JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Modern Physics

The first three spectral of H -atom in the Balmer series are given

λ_{1}, λ_{2}, λ_{3}

considering the Bohr atomic model, the wave lengths of first and third spectral lines

(\frac{λ _{1}}{λ _{3}})

are related by a factor of approximately ' x '

\times 1 0^{- 1}

.
The value of x , to the nearest integer, is ____

Answer: 15

Solution

Every Balmer line ends on

n = 2

, and the first and third lines of the series start from

n = 3

and

n = 5

\frac{1}{λ _{1}} = R (\frac{1}{4} - \frac{1}{9}) = \frac{5 R}{36}, \frac{1}{λ _{3}} = R (\frac{1}{4} - \frac{1}{25}) = \frac{21 R}{100}

Dividing one by the other,

\frac{λ _{1}}{λ _{3}} = \frac{36}{5} \times \frac{21}{100} = \frac{756}{500} = 1.512

Written in the form

x \times 1 0^{- 1}

this is

15.12 \times 1 0^{- 1}

, so to the nearest integer

x = 15

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Integer answer