Energy levels for H atom [closed]








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Problem Statement:



> 
> The number of orbitals (for H-atom) which have greater energy than $3p\_y$ orbitals: $3s, 3p\_z,3d\_{z^{2}},3d\_{x^{2}-y^{2}},2p\_y, 4d\_{z^2}, 4p\_{y}$
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The solution says that energies of all orbitals with same $n$ (principal quantum number) will be same, only for hydrogen atom.


Can someone explain why is that so? And when not to use the "$n+l$" thing?
[![Image of the question ](https://i.stack.imgur.com/lwWg2.png)](https://i.stack.imgur.com/lwWg2.png)




Since (atomic) hydrogen has only one electron, there is *no electron-electron interaction* to differentiate internal levels.


Of course, an energy level *can* be split [if there is an external interaction](http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html). See the [Feynman lectures](https://www.feynmanlectures.caltech.edu/III_12.html) also. For example, in a magnetic field, the Zeeman effect splits spectral lines. The corresponding [Stark effect](https://en.wikipedia.org/wiki/Stark_effect) shows a similar splitting of levels in an electrostatic field.


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