Question

A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. Mass of a hydrogen atom = 1.67×${10}^{-27}$ kg. The value of v is .

• A. 3.25 m/s
• B. 5.48 m/s
• C. 6.50 m/s
• D. 2.16 m/s.

Answer 1

The correct option is A 3.25 m/s

Einstein's relation for the linear momentum of the photon (denoted by p_γ ) is given a

$p_{\gamma }=\frac{h}{\lambda }=\frac{6.63\times {10}^{-34}Js}{122\times {10}^{-9}m}=5.43\times {10}^{-27}kgm/s$

This is a simple elastic collision between a photon and a hydrogen atom, and from the momentum point of view, can be treated as a problem in conservation of momentum. The useful fact given is that the photon was absorbed, and the hydrogen atom stopped - which means the final momentum of the $H-\gamma$ pair is zero ($\gamma$ is an oft-used symbol for the photon). Naturally, their initial momenta must have been equal and opposite, so that the net momentum is conserved. Comparing the magnitudes, we can write -

$p_H=p_{\gamma }$
mv$=5.43\times {10}^{-27}kgm/s$
$v=\frac{5.43\times {10}^{-27}kgm/s}{1.67\times {10}^{-27}kg}=3.25m/s$