Bad Qubits — Learn Quantum by Doing

Multiple choice

For electric-dipole transitions in hydrogen, the angular-momentum selection rules are

\Delta \ell = \pm 1

and

\Delta m = 0, \pm 1

. Based on these rules, why is the 1s -> 2s transition dipole-forbidden?

The 1s and 2s states have different principal quantum numbers, which is always forbidden
The 2s state has higher energy, and dipole transitions only go downward
Both 1s and 2s have $\ell = 0$ , so $\Delta \ell = 0$ , which violates the required $\Delta \ell = \pm 1$ ; thus $\langle 2s|z|1s\rangle = 0$
The transition requires $\Delta m = 2$ , which is not allowed