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(C) The ultraviolet region of the hydrogen spectrum corresponds to the Lyman series,where transitions occur to the ground state $(n_1 = 1)$.If there a

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$3$

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(C) The ultraviolet region of the hydrogen spectrum corresponds to the Lyman series,where transitions occur to the ground state $(n_1 = 1)$.If there are $4$ lines in the ultraviolet region,the transitions are from $n_2 = 5, 4, 3, 2$ to $n_1 = 1$.This implies the electron is initially in the $n = 5$ excited state.For an electron transitioning from $n = 5$ to lower energy levels,the total number of possible spectral lines is given by the formula $\frac{n(n-1)}{2}$,where $n = 5$.Total lines = $\frac{5(5-1)}{2} = 10$.The lines in the infrared region correspond to the Paschen series $(n_1 = 3)$ and the Brackett series $(n_1 = 4)$.Possible transitions in the infrared region from $n = 5$ are:$5 \rightarrow 4$ (Brackett series)$5 \rightarrow 3$ (Paschen series)$4 \rightarrow 3$ (Paschen series)Thus,there are $3$ lines in the infrared region.Hence,the correct option is $C$.

$A$ certain atomic transition from an excited state to the ground state of the hydrogen atom in one or more steps gives rise to four lines in the ultraviolet region of the spectrum. How many lines does this transition produce in the infrared region of the spectrum?

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