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  4. A hydrogen atom is in fifth excited state. When the electron jumps to ground state, the velocity of recoiling hydrogen atom is

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Q. A hydrogen atom is in fifth excited state. When the electron jumps to ground state, the velocity of recoiling hydrogen atom is

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

$\Delta E=13.6\left(\frac{1}{1^{2}} - \frac{1}{6^{2}}\right)$
$\Delta E=13.22 \, eV$
$p=\frac{\Delta E}{c}$
$\Rightarrow \, \, v=\frac{\Delta E}{m C}=\frac{13.22 \times 1.6 \times 1 0^{- 19}}{1.67 \times 1 0^{- 27} \times 3 \times 1 0^{8}}=4.2 \, m \, s^{- 1}$