A radioactive nucleus (initial mass number A and atomic number Z) emits `3alpha`-particles 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-8)/(Z-4)`
C. `(A-Z-4)/(Z-8)`
D. `(A-Z-12)/(Z-4)`

Answer

C

Explanation

When a radioactive nucleus emits an alpha particle, its mass number decreases by 4 while the atomic number decreases by 2.
When a radioactive nucleus, emits a `beta^(+)` particle (or positron `(e^(+))` its mass number remains unchanged while the atomic number decreases by 1.
`""_(Z)X^(A) overset(3alpha)rarr ""_(Z-6)Y^(A-12)overset(2e^(+))rarr""_(Z-8)W^(A-12)`
In the final nucleus,
Number of protons, `N_(o)=Z-8`
Number of neutrons, `N_(n)=A-12-(Z-8)=A-Z-4`
`therefore" "(N_(n))/(N_(p))=(A-Z-4)/(Z-8)`