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Hydrogen spectrum – Balmer series limit
Concepts tested here
- balmer-series-limit-wave-number
All Questions
2016 1 question
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Given the value of Rydberg constant is $10^{7}\ m^{-1}$, the wave number of the last line of the Balmer series in hydrogen spectrum will be
Series limit of Balmer: $\bar{\nu} = R/4$.
$\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$
For the last line of the Balmer series, $n_1 = 2$, $n_2 = \infty$.
$\frac{1}{\lambda} = 10^{7}\left(\frac{1}{2^2} - \frac{1}{\infty}\right) = \frac{10^{7}}{4}$
$\frac{1}{\lambda} = 0.25\times10^{7}\ m^{-1}$
Note: the source paper prints the Rydberg constant as '10 $m^{-1}$'; the source solution notes it should be $10^{7}\ m^{-1}$, which is used here.