When a hydrogen atom going from n = 2 to n = 1 emits a photon, its recoil speed is x/5 m/s. Where x = ________. (Use, mass of hydrogen atom = 1.6 × 10⁻²⁷ kg) Numerical answer type. Work it out, then open the answer.

Answer: 17. Photon energy E = 10.2 eV = 10.2 × 1.6 × 10⁻¹⁹ = 1.632 × 10⁻¹⁸ J. Recoil momentum equals photon momentum: Mv = E/c. v = 1.632 × 10⁻¹⁸3 × 10⁸ × 1.6 × 10⁻²⁷ = 3.4 m/s = 17/5 m/s. So x = 17.

When a hydrogen atom going from n = 2 to n = 1 emits a photon, its… | JEE Main 2024 (29 Jan, Shift 1)

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Transitions, Photon Emission & Excitation

When a hydrogen atom going from $n = 2$ to $n = 1$ emits a photon, its recoil speed is $\frac{x}{5}\text{ m/s}$ . Where $x =$ ________. (Use, mass of hydrogen atom $= 1.6 \times 10^{-27}\text{ kg}$ )

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

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Answer: 17

Photon energy $E = 10.2\text{ eV} = 10.2 \times 1.6 \times 10^{-19} = 1.632 \times 10^{-18}$ J.
Recoil momentum equals photon momentum: $Mv = \frac{E}{c}$ .
$v = \frac{1.632 \times 10^{-18}}{3 \times 10^{8} \times 1.6 \times 10^{-27}} = 3.4\text{ m/s} = \frac{17}{5}$ m/s.
So $x = 17$ .

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