Find the recoil speed of a hydrogen atom after it emits a photon in going from n= 5 state to n= 1 state `(R= 1.097 xx 10^7 m^(-1)):`

Options

A. `2.4 ms^(-1)`
B. `4.18 ms^(-1)`
C. `3.2 ms^(-1)`
D. `6.4 ms^(-1)`

Answer

B

Explanation

`1/lambda=R [1/n_(1)^(1)-1/n_(2)^(2)]`
`1/lambda=1.097 xx 10^(7) [1/1^(2)-1/5^(2)]`
`=1.097 xx 10^(7) xx (24)/(25) m^(-1)`
As external force is zero, so linear momentum remains constant i.e.
`P_("atom")+P_("photon")=0`
`P_("atom")=-P_("Photon")=-h/lambda`
`mv=-h/lambda, v=-(h)/(m lambda)=(-h)/(m). 1/lambda`
`rArr v=(6.63 xx 10^(-34))/(1.67 xx 10^(-27))xx 1.097 xx 10^(7) xx (24)/(25)`
`=4.18mm`