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 lambda`
B. `lambda//5`
C. `lambda`
D. `25 lambda`

Answer

C

Explanation

`P_(i)=0`
`P_(f)=P_(1)+P_(2)`
`P_(i)=P_(f)`
`0=P_(1)+P_(2)`
`(P_(1)=-P_(2))`
`lambda_(1)=(h)/(P_(1))`
`lambda_(2)=(h)/(P_(2))`
`|lambda_(1)|=|lambda_(2)|`
`lambda_(1)=lambda_(2)=lambda`