Question

Calculate the mean lifetime of excited atoms if it is known that the intensity of the spectral line appering due to transition to the ground state diminishes by a factor `eta=25` over a distance `l=2.5mm` along the stream of atoms whose velocity is `v=600m//s`.

Answer 1

Let `T=` mean life time of the excited atoms. Then the number of exicted atoms will decrease with time as `e^(-t//T)`. In time `t` the atom travels a distance `vt` so `t=(l)/(v)`. Thus the number of excited atoms a in a beam that has travesed a distance `l` has decreased by
`e^(-l//vT)`
The intensity of the line is proportional to the number of excited atoms in the beam. Thus
`e^(-l//vtau)=(1)/(eta) or tau=(l)/(V i n eta)=1.29xx10^(-16)` second.