Selection rules in one electron atoms are:
$\Delta n=$ any
Parity must change
Under strong spin orbit interaction:
$\Delta j=0,\pm 1$, but $j=0\nRightarrow\: j'=0 $
In my notes, it states that while considering a $\rm H$ atom in the $2p$ state with $m_l=0$, the only possible decay is to the $1s$ ground state with $m_l=0$. This implies that the $2p\rightarrow2s$ transition is not possible but upon looking at the selection rules, I can't find anything wrong with it. What am I missing?