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Question
The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.
Solution
The 'series limit' refers to the 'shortest wavelength' (corresponding to the maximum photon energy).
The frequency of the radiation emitted for transition from n1 to n2 is given by
`f = k (1/n_1^2 - 1/n_2^2)`
Here, k is a constant.
For the series limit of Lyman series,
`n_1 = 1`
`n_2 = ∞`
Frequency, `f_1 = k( 1/1^2 - 1/∞ ) = k`
For the first line of Lyman series,
`n_1 = 1`
`n_2 = 2`
Frequency, `f_2 = k(1/1^2 - 1/2^2) = (3k)/4`
For series limit of Balmer series,
`n_1 = 2`
`n_2 = ∞ `
`f_1 = k(1/2^2 - 1 /∞) = k/4`
`f_1 - f_3 = f_2`
Thus, the difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series.
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