Answer to Question #154845 in Classical Mechanics for Akash

Question

For the 2P → 1S transition in the hydrogen atom calculate ω. Assuming the 

spontaneous emission lifetime of the 2P state to be 1.6 ns, calculate the Einstein B 

coefficient. Assume n0 ≈1.

Answer 1

We know that energy of the photon during $2p\rightarrow1s$ transition $\hbar\omega =\frac{E_o}{4}-E_o$

$\Rightarrow \hbar\omega =\frac{-3E_o}{4}$

$\Rightarrow \hbar\omega =10.2eV$

$\Rightarrow \omega=\frac{10.2\times 1.6\times 10^{-19}}{6.6\times 10^{-34}}J/J.s$

$\Rightarrow \omega =2.47\times 10^{15} rev/s$

$B=\frac{\pi e^2}{\epsilon_o \hbar}=\frac{3.14\times 1.6\times 1.6\times10^{-38}}{8.85\times 6.6\times 10^{-46}}$ T

$=0.137\times 10^{8}T$