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Phys 728, Spring 2012
Homework Problem Set #2

2.1. Show that radio recombination lines for He and C (recombining
from singly-ionized to neutral state) will be shifted by about 120 km/s
and 150 km/s, respectively, relative to the same line for H. (*hint:
this is due to the dependence of the Rydberg constant on reduced mass*.) Note that these velocity units come from interpreting wavelength shifts as doppler shifts, Dn* = v/c*, so first calculate the frequency (or wavelength) shifts and convert to velocity.
2.2 Calculate the relative emissivities for the first three harmonics
of thermal gyroresonance emission, for a temperature of 10^{6}
K. For a temperature of 10^{7} K. Note that you only
need relative emissivities, so use ratios so that some quantities cancel.
Assume that the index of refraction is unity, and use that fact that b^{2}
= *kT*/*mc*^{2}. Ignore the line-shape (i.e. calculate
it at line-center, n = *s*n_{B}).

2.3 Considering only the line-shape (exponential in the expression
for thermal gyroresonance emission), plot the line shape for the 2nd harmonic
for the two temperatures given above. Comment on the tendency as
temperature increases.