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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.` |
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Answer» 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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