Q101 / 150 · MHT CET 2017 · Physics

The frequency for a series limit of Balmer and Paschen series respectively are $f_{1}$ and $f_{3}$ . If the frequency of the first line of Balmer series is $f_{2}$ then the relation between $f_{1}, f_{2}$ and $f_{3}$ is

Correct answer
A
$f_{1} - f_{2} = f_{3}$
B
$f_{1} + f_{3} = f_{2}$
C
$f_{1} + f_{2} = f_{3}$
D
$f_{2} - f_{3} = 2 f_{1}$

Solution

v = f λ, \frac{1}{λ} = \frac{f}{v}

\frac{1}{λ} = R (\frac{1}{P^{2}} - \frac{1}{n^{2}})

f = R c (\frac{1}{P^{2}} - \frac{1}{n^{2}})

f_{2} = R c (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = R c (\frac{1}{4} - \frac{1}{9})

f_{1} = R c (\frac{1}{2^{2}}) = \frac{R c}{4}

f_{3} = R c (\frac{1}{3^{2}}) = \frac{R c}{9}

∴ f_{1} - f_{3} = R c (\frac{1}{4} - \frac{1}{9})

∴ f_{1} - f_{3} = f_{2}

∴ f_{1} - f_{2} = f_{3}

Hence, the correct answer is option: 'A'.

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