There is a stream of neutrons with KE=2eV. If the half life of neutrons is 100 sec, what fraction of neutrons will decay before they travel a distance of 1000 km. [Mass of neutrons `=1.6 xx10^(-24)g`]

Options

A. `0.75`
B. `0.25`
C. `0.707`
D. `0.293`

Answer

D

Explanation

`(1)/(2)MV^(2) rArr 2 eV`
`V=sqrt((4eV)/(m))`
`V=sqrt((4eV)/(1.6 xx 10^(-27))) " " l eV=1.6 xx 10^(-19)J`
`sqrt((4 xx1.6 xx 10^(-19 )J)/(1.6 xx 10^(-27))) rArr V= sqrt(4 xx 10^(8))=2 xx 10^(4)m//s`
`t=(1000 xx 1000m)/(V) rArr t= (10^(6)m)/(2 xx 10^(4))= 50 sec`
`t=(t_(1//2))/(ln2) ln .(1)/((1-x)) rArr 50 = (100)/(ln2)ln .(1)/(1-x) rArr x=0.293`