In which energy level would the f orbital make their first apperance? ( use quantum mechanical proof your answer)

Question

Please help, I don't get what's the question asking! Thank you

Answer 1

The orbitals, in order, are
1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f etc.
However, this is not the order if which they fill since the energy levels don't follow sequentially as in the listing above. For example, 1s fills first, 2s next, 2p next, 3s, then 3p, then 4s followed by 3d. The question is asking which n (1,2,3,4,5, etc) level the f orbital fills first AND to prove it by quantum mechanics.

Answer 2

Is it going to be n= 4 right ? Because 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f <- s this the quantum mechanics?

Answer 3

I don't think so. Ce (#58) is the first element to have an f electron and Ce is in period 6. And no, that is not a quantum mechanical answer or proof.
http://www.webelements.com/cerium/atoms.html