Question

If the half life of an element is 10 minutes, then the time taken (in minutes) for the element to decay from 20% to 80% is

• A. 20
• B. 10
• C. 5
• D. 15

Hint:

Decay questions often specify "decayed amount" or "remaining amount". Always convert to "remaining amount" ($N$) to apply standard radioactive decay laws.

Answer 1

The Correct Option is A

Step 1: Interpreting the Question:
The phrase "decay from 20% to 80%" refers to the percentage of the substance that has decayed.

• Initial state (20% decayed): Amount remaining $N_1 = 100% - 20% = 80%$ of $N_0$.
• Final state (80% decayed): Amount remaining $N_2 = 100% - 80% = 20%$ of $N_0$.

We need to find the time taken for the remaining amount to decrease from 80% to 20%.
Step 2: Calculating Number of Half-Lives:
Let's see the decay progression: $80% \xrightarrow{T_{1/2}} 40% \xrightarrow{T_{1/2}} 20%$. This transition takes exactly 2 half-lives.
Step 3: Calculating Time:
Half-life ($T_{1/2}$) = 10 minutes. Total time $t = 2 \times T_{1/2} = 2 \times 10 = 20$ minutes.
Step 4: Final Answer:
The time taken is 20 minutes.