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`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?A. `Q_(1)=(M_(X)-M_(Y))c^(2)" &"` `Q_(2)=(M_(X)-M_(Y)-2m_(e))c^(2)`B. `Q_(1)=(M_(X)-M_(Y))c^(2)" &"` `Q_(2)=(M_(X)-M_(Y))c^(2)`C. `Q_(1)=(M_(X)-M_(Y)-2m_(e))c^(2)" &"` `Q_(2)=(M_(X)-M_(Y)+2m_(e))c^(2)`D. `Q_(1)=(M_(X)-M_(Y)+2m_(e))c^(2)" &"` `Q_(2)=(M_(X)-M_(Y)+2m_(e))c^(2)` |
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Answer» Correct Answer - A `beta^(-)` decay: As `""_(Z)^(A)Xto""_(Z+1)^(" "A)Y+""_(-1)^(" "0)e+Q_(1)` `Q_(1)=[m_(N)(""_(Z)^(A)X)-m_(N)(""_(Z+1)^(" "A)Y)-m_(e)]c^(2)` `=[{m(""_(Z)^(A)X)-Zme}-{m(""_(Z+1)^(" "A)Y)-(Z+1)m_e)}-m_(e)]c^(2)` `=[M_(X)-M_(Y)-Zm_(e)+(Z+1)m_(e)-m_(e)]c^(2)` `=(M_(X)-M_(Y))c^(2)` `B^(+)" decay:"` `""_(Z)^(A)Xto""_(Z+1)^(" "A)Y+""_(-1)^(" "0)e+Q_(2)` `Q_(2)=[m_(N)(""_(Z)^(A)X)-m_(N)(""_(Z+1)^(" "A)Y)-m_(e)]c^(2)` `=[{m(""_(Z)^(A)X)-Zm_(e)}-{m(""_(Z)^(A)Y)-(Z-1)m_(e)}-m_(e)]c^(2)` `=(M_(X)-M_(Y)-2m_(e))c^(2)` |
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