A radioactive nucleus (initial mass number A and atomic number Z) emits 3 `alpha`-paticles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

Options

A. `(A-Z-4)/(Z-2)`
B. `(A-Z-B)/(Z-4)`
C. `(A-Z-4)/(Z-8)`
D. `(A-Z-12)/(Z-4)`

Answer

C

Explanation

`._(Z)X^(A) underset(3(alpha^(+)))(rarr) ._(Z-6)( )^(A-12) underset(2(beta^(0)))(rarr) ._(Z-6)( )^(A-12)`
`:. ("No. of neutrons")/("No. of protons")=((A-12)-(Z-8))/(Z-8)=(A-Z-4)/(Z-8)`