1 answer

Energy levels in He+ ion and Hydrogen.

Question:

Hello, could someone please help me with this physics question. Thank you very much in advance.
Suppose the first electron in the He+ ion (singly ionised, hydrogen-like ion) is in the ground (n=1) state, and a second electron is added in the n=10 level.
Explain why the energy of the second electron is almost identical to that of an electron in the same level in hydrogen atom and despite the second electron being in ahigh energy orbit why there is still an effect on the energy of the first electron. Is the energy increased or decreased? Explain your reasoning.

Answers

You got 2 protons instead of 1 - thus it is like H except the potential well is 2x that of H
so energy levels are 2x more than H


in your 1s1 10s1 case

as as far the 10s1 electron is concerned it is way beyond the cloud of the 1s1 - so it sees
2 protons that are almost 100% shielded by 1 electron (the 1s1 one) thus it sees a potential (at n=10) like that of hydrogen.

because there is some (real small) probability of 10s1 being in the face of the 1s1 electron the shielding is not always 100% for all radii and the energylevel is slightly shifted wrt the H case.

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