A nucleus kept at rest in free space, brakes up into smaller nuclei of masses `'m'` and `'2m'`. Total energy generated in this fission is `E`. The bigger part is radioactive, emits five gamma ray photons in the direction opposite to its velocity and finally comes torest. `["Given" h=6.6xx10^(-34)Js,m=1xx10^(-26)Kg,E= 3.63xx10^(-8) mc^(2), C=3xx10^(8)m//s)`
The wavelength of the gamma ray is

Options

A. `0.02 A^(0)`
B. `0.03 A^(0)`
C. `0.15 A^(0)`
D. `0.05 A^(0)`

Answer

D

Explanation

`mv_(2)^(2)=(E)/(3)`. Momentum of the photon
`=(5 hc)/(lambda)`=Momentum of the large nucleus.
Hence `(5 hc)/(lambda)=2mv_(2)=sqrt((4Em)/(3))rArr lambda (5 hc)/(2 mc)sqrt((3)/(3.63))`