Physics · Nuclear Physics

NEET (UG) 2023 — Question 25

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $\left(\frac{1}{16}\right)^{\text {th }}$ of its initial value?

Option A:
40 minutes
Option B:
60 minutes
Option C:
80 minutes
Correct
Option D:
20 minutes

Answer: C

Step-by-step solution

& A=\frac{A_0}{2^n} \\ & \frac{A}{A_0}=\frac{1}{2^n} \\ & \frac{1}{16}=\frac{1}{2^n} \\ & \frac{1}{2^4}=\frac{1}{2^n} \\ & n=4 \\ & n=\frac{t}{T_{\frac{1}{2}}}, t=4 \times T_{\frac{1}{2}}=4 \times 20 \\ & =80 \text { minutes } \end{aligned}$$

Answer key and solution verified before publishing.

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Exam: NEET (UG) 2023
Paper: 2023 paper
Subject: Physics
Chapter: Nuclear Physics
Topic: Laws of Radioactive Decay