Question 27: 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?
(1) 60 minutes
(2) 80 minutes
(3) 20 minutes
(4) 40 minutes
Answer: Option (2)
Explanation:
Activity of a radioactive substance is directly proportional to the number of undecayed nuclei.
After one half-life, the activity becomes half of its initial value.
\frac{1}{16} can be written as \left(\frac{1}{2}\right)^4.
This means the substance has undergone 4 half-lives.
Given, one half-life = 20 minutes.
Total time taken = 4 \times 20 minutes.
Total time = 80 minutes.
Hence, the correct answer is Option (2).