When a photon is emited by a hydrogen atom , the photon carries a momentum with it (a) calculate the momentum carreied by the photon when a hydrogen atom emits light of wavelength `656.3 nm`(b) with what speed does the atoms recoil during this transition? Take the mass of the hydrogen atom` = 1.67 xx 10^(-27) kg` (c ) Find the kinetic energy of recoil of the atom

Answer

A, B, C

Explanation

(a) Here `lambda = 656.3 nm`
Momentum `'P' = E/c = (hc)/lambda xx 1/c = h/lambda`
`=(6.63 xx 10^-34)/(656.3 xx 10^-9)`
`=0.01 xx 10^-25`
`=1 xx 10^-27 kg-m//s`
(b) ` 1 xx 10^-27 = 1.67 xx 10^-27 xx v`
implies `v=(1)/(1.67)`
`=0.598 = 0.6 m//s`
(c) KE of atom`=1/2 xx 1.67 xx 10^-27 xx(0.6)^2`
`=(0.3006 xx 10^-27)/(1.6 xx 10^-19)eV`
`=1.9 xx 10^-9 eV`