SATHEE: Nuclei - Result Question 60

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

(d) 30

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Answer:

Correct Answer: 61. (a)

Solution:

(a) Number of nuclei remaining, $N = 600 - 450$ $= 150$ after time ’ $t$ '

$\begin{aligned} \frac{N}{N_{0}} = \frac{150}{600} = \frac{1}{4} \\ N = N_{0} e^{- λ t} \Rightarrow \ln \frac{N_{0}}{N} = λ t \\ \Rightarrow & t = \frac{1}{λ} \ln \frac{N_{0}}{N} \\ \Rightarrow & t = \frac{2.303 \times T_{\frac{1}{2}}^{2}}{0.693} \log_{10} \frac{N_{0}}{N} \\ = \frac{2.303 \times 10}{0.693} \log_{10} 4 \end{aligned}$

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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

Answer:

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