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.
Value of d is

Options

A. `R_(0)(2^(1//3)+7^(1//3))`
B. `R_(0)(2^(2//3)+7^(2//3))`
C. `R_(0)(2^(2//3)+14^(2//3))`
D. `R_(0)(2^(2//3+14^(1//3))`

Answer

D

Explanation

`d=R_(N)+R_(p)`
`R=R_(0)A^(1//3)=R_(0)14^(1//3)+R_(0)4^(1//3)`