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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.
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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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