The rate of decay of an assembly of atoms with population density N2 at excited energy lev...

The rate of decay of an assembly of atoms with population density N2 at excited energy level E2 when spontaneous emission is the only important process is

Show that an initial population density N20 decreases to a value N20/e in a time τ equal to 1/A21. That is, show that A21 is the inverse of the lifetime of the atomic level.