Question

Not considering the electronic spin, the degeneracy of the second excited state of $H-atom$ is 9, while the degeneracy of the second excited state of $H^{-}$ is :

Answer 1

We know, single electron species do not follow $(n+l)$ rule but a multi electron species do.
The ground state electronic configuration of $H-atom$ is $1s^1$
Thus for second excited state $n=3$.
Hence degeneracy is $3^2=9$

Ground state of electronic configuration $H^{-}=1s^2$
First excited state of $H^{-}=1s^{1}2s^1$
Second excited state of $H^{-}=1s^{1}2s^{0}2p^1$
Again P subshell has 3 degenerate orbitals.
Thus the degeneracy of the second excited state of $H^{-}$ is 3