1 If only life were so simple [16 points] (a) [6 points] Accelerating charges emit light. The power emitted by an accelerating charge is is
given by the famous “Larmor formula” (given below in CGS):
2 q2a2
P = —— 1
where a is the acceleration of the charge, q is the magnitude of the charge, and c is the speed of lightl. If we combine the Larmor formula with the Bohr model, should the electron move inward
or outward in its orbit? Justify your answer. (b) [10 points] Derive a simple order—of—magnitude expression, in terms of fundamental constants,
for the lifetime of a one-electron ground—state atom with Z protons. Express your answer in terms
of fundamental constants c, 71, me, Z, and the fundamental charge 6. Numerically evaluate for
an electron in the ground state of hydrogen. Comment on the stability of life, the Universe, and
everything if the Bohr model were indeed correct.
