`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_9x)-M_(y))` and
`Q_(2)=[M_(x)-M_(y)-2m_(e )]c^(2)`
B. `Q_(1)(M_9x)-M_(y))` 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)+2c_(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)`

Answer

A

Explanation

`beta` decay, `_(z)X^(A)rarr_(z-1)A^(Y)+_(-1)e^(0)+bar(v)`
`Q_(1)=[m_("nucleus")(._(z)X^(A))-m_("neucleaus")(._(z+1)Y^(A))-m_(e )]c^(2)`
`:. M_("nucleus") = m_("atom") - z_(me)`
`:. Q_(1) = [(m_(x) - z_(me)) - (m_(y) - (z+1) me)]c^(2)`
`=(M_(x)-M_(y))C^(2)`
Similarly in `beta^(+)` decay.
`Q_(2)(M_(x)-M_(y)-2me)c^(2)`