A particle A of mass m and initial velocity v collides with a particle of B of mass `m/2`which is at rest. The collision is head-on and elastic. The ratio of the de Broglie wavelengths `lamda_(A) "to" lamda_(B)` after collision is

Options

A. `(lamda_(A))/(lamda_(B)) = (1)/(3)`
B. `(lamda_(A))/(lamda_(B)) = 2`
C. `(lamda_(A))/(lamda_(B)) = (2)/(3)`
D. `(lamda_(A))/(lamda_(B)) = (1)/(2)`

Answer

B

Explanation

Let after collision the velocities of A and B respectively `v_(A) and v_(B)`.
`:.` According to the law of conservation of momentum,
`mv = mv_(A) + (m)/(2) v_(B)` …(1)
and according to the law of conservation of relative velocity,
`v = v_(B) - v_(A)`...(2)
Solving (1) and (2) we get, `v_(A) = (v)/(3) and v_(B) = (4v)/(3)`
`:. (lamda_(A))/(lamda_(B)) = ((h)/(p_(A)))/((h)/(p_(B))) = (p_(B))/(p_(A)) = ((m)/(2) v_(B))/(mv_(A)) = ((4v)/(3 xx 2))/((v)/(3))= 2`