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.

Answer 1

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
$f=k\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
Here, k is a constant.

For the series limit of Lyman series,
n₁ = 1
n₂ = $\infty$

Frequency, $f_1=k\left(\frac{1}{1^2}-\frac{1}{\infty }\right)=k$

For the first line of Lyman series,
n₁ = 1
n₂ = 2

Frequency, $f_2=k\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3k}{4}$

For series limit of Balmer series,
n₁ = 2
n₂ = $\infty$

$f_1=k\left(\frac{1}{2^2}-\frac{1}{\infty }\right)=\frac{k}{4}$

f₁ $-$ f₃ = f₂

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.