Question

The recoil speed of hydrogen atom after it emits a photon in going from `n = 2 state to n = 1` state is nearly `[Take R_(oo) = 1.1 xx 10^(7) m and h = 6.63 xx 10^(-34) J s]`
A. `1.5 m s^(-1)`
B. `3.3 m s^(-1)`
C. `4.5 m s^(-1)`
D. `6.6 m s^(-1)`

Answer 1

Correct Answer - B
`E = R_(oo) ch xx [1 - (1)/(2^(2))] = (3)/(4) R_(oo) xx hc`
momentum of the photon emitted is,
`p = (E)/(c ) = (3 R_(oo) h)/(4)`
Recoiling speed of hydrogen atom is given by `v = P//m`. where `m` is the mass of hydrogen atom
`v = (3 R_(oo) h)/(4 m) = (3 xx 1.1 xx 10^(7) xx 6.63 xx 10^(-34))/(4 xx 1.67 xx 10^(-27)) = 3.3 m s^(-1)`