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 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 .
The correct option is A 3.25 m/s
Einstein's relation for the linear momentum of the photon (denoted by pγ ) is given a
pγ=hλ=6.63×10−34Js122×10−9m=5.43×10−27kgm/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−γ pair is zero (γ 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 -
pH=pγ
mv=5.43×10−27kgm/s
v=5.43×10−27kgm/s1.67×10−27kg=3.25m/s
Einstein's relation for the linear momentum of the photon (denoted by pγ ) is given a
pγ=hλ=6.63×10−34Js122×10−9m=5.43×10−27kgm/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−γ pair is zero (γ 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 -
pH=pγ
mv=5.43×10−27kgm/s
v=5.43×10−27kgm/s1.67×10−27kg=3.25m/s
