There is a stream of neutrons with kinetic energy of 0.0327 eV. If half life of neutrons is 700s, what fraction of neutrons will decay before they travel a distance of 10m? Take mass of neutron =`1.675xx10^(-27)kg.`

Explanation

`K = (1)/(2)mv^(2) rArr v = sqrt((2K)/(m))`
`=sqrt((2xx0.0327xx1.6xx10^(-19))/(1.675xx10^(-27)))= 0.25xx10^(4)m//sec`
Time taken by neutrons to travel a distance `10 km`
`t = (10)/(0.25xx10^(4)) = 4xx10^(-3)`
Number of neutrons decayed `N' = N_(0) (1-e^(-lambdat))`
`(N')/(N_(0)) = 1-e^(-lambdat) = lambdat = (ln2)/(T_(1//2)) xx t`
`= (0.7)/(700)xx4xx10^(-3)`
`=4 xx 10^(-6)`
`e^(-lambdat) = 1- lambdat+ ((lambdat)^(2))/(|__2)-....`