In a laser cooling experiment...

Question 2 b) of the attatched PDF

In a laser cooling experiment, the transition 5²S_{1/2 :} F = 2   to   5²P_3/2; F' = 3 is
excited by light that has frequency detuning  delta = Gamma / 2.

Selection rules dictate that the excited state decays back to the initial state so there is a nearly closed cycle of absorption and spontaneous emission, but there is some off-resonant excitation to

the F' = 2 hyperne level which can decay to F = 1 and be 'lost' from the cycle.
The F' = 2 level lies about 45Gamma below the F' = 3 level.

Estimate the average number of photons scattered by an atom before it falls into the lower hyperfine
level of the ground state conguration. Assume I = I_SAT and that the transitions
have similar strengths.