Q. When a hydrogen atom emits a photon in going from $n = 5$to $n = 1$, its recoil speed is almost
A) $10^{- 4}\ ms^{- 1}$
B) $8 \times 10^{2}\ ms^{- 1}$
C) $2 \times 10^{- 2}\ ms^{- 1}$
D) $4\ ms^{- 1}$
Explanation
(d) Energy of photon emitted,
$E = 13.6\left( \frac{1}{1^{2}} - \frac{1}{5^{2}} \right)eV = 13.6 \times \frac{24}{25}eV$
Momentum of photon $= \frac{E}{c}$
The momentum of hydrogen atom is equal and opposite to the momentum of photon. If $m$ is the mass of hydrogen atom $( = 1.67 \times 10^{- 27}kg)$and $v$ is recoil speed of hydrogen atom , then
$mv = \frac{E}{c}$
$v = \frac{E}{mc} = \frac{13.01 \times 1.6 \times 10^{- 19}}{1.67 \times 10^{- 27} \times 3 \times 10^{8}}$
$v = 4.15\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.