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(B) The visible region corresponds to the Balmer series $(n_f = 2)$.For $n$ transitions resulting in $4$ lines in the Balmer series,the electron must

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$6$

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(B) The visible region corresponds to the Balmer series $(n_f = 2)$.For $n$ transitions resulting in $4$ lines in the Balmer series,the electron must jump from $n_i = 6$ to $n_f = 2$ (since the number of lines $= n_i - n_f = 6 - 2 = 4$).The infrared $(IR)$ region includes the Paschen $(n_f = 3)$,Brackett $(n_f = 4)$,and Pfund $(n_f = 5)$ series.For transitions from $n_i = 6$ to lower energy levels:Paschen series $(n_f = 3)$: $6$ $\rightarrow 3, 5$ $\rightarrow 3, 4$ $\rightarrow 3$ ($3$ lines).Brackett series $(n_f = 4)$: $6$ $\rightarrow 4, 5$ $\rightarrow 4$ ($2$ lines).Pfund series $(n_f = 5)$: $6 \rightarrow 5$ ($1$ line).Total lines in the $IR$ region $= 3 + 2 + 1 = 6$.

If an electron moves from an excited state to the ground state in multiple steps in the hydrogen spectrum,and the number of lines in the visible region is $4$,then the number of lines in the infrared region is:

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