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(C) When an electron is excited from the ground state $(n_1 = 1)$ to an excited state $(n_2 = 3)$,it will return to the ground state by emitting photo

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$3$

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(C) When an electron is excited from the ground state $(n_1 = 1)$ to an excited state $(n_2 = 3)$,it will return to the ground state by emitting photons.The number of spectral lines emitted when an electron transitions from an excited state $n_2$ to a lower state $n_1$ is given by the formula:$N = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2}$Here,$n_2 = 3$ and $n_1 = 1$.Substituting the values:$N = \frac{(3 - 1)(3 - 1 + 1)}{2}$$N = \frac{2 	imes 3}{2} = 3$The possible transitions are:$1$. $n = 3 ightarrow n = 2$$2$. $n = 3 ightarrow n = 1$$3$. $n = 2 ightarrow n = 1$Thus,the total number of spectral lines is $3$.

How many spectral lines are obtained when an electron in the ground state of hydrogen is excited to the principal quantum number $n = 3$?

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