According to classical electromagnetic theory an accelerated electron radiates energy at the rate Ke2a2/c3, where K=6×109 N−m2/C2, e= electronic charge (C), a= instantaneous acceleration (m/sec2), and c= speed of light (m/sec).
(a) If an electron were oscillating along a straight line with frequency ν (Hz) and amplitude A, how much energy would it radiate away during 1 cycle? (Assume that the motion is described adequately by x=Asin2πνt during any one cycle.)
(b) What is the Q of this oscillator?
(c) How many periods of oscillation would elapse before the energy of the motion was down to half the initial value?
(d) Putting for ν a typical optical frequency (i.e., for visible light) estimate numerically the approximate Q and ``half-life'' of the radiating system.