A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. The value of v is (mass of hydrogen atom `=1.67xx10^(-27)` kg)

Options

A. `6.15 ms^(-1)`
B. `5.45 ms^(-1)`
C. `2.95 ms^(-1)`
D. `3.25 ms^(-1)`

Answer

D

Explanation

The linear momentum of the photon
`p = (h)/(lambda) = (6.63 xx 10^(-34))/(122 xx 10^(-9))= 5.43 xx 10^(-27) kg ms^(-1)`
As the photon is absorbed and the atom stops, the total final momentum is zero. From conservation of linear momentum , the initial momentum must be zero. The atom should move opposite to the direction of motion of the photon and they should have the same magnitudes of linear momentum. Thus,
`(1.67 xx 10^(-27) kg) v=5.43 xx 10^(-27) kg ms^(-1)`
or, `v= (5.43 xx 10^(-27))/(1.67 xx 10^(-27)) ms^(-1) = 3.25 ms^(-1)`