1.

The first nuclear reaction ever observed was by ernest Rutherford in 1919. It was triggered by alpha particles incident on an isotope of nitrogen ._(7)^(14) N. He observed a proton was emitted along with another element x. Let us assume that ._(7)^(14) N nucleus was initially stationary. For this reaction to occur, alpha-particle must touch the nitrogen nucleus. The distance between their centres at this moment is d. For this problem, we will neglect the effect of outer electrons in ._(7)^(14) N. Symbols have their usual meanings. The minimum initial kinetic energy of alpha-particle so that reaction can occur is

Answer»

`(18ke^(2))/(R_(0)(2^(2//3)+14^(2//3)))`
`(14ke^(2))/(R_(0)(2^(2//3)+14^(1//3)))`
`(18ke^(2))/(R_(0)(2^(2//3)+14^(1//3)))`
`(14ke^(2))/(R_(0)(2^(2//3)+7^(2//3)))`

Solution :`1/2muv_(REL)^(2) =(kq_(1)q_(2))/d`
`1/2xx(4mxx14m)/(4m+14m)v_(rel)^(2)=(kxx2xxexx7e)/(R_(0)(14^(1//3)+2^(2//3)))`
`1/2xx4m v_(rel)^(2)=(18ke^(2))/(R_(0)(14^(1//3)+2^(2//3)))`


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