InterviewSolution
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InterviewSolution
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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` 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` |
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Answer» Correct Answer - a `beta^(-)` decay is represented as `._ZX^A to ._(Z+1)Y^A + ._(-1)e^0 + barupsilon+Q_1` `therefore Q_1=[m_N(._ZX^A)-m_N(._(Z+1)Y^A)-m_e]c^2` `=[m_N(._ZX^A)+Zm_e-m_N(._(Z+1)Y^A) - (Z+1)m_e]c^2` `=[m(._ZX^A)-m(._(Z+1)Y^A)]c^2=(M_x- M_y)c^2` `beta^+` decay is represented as `._ZX^A=._(Z-1)Y^A + ._1e^0 + upsilon + Q_2` `therefore Q_2=[m_N(._ZX^A)-m_N(._(Z-1)Y^A)-m_e]c^2` `=[m_N(._ZX^A)+Zm_e-m_N(._(Z-1)Y^A) - (Z-1)m_e-2m_e]c^2` `=[m(._ZX^A)-m(._(Z-1)Y^A)-2m_e] c^2=(M_x-M_y-2m_e) c^2` |
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