After absobing a slowly moving neutron of mass `m_(N)` (mometum `~0`), a nucleus of mass M breaks into two nuclei of masses `m_(1) and 5m_(1)(6m_(1)=M+m_(N))`, respectively. If the de - Broglie wavelength of the nucleus with mass `m_(1)` is `lambda`, then de - Broglie wavelength of the other nucleus will be

Options

A. `5 lamda`
B. `lamda//5`
C. `lamda`
D. `25 lamda`

Answer

C

Explanation

`P_(i)=0 rArr P_(f) = P_(1)+P_(2)`
`P_(i)=P_(f) rArr 0=P_(1)+P_(2)`
`(P_(1)=-P_(2))rArr lamda_(1) =(h)/(P_(1))`
`lamda_(2)=(h)/(P_(2))`
`rArr |lamda_(1)|=|lamda_(2)|`
`rArr lamda_(1)=lamda_(2) = lamda`