Question

When a hydrogen atom emits a photon in going from n=5 to n=1, its recoil speed is almost
A. `10^(-4) m//sec`
B. `2xx10^(-2) m//sec`
C. `4 m//sec`
D. `8xx10^(2) m//sec`

Answer 1

Correct Answer - C
`(1)/(lamda)=R((1)/(1^(2))-(1)/(5^(2)))=(24R)/(25)`

By momentum conservation
`0=-mv+(h)/(lamda) implies v=(h)/(m lamda)=(h)/(mxx25//24R)`
`=(hxx24R)/(mxx25)`
`=(6.6xx10^(-34)xx24xx1.097xx10^(7))/(1.67xx10^(-27)xx25)=4 m//sec`