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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 isA. `(18ke^(2))/(R_(0)(2^(2//3)+14^(2//3)))`B. `(14ke^(2))/(R_(0)(2^(2//3)+14^(1//3)))`C. `(18ke^(2))/(R_(0)(2^(2//3)+14^(1//3)))`D. `(14ke^(2))/(R_(0)(2^(2//3)+7^(2//3)))` |
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Answer» Correct Answer - C `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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