State whether the following statements are true or false:
$(i)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits frequencies corresponding to lines in the Lyman,Balmer,and Paschen series.
$(ii)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits radiation with wavelengths corresponding to the Pfund series,which has very high frequencies.

(A) $(i)$ False. When an electron returns from the third excited state $(n=4)$ to the ground state $(n=1)$,the possible transitions are $4$ $\rightarrow 3, 4$ $\rightarrow 2, 4$ $\rightarrow 1, 3$ $\rightarrow 2, 3$ $\rightarrow 1, 2$ $\rightarrow 1$. These correspond to the Lyman $(n_f=1)$,Balmer $(n_f=2)$,and Paschen $(n_f=3)$ series. Thus,the statement is true. Wait,re-evaluating: The transitions $4 \rightarrow 1$ (Lyman),$4 \rightarrow 2$ (Balmer),and $4 \rightarrow 3$ (Paschen) are indeed possible. Therefore,statement $(i)$ is True.
$(ii)$ False. The Pfund series corresponds to transitions ending at $n_f=5$. Since the electron is returning from $n=4$,it cannot emit radiation in the Pfund series. Thus,statement $(ii)$ is False.