PROBLEMS

1. (a) Show that the spectrum of thermal radiation for T = 300K peaks at approximately 10 microns.

(b) At what frequency v does p(v) have its maximum?

(c) Support or refute the statement (from S. Weinberg, The First Three Afintiles Bantam Books, New York, 1977, p. 57) that "the average distance between photons in black-body radiation is roughly equal to the typical photon wavelength.

2. Assuming the classical force F = eE + ev x B acting on a charge e in electric and magnetic fields E and B, respectively, show that the magnetic force is small com. pared to the electric force when the charge has a velocity |v| << c in a plane-wave electromagnetic field.

3. Assume the "spring constants" k_s for the binding of electrons in atoms are approximately the same as those for the binding of atoms in molecules. If v 5 x 10¹⁴ Hz is a typical electronic oscillation frequency, estimate the range of fre-quencies typical of atomic vibrations in molecules, given typical electron-atom mass differences. Does your estimate indicate that molecular vibrations lie in the infrared region of the spectrum?