When a hydrogen atom emits a photon during the transition n=5 to n=1 , its recoil speed is approximately

Options

A. `10^(- 4) m s^(-1)`
B. `2 xx 10^(- 2) m s^(-1)`
C. ` 4 m s^(-1)`
D. `8 xx 10^(2) m s^(-1)`

Answer

C

Explanation

Photon energy `= h f = 13.6 [(1) - (1)/(25)] eV = 13 eV`
photon momentum = momenyum of hydrogen atom :
`implies p = (h f)/( c) or m v = (h f)/( c)`
`v = (h f)/( c) = (13 xx 1.6 xx 10^(-19))/(1.67 xx 10^(-27) xx 3 xx 10^(8)) = 4 m s ^(-1)`