A monochromatic light is incident on a hydrogen sample in ground… | JEE Main 2023 (11 Apr, Shift 1)

Q38JEE Main 2023 · 11 APR · SHIFT 1Medium

Transitions, Photon Emission & Excitation

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x \times 10^{15}\text{ Hz}$ . The value of $x$ is ____________.

(Given h $= 4.25 \times 10^{-15}\text{ eV s}$ )

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

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Answer: 3

Six wavelengths: $\frac{n(n-1)}{2} = 6 \Rightarrow n = 4$ .
Absorbed energy $= 13.6\left(1 - \frac{1}{16}\right) = 12.75$ eV
$\nu = \frac{E}{h} = \frac{12.75}{4.25 \times 10^{-15}} = 3 \times 10^{15}$ Hz
So $x = 3$ .

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