A certain transition in the hydrogen spectrum | vedclass

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(A) The total number of spectral lines emitted when an electron transitions from an excited state $n$ to the ground state is given by the formula: $

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$3$

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(A) The total number of spectral lines emitted when an electron transitions from an excited state $n$ to the ground state is given by the formula: $	ext{Total lines} = \frac{n(n-1)}{2}$.Given that the total number of lines is $10$,we have:$\frac{n(n-1)}{2} = 10$$n(n-1) = 20$$n^2 - n - 20 = 0$$(n-5)(n+4) = 0$Since $n$ must be positive,$n = 5$.The visible spectrum corresponds to the Balmer series,where transitions occur to the $n_1 = 2$ energy level.For an electron falling from $n = 5$ to $n = 2$,the possible transitions are:$5 ightarrow 2$,$4 ightarrow 2$,and $3 ightarrow 2$.Thus,there are $3$ lines in the visible region.

$A$ certain transition in the hydrogen spectrum from an excited state in one or more steps gives rise to a total of $10$ lines. The number of lines lying in the visible spectrum is:

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