First slide

Hydrogen spectrum

Question

Let $v_{1}$ be the frequency of series limit of Lyman series, $v_{2}$ the frequency of the first line of Lyman series, and $v_{3}$ the frequency of series limit of Balmer series. Then which of the following is correct?

Moderate

A

$v_{1} - v_{2} = v_{3}$
B

$v_{2} - v_{1} = v_{3}$
C

$v_{3} = \frac{1}{2} (v_{1} + v_{2})$
D

$v_{2} + v_{1} = v_{3}$

Solution

Series limit means the shortest possible wavelength (maximum photon energy) and first line means the largest possible wavelength (minimum photon energy) in the series.
$v = C [\frac{1}{n^{2}} - \frac{1}{m^{2}}]$ (where C is a constant)
For series limit of Lyman series:
$n = 1, m = \infty \Rightarrow v_{1} = C$
For first line of Lyman series:
$n = 1, m = 2 \Rightarrow v_{2} = 3 C / 4$
For series limit of Balmer series:
$n = 2, m = \infty \Rightarrow v_{3} = C / 4$
Only option (a) is correct.

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