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In my Modern Physics class, we are looking at the spectral lines of a hydrogen atom, and the question came up of

What wavelength would you expect to see for the emission line from the 2s orbital to the 1s? What about from the 2p orbital?

I know that I can calculate the wavelength with the Rydberg formula, but my question is whether the "shape" of the orbital changes the wavelength of emission. My book implies no, but never explicitly states this.

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    $\begingroup$ Decay of the $2s$ is not dipole-allowed. Its lifetime is very long. $\endgroup$
    – user137289
    Apr 13, 2018 at 19:26
  • $\begingroup$ The 2s and 2p will emit photons of the same wavelength, but they will emit photons of different angular momenta, with different angular distributions. $\endgroup$
    – user4552
    Apr 17, 2018 at 21:25

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In the hydrogen atom (ignoring fine structure), the energy of an orbital is independent of the angular momentum quantum number (s,p,d,f), which governs the shape. Since wavelength depends on energy only, the wavelengths are the same for both the 2s and 2p transitions.

Its also worth noting what Pieter said: the 2s to 1s transition is incredibly slow, but when it does happen the energy of radiated light should be the same as as the 2p to 1s transition.

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