When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number $n$. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum $\ell$. This is the selection rule, which states that $\Delta \ell= \pm 1$; that is, in a transition, the value of $\ell$ can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) $2 s \rightarrow 1 s$, (b) $3 p \rightarrow 1 s$, (c) $3 d \rightarrow 4 f$, (d) $4 d \rightarrow 3 s$ ? In view of this selection rule, explain why it is possible to observe the various emission series shown in Figure 7.15.