SATHEE: Modern Physics 3 Question 35

Modern Physics 3 Question 35

36. A radioactive element decays by $β$ -emission. A detector records $n$ beta particles in $2 s$ and in next $2 s$ it records $0.75 n$ beta particles. Find mean life correct to nearest whole number. Given $\ln | 2 | = 0.6931, \ln | 3 | = 1.0986$ .

(2003, 2M)

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Solution:

Let $n_{0}$ be the number of radioactive nuclei at time $t = 0$ . Number of nuclei decayed in time $t$ are given by $n_{0} (1 - e^{- λ t})$ , which is also equal to the number of beta particles emitted during the same interval of time. For the given condition,

$\begin{aligned} n & = n_{0} (1 - e^{- 2 λ}) \\ (n + 0.75 n) & = n_{0} (1 - e^{- 4 λ}) \end{aligned}$

Dividing Eq. (ii) by (i), we get

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Modern Physics 3 Question 35

36. A radioactive element decays by β-emission. A detector records n beta particles in 2s and in next 2s it records 0.75n beta particles. Find mean life correct to nearest whole number. Given ln⁡|2|=0.6931,ln⁡|3|=1.0986.

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36. A radioactive element decays by $β$ -emission. A detector records $n$ beta particles in $2 s$ and in next $2 s$ it records $0.75 n$ beta particles. Find mean life correct to nearest whole number. Given $\ln | 2 | = 0.6931, \ln | 3 | = 1.0986$ .