If an atom has x energy levels,what will be t | vedclass

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Question

(C) When an electron transitions from an excited state $n_2$ to a lower state $n_1$,the number of spectral lines is given by the formula $\frac{n(n-1)

Vedclass · Accepted Answer

$1 + 2 + 3 + \dots + (x - 1)$

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(C) When an electron transitions from an excited state $n_2$ to a lower state $n_1$,the number of spectral lines is given by the formula $\frac{n(n-1)}{2}$,where $n$ is the number of energy levels.For $x$ energy levels,the transitions occur from level $x$ to all lower levels $(x-1, x-2, \dots, 1)$.The total number of lines is the sum of the first $(x-1)$ integers: $1 + 2 + 3 + \dots + (x - 1)$.Therefore,the correct option is $C$.

If an atom has $x$ energy levels,what will be the total number of spectral lines in its emission spectrum?

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