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 106 K.  For a temperature of 107 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 b2 = kT/mc2.  Ignore the line-shape (i.e. calculate it at line-center, n = snB).

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.