In a stationary hydrogen atom, an electron jumps from n = 3 ot n =1. The recoil speed of the hydrogen atom is about

Options

A. `4 m//s`
B. `4 cm//s`
C. `4 mm//s`
D. `4xx10^(-4) m//s`

Answer

A

Explanation

`E_3 - E_1 = (-13//6)/((3))^2 + 13.6 = 12.1 eV`
From momentum conservation,
Momentum of photn = Momentum of hydrogen
atom `:. (E )/(c ) = mv`
or `v = (E )/(mc) = (12.1xx1.6xx10^(-19)/(1.67xx10^(-27)xx3xx10^8)`
=3.86 m//s.