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There is a stream of neutrons with kinet...

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.`

Text Solution

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Here, `KE=0.0327eV=0.0327xx1.6xx10^(-19)J`
`T=700s, s=10m, m=1.675xx10^(-27)kg`
As `KE=1/2mv^2`
`:. v=sqrt((2KE)/m)=sqrt((2xx0.0327xx1.6xx10^(-19))/(1.675xx10^(-27)))`
`v=2.5xx10^3m//s`
Time taken by these neutrons to travel s=10m is
`t=s/v=10/(2.5xx10^3)=4xx10^(-3)s`
form `N=N_0(1/2)^(t//T)`
`N/(N_0)=(1/2)^(4xx10^-3//700)=0.999952`
`:.` Fraction of neutrons decayed
`=1-N/(N_0)=1-0.999952=0.000048`
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