A particle of mass M at rest decays into two masses `m_(1) and m_2` with non zero velocities. The ratio of de-Broglie wavelengths of the particles `(lamda_(1))/(lamda_(2))` is

Options

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

Answer

D

Explanation

According to principle of conservation of momentum
`m_(1)v_(1)+m_(2)v_(2)=0impliesm_(1)v_(1)=-m_(2)v_(2)`
de-Broglie wavelength is given by
`lamda_(1)=(h)/(m_(1)v_(1)),lamda_(2)=(h)/(m_(2)v_(2))`
`therefore (lamda_1)/(lamda_(2))=(1)/(1)=1`.