Mx and My denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a β– decay is Q1 and that for a β+ decay is Q2. If m e denotes the mass of an electron, then which of the following statements is correct?

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Q1 = (Mx – My) c2 and Q2 = [Mx – My – 2me]c2 Explanation: Q value or energy of nuclear reaction: The energy absorbed or released during a nuclear reaction is known as the Q-value of nuclear reaction. Q-value = (Mass of reactants – mass of products)c2 Joules = (Mass of reactants – mass of products) amu If Q < 0, the nuclear reaction is known as endothermic. (The energy is absorbed in the reaction) If Q > 0, the nuclear reaction is known as exothermic. (The energy is released in the reaction) Let the nucleus be ZXA β– decay is represented as: zXA → z+1AY + –1e0 + barv + Q1 Q1 = [mn(zXA) – mn(z+1YA) – me]c2 = [mn(zXA) + Zme – mn(z+1YA) – (Z + 1)me]c2 = [m(zXA) – m(z–1YA)]c2 ⇒ Q1 = (Mx – My)c2 β+ decay is represented as: zXA → z–1YA + –1e0 + v + Q2 Q2 = [mn(zXA) – mn(z–1YA) – me]c2 = [mn(zXA) + Zme – mn(z–1YA) – (Z – 1)me – me]c2 = [m(zXA) – m(z–1YA) – 2me]c2 ⇒ Q2 = (Mx – My – 2me)c2

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