Test Index

Atoms and Nuclei

Section: Physics

Question : 10 of 33

Marks: +1, -0

Solution:

Frequency of a spectral line in the hydrogen atom,

v = R c \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

For the first line of Paschen series,

n_1 = 3 \text{ and } n_2 = 4

\therefore v_1 = R c \left( \frac{1}{3^2} - \frac{1}{4^2} \right)

\Rightarrow v_1 = \frac{7 R c}{144}

For the second line of Paschen series,

n_1 = 3 \text{ and } n_2 = 5

\therefore v_2 = R c \left( \frac{1}{3^2} - \frac{1}{5^2} \right) \Rightarrow v_2 = \frac{16 R c}{225}

\because v_2 - v_1 = \frac{16 R c}{225} - \frac{7 R c}{144}

= \frac{81 R c}{3600} = \frac{9 R c}{400}

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