Answer to Question #154845 in Classical Mechanics for Akash

Question #154845

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.


1
Expert's answer
2021-01-12T12:13:09-0500

We know that energy of the photon during 2p1s2p\rightarrow1s transition ω=Eo4Eo\hbar\omega =\frac{E_o}{4}-E_o

ω=3Eo4\Rightarrow \hbar\omega =\frac{-3E_o}{4}

ω=10.2eV\Rightarrow \hbar\omega =10.2eV

ω=10.2×1.6×10196.6×1034J/J.s\Rightarrow \omega=\frac{10.2\times 1.6\times 10^{-19}}{6.6\times 10^{-34}}J/J.s

ω=2.47×1015rev/s\Rightarrow \omega =2.47\times 10^{15} rev/s

B=πe2ϵo=3.14×1.6×1.6×10388.85×6.6×1046B=\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

=0.137×108T=0.137\times 10^{8}T


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