`M_(x) and M_(y)` denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q - value for a `beta-` decay is `Q_(1)` and that for a `beta^(+)` decay is `Q_(2)`. If `m_(e)` denotes the mass of an electrons, then which of the following statements is correct?

Options

A. `Q_(1) = (M_(x) -M_(y))c^(2)` and `Q_(2) =(M_(x)-M_(y) -2m_(e))c^(2)`
B. `Q_(1)-(M_(x)-M_(y))c^(2)` and `Q_(2)=(M_(x)-M_(y))c^(2)`
C. `Q_(1)=(M_(x)-M_(y) -2m_(e))c^(2)` and `Q_(2)=(M_(x)-M_(y) + 2m_(e))c^(2)`
D. `Q_(1) =(M_(x) -M_(y) + 2m_(e))c^(2)` and `Q_(2) =(M_(x) - M_(y)+ 2m_(e))c^(2)`

Explanation

For `beta^(-)`, decay, `""_(z)X^(A) to ""_(z+1)Y^(A) + ""_(-1)e^(0) +barv+Q_(1)`
Q = energy for this decay is given by
`Q_(1)=[m(""_(2)X^(A))-m(""_(z+1)Y^(A))]c^(2)`
Where mN represents mass of nucleus and m represent mass of an atom
`therefore Q_(1) =(M_(x) -M_(y))c^(2)`
(ii) For `beta^(-)`, decay: `""_(Z)X^(A) to ""_(z+1)Y^(A) +""_(1)e^(0) +v +Q_(2)`
Q-energy for this decay is given by:
`Q_(2)=[m(""_(Z)X^(A))-m(""_(z-1)Y^(A))-2m_(e)]c^(2)`
`therefore Q_(2) =(M_(x)-M_(y) -2m_(e))c^(2)`
The correct option is (a).