When a hydrogen atom going from emits a photon, its recoil speed is m/s. Where

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Solution

Q.
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 = $1.6 \times 10^{- 27} kg$ ) [2024]

Ans.
(17)

The hydrogen atom transitions from $n = 2$ to $n = 1,$

$Δ E = - 10.2 eV$

Recoil speed $v = \frac{Δ E}{m c}$

$= \frac{10.2 eV}{1.6 \times 10^{- 27} \times 3 \times 10^{8}} = \frac{10.2 \times 1.6 \times 10^{- 19}}{1.6 \times 10^{- 27} \times 3 \times 10^{8}}$

$v = 3.4 m/s = \frac{17}{5} m/s$

Therefore, $x = 17$

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