Q: A radioactive nuclide can decay either via alpha emission or beta emission, the partial half – lives for the two decay modes being T_{1} and T_{2} respectively. In a given set – up, the detector cannot distinguish between alpha and beta particles. The observed half – life time T is related to T_{1} and T_{1} by the formula.

(a) T = T_{1} + T_{2}

(b) T = (T_{1} + T_{2})/2

(c) $ \displaystyle T = \frac{T_1 \times T_2}{T_1 + T_2} $

(d) T = T_{1} × T_{2}

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Ans: (c)

Sol: As decacy constants are additive , i.e.,

λ = λ _{1} + λ _{2}

$ \displaystyle \frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2} $

$ \displaystyle T = \frac{T_1 \times T_2}{T_1 + T_2} $