Excitation of hydrogen atom

Question

I studied the Bohr's model of atom that says electron can jump to higher energy level by absorbing photon, but the quantum model says we have more than that (quantum numbers). Therefore, when the electron of hydrogen atom absorbs a photon, will it move according to the Aufbau principle (1s, 2s, 2p ...), or will it stay in the s subshell with an increasing value of n?

Answer 1

[...] will it stay in the s subshell with an increasing value of n?

Quite the opposite, in fact: it can't go from $\mathrm{1s} \to \mathrm{2s}$, $\mathrm{1s} \to \mathrm{3s}$, or any $\mathrm{1s} \to n\mathrm{s}$ for that matter. The selection rules for electronic transitions state that the quantum number $l$ must change by $\pm 1$, and starting from an s-orbital ($l = 0$) the only place you can go to is $l = 1$, i.e. a p-orbital.

However, there's no restriction on the principal quantum number $n$. So $\mathrm{1s} \to \mathrm{2p}$, $\mathrm{1s} \to \mathrm{3p}$, or any $\mathrm{1s} \to n\mathrm{p}$ are OK.

(Very loosely speaking, the reason for this is because a photon carries one unit of angular momentum, and essentially that must be reflected in the transition; the quantum number $l$ represents angular momentum, so it must change by one unit. Formally speaking, these are derived from angular momentum coupling rules, which is covered in typical graduate QM textbooks e.g. Sakurai. $n$ on the other hand has no relationship to angular momentum, so the only requirement for changes in $n$ is that the incident photon must have the correct energy.)

This is illustrated nicely in a Grotrian diagram, see https://en.wikipedia.org/wiki/Grotrian_diagram. The allowed transitions are depicted by arrows, and you'll see that they only correspond to $\Delta l = \pm 1$.