The wavelength of the radiation emitted is λ₀ when an electron jumps… | JEE Main 2023 (25 Jan, Shift 1)

Q36JEE Main 2023 · 25 JAN · SHIFT 1Medium

Transitions, Photon Emission & Excitation

The wavelength of the radiation emitted is $\lambda_{0}$ 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 $\frac{20}{x}\lambda_{0}$ . The value of $x$ is _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 27

$\lambda_0$ : second excited ( $n=3$ ) to first excited ( $n=2$ ): $\frac{1}{\lambda_0} = R\left(\frac{1}{4} - \frac{1}{9}\right) = \frac{5R}{36}$
Third excited ( $n=4$ ) to $n=2$ : $\frac{1}{\lambda} = R\left(\frac{1}{4} - \frac{1}{16}\right) = \frac{3R}{16}$
$\lambda = \lambda_0 \times \frac{5/36}{3/16} = \frac{20}{27}\lambda_0$
So $x = 27$ .

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