When a hydrogen atom emits a photon in going from n=5 to n=1, its recoil speed is almost

Explanation

Wavelength of emitted photon can be written as follows :
`1/lambda=R[1/n_1^2-1/n_2^2]=(1.097xx10^7m^(-1))(1/1^2-1/5^2)`
`=1.053xx10^7 m^(-1)`
Linear momentum of photon can be written as follows :
`p=h//lambda=6.63xx10^(-34)xx1.053xx10^7=6.98xx10^(-27)` kg-m/s
When photon is emitted then according to the conservation of linear momentum hydrogen atom must also recoil with the same momentum . Let v be the speed of hydrogen atom then
`M_H xx v =6.98xx10^(-27)`
`1.67xx10^(-27)v = 6.98xx10^(-27)`
`rArr` v=4.18 m/s