JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Modern Physics

The wavelength of the radiation emitted is

λ_{0}

when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be

\frac{20}{x} λ_{0}

. The value of x is ______.

Answer: 27

Solution

For a hydrogen transition

\frac{1}{λ} = R (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})

. The second excited state to the first excited state is

n = 3 \to 2

, giving

\frac{1}{λ _{0}} = R (\frac{1}{4} - \frac{1}{9}) = R \cdot \frac{5}{36}

. The third excited state to the second orbit is

n = 4 \to 2

, giving

\frac{1}{λ} = R (\frac{1}{4} - \frac{1}{16}) = R \cdot \frac{3}{16}

. Dividing,

\frac{λ _{0}}{λ} = \frac{3/16}{5/36} = \frac{27}{20}

, so

λ = \frac{20}{27} λ_{0}

. Comparing with

\frac{20}{x} λ_{0}

gives

x = 27

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Modern Physics →

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Modern Physics

Solution

More JEE Main questions on Modern Physics