In the hydrogen atomic spectrum,a series limi | vedclass

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(C) The series limit corresponds to the transition from $n_2 = \infty$ to $n_1$.The Rydberg formula for the wavenumber is $\bar{v} = R \left( \frac{1}

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Paschen series

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(C) The series limit corresponds to the transition from $n_2 = \infty$ to $n_1$.The Rydberg formula for the wavenumber is $\bar{v} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.For the series limit,$n_2 = \infty$,so $\bar{v} = \frac{R}{n_1^2}$.Given $\bar{v} = 12186.3 \ cm^{-1}$ and $R = 109677.76 \ cm^{-1}$,we have:$12186.3 = \frac{109677.76}{n_1^2}$$n_1^2 = \frac{109677.76}{12186.3} \approx 9$$n_1 = 3$.Since $n_1 = 3$,the series is the Paschen series.

In the hydrogen atomic spectrum,a series limit is found at $12186.3 \ cm^{-1}$. To which series does it belong?

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