what is the approximate temperature of the source? An order of magnitude answer will suffice. (d) (2 marks) The intergalactic medium within galaxy clusters has a temperature of ~ 107 K but we don't see the Balmer series emission lines being produce by the cluster intergalactic medium Why is this the case?

## Answers

We know that at higt temperature gas follow max well belt man statistics. Number of particles in energy state E is proportional to e^- E/K T. so the intensity of line produced from upper to lower transition alpha e^- E/K T. so measuring intensity of various energy line and potting with 6 five T continuous spectra is due to black body we can get Temperature estimate by we in displacement law lambda T = constant, constant = 2.897 times 10^- 3 m - k where lambda is peak wave length, lambda = 100 um = 10^- 4 m so T = constant/lambda = 2.8977 times 10^- 3/lambda = 2.89 times 10^- 3/106- 4 = 28.9 k for T ~ 10^7 k, All gas is in lionized form so recombination, excitation and excitation is difficult. Also at very high temperature black body spectrum

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