A particle of mass `M` at rest decay's into two particle of masses `m_(1)` and `m_(2) ` having non zero velocity. The ratio of the de Broglie wavelengths of the masses `lambda _(1) // lambda_(2)` is

Options

A. `m_(1)//m_(2)`
B. `m_(2)//m_(1)`
C. `1.0`
D. `sqrt(m_(2))// sqrt(m_(1))`

Answer

C

Explanation

By law of conservation of momentum
`0 = m_(1) vec(v_(1)) + m_(2) vec(v_(2)) rArr m_(1) vec (v_(1)) = - m_(2) vec(v_(2))`
`- ve` sign indicates that both the particles are moving in opposite direction. Now de - Broglie wavelengths
`lambda_(1) = (h)/(m_(1) v_(1))` and `lambda_(2) = (h)/(m_(2) v_(2)), :. (lambda_(1))/(lambda_(2)) = (m_(2) v_(2))/(m_(1) v_(1)) = 1`