Calculating Einstein Coefficient for Nitrogen Transition from 32P1/2 to 32S1/2

[sunrah]

Homework Statement

Calculate the Einstein coefficient of spontaneous emission for nitrogen transitioning from E_i: 3²P_1/2 to E_k: 3²S_1/2. Total duration τ = 16ns, emission wavelength λ = 589.593 nm.

Homework Equations

The Attempt at a Solution

I want to use

$A_{ik} = \frac{2}{3}\frac{e^{2}\omega^{3}_{ik}}{\epsilon_{0}c^{3}h}\cdot \left|\left\langle \psi_{i}| \hat{r} |\psi_{k}\right\rangle\right|^{2}$

but I've never done calculations with the wave functions of multi-electron atoms - can I just use the wave functions for H seeing as $\psi_{i},\psi_{k}$ are really the wave functions of a single electron in two states?

 

[mark726]

Yes, you can use the wave functions for hydrogen since the Einstein coefficient is only dependent on the transition between two energy levels and the wave functions are only used to calculate the transition probability. However, keep in mind that the wave functions for hydrogen and nitrogen may have different normalization factors and you may need to adjust for that in your calculation. Additionally, make sure to use the correct values for the energy levels and transition wavelength for nitrogen in your calculation.