Nuclei - Result Question 60
61. For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
[2018]
(a) 20
(b) 10
(c) 15
(d) 30
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Answer:
Correct Answer: 61. (a)
Solution:
- (a) Number of nuclei remaining, $N=600-450$ $=150$ after time ’ $t$ '
$ \begin{aligned} & \frac{N}{N_0}=\frac{150}{600}=\frac{1}{4} \\ & N=N_0 e^{-\lambda t} \Rightarrow \ln \frac{N_0}{N}=\lambda t \\ \Rightarrow \quad & t=\frac{1}{\lambda} \ln \frac{N_0}{N} \\ \Rightarrow \quad & t=\frac{2.303 \times T _{\frac{1}{2}}^{2}}{0.693} \log _{10} \frac{N_0}{N} \\ & =\frac{2.303 \times 10}{0.693} \log _{10} 4 \end{aligned} $
