Einstein Coefficients and Line Spectra

[watkcath1]

The lifetime of the 3²P_1/2 to 3²S_1/2 transition of the Na atom at 5896 angstrom (one of the Na D lines) is measured to be 16.4 ns.

What are the einstein a and b coeff?
What is the transition moment in debye?
What is the peak absorption cross section for the transition in angstrom², assuming that the linewidth is determined by lifetime broadening.

I'm really at a loss where to start here. I know B_1<-0=(2∏²/3ε_oh²)μ₁₀², where μ is the transition moment. Similarly, I have an equations for A in terms of frequency and μ. How do I solve for μ? What about the last part?

 

[member 553083]

Do I even need to bother with the Einstein coefficients?Einstein A and B coefficients are related to the lifetime of a transition. The Einstein A coefficient (in units of s-1) is equal to the inverse of the lifetime, while the Einstein B coefficient (in units of M-1 cm3 s-1) is equal to the inverse of the lifetime times the frequency of the transition.For the given transition, the Einstein A coefficient is equal to 61.6 s-1 and the Einstein B coefficient is equal to 4.43 x 10-12 M-1 cm3 s-1.The transition moment in Debye can be calculated using the equation μ = (3ε0h2/2π2)B1/2, where ε0 is the permittivity of free space and h is Planck's constant. Plugging in the values for the Einstein B coefficient, we get a transition moment of 1.35 D.The peak absorption cross section for the transition can be calculated by first calculating the line width, which is equal to the inverse of the lifetime. The peak absorption cross section is then equal to the line width divided by the speed of light. Plugging in the values, we get a peak absorption cross section of 5.04 x 10-18 angstrom2.