Question

If 10% of a radioactive substance decays in every 5 years, then the percentage of the substance that will have decayed in 20 years, will be:

• A. 40%
• B. 50%
• C. 65.6%
• D. 34.4%

Hint:

For exponential decay, the remaining quantity after each time interval is a fraction of the previous amount. To find the total decay after multiple intervals, apply the decay factor iteratively.

Answer 1

The Correct Option is D

Let the initial amount of the substance be \( N_0 \).
The percentage decayed after 5 years is 10%, so the remaining percentage after 5 years is 90%.
This is the same as saying: \[ N_1 = 0.9 N_0 \] After another 5 years (i.e., 10 years in total), the remaining amount is 90% of \( N_1 \), so: \[ N_2 = 0.9 \times 0.9 N_0 = 0.9^2 N_0 \] After 15 years, the remaining amount is: \[ N_3 = 0.9^3 N_0 \] After 20 years, the remaining amount is: \[ N_4 = 0.9^4 N_0 \] Now, we calculate the percentage decayed after 20 years: \[ \text{Percentage decayed} = 100% - 0.9^4 \times 100% = 100% - 0.6561 \times 100% = 34.39% \]
Thus, the correct answer is (d).