Consider a transition of 5000Å with a width of 1Å, a cavity of 2 cm3 in volume and let n=1. a) Convert this wavelength interval (1Å) to frequency units (i. e. GHz and cm-1 ). b) How many electromagnetic modes exist in this frequency band for this cavity? c) Suppose that the cavity were in the form of a cylinder with a cross-sectional area of 0.1 cm2 (and thus is 20 cm long). How many TEM0,0,q cavity modes would fit within the frequency band specified by this 1 Å? (Do not forget the 2 polarizations.) d) Combine the results of b) and c) to estimate the probability of a spontaneous photon appearing in one of the polarized TEM0,0,q modes. e) If the A coefficient for this transition is 10 7 sec-1 , what is the stimulated emission cross section? (20 points)