Let's say we have a transition from state 2p to 1s of an hydrogen atom's electron. The intensity radiated by the electron is given by I = 4/3 ω(adsbygoogle = window.adsbygoogle || []).push({}); _{fi}^{4}e^{2}/c^{3}|< f | r | i >|^{2}.

If we take the the | 2 1 1 > → | 1 0 0 > transition for example, we must compute the following integral :

< f | r | i > = C_{1}∫∫∫ e^{-r/a}r sin(θ) e^{i*Φ}* e^{-r/2a}sin(theta) r^{2}sin(θ)dr dθ dΦ

, r = [ 0→ ∞], θ = [0 → pi], Φ = [0 → 2π]

Which can be separated in three integrals (depending on r, θ and Φ respectively). The integral in Φ is

I_{Φ}= ∫ e^{i*Φ}dΦ = 0

, Φ = [0 → 2π]

Which means that < f | r | i > = 0 and that the transition is not allowed.

However in the literature (and logically), this transition is allowed.

I'm not quite sure if it's a comprehension issue or a simple computation error.

Thank you !

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# I Hydrogen electron transition intensity 2p - 1s

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