Nuclei - Result Question 70

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71. The activity of a radioactive sample is measured as $N_0$ counts per minute at $t=0$ and $N_0 / e$ counts per minute at $t=5$ minutes. The time (in minutes) at which the activity reduces to half its value is

======= ####71. The activity of a radioactive sample is measured as $N_0$ counts per minute at $t=0$ and $N_0 / e$ counts per minute at $t=5$ minutes. The time (in minutes) at which the activity reduces to half its value is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/nuclei/nuclei—result-question-70.md (a) $\log _{e} 2 / 5$

(b) $\frac{5}{\log _{e} 2}$

(c) $5 \log _{10} 2$

(d) $5 \log _{e} 2$

[2010]

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Answer:

Correct Answer: 71. (d)

Solution:

  1. (d) $N=N_0 e^{-\lambda t}$

Here, $t=5$ minutes

$\frac{N_0}{e}=N_0 \cdot e^{-5 \lambda}$

$\Rightarrow 5 \lambda=1$,

$\lambda=\frac{1}{5}$,

Now, $T _{1 / 2}=\frac{\ln 2}{\lambda}=5 \ln 2$