Modern Physics 3 Question 35
36. A radioactive element decays by $\beta$-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)
Show Answer
Solution:
- Let $n _0$ be the number of radioactive nuclei at time $t=0$. Number of nuclei decayed in time $t$ are given by $n _0\left(1-e^{-\lambda t}\right)$, which is also equal to the number of beta particles emitted during the same interval of time. For the given condition,
$$ \begin{aligned} n & =n _0\left(1-e^{-2 \lambda}\right) \\ (n+0.75 n) & =n _0\left(1-e^{-4 \lambda}\right) \end{aligned} $$
Dividing Eq. (ii) by (i), we get
$$
