The half life of radioactive element is `20 min`. The time interval between the stages of its `33%` and `67%` decay is

Options

A. `40 min`
B. `20 min`
C. `30 min`
D. `25 min`

Explanation

To solve the problem, we need to determine the time interval between the stages of 33% and 67% decay of a radioactive element, given that its half-life is 20 minutes.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
The half-life (t₁/₂) of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 20 minutes.

2. **Decay Percentages**:
- At 33% decay, 67% of the original substance remains.
- At 67% decay, 33% of the original substance remains.

3. **First Order Kinetics**:
Radioactive decay follows first-order kinetics, which means the rate of decay is proportional to the amount of substance that remains.

4. **Using Half-Life to Find Time Intervals**:
- From the initial amount (100%), after one half-life (20 minutes), 50% remains.
- To find the time taken to go from 33% to 67% decay, we can use the concept of half-life.
- The time taken to go from 67% to 50% (which is a decrease of 17%) is half of the half-life, which is 10 minutes.
- The time taken to go from 50% to 33% (which is a decrease of 17%) is also half of the half-life, which is another 10 minutes.

5. **Calculating Total Time**:
- Therefore, the total time to go from 33% to 67% decay is the sum of the time taken to go from 33% to 50% and from 50% to 67%.
- This gives us: 10 minutes (from 33% to 50%) + 10 minutes (from 50% to 67%) = 20 minutes.

6. **Conclusion**:
The time interval between the stages of 33% and 67% decay is 20 minutes.

### Final Answer:
The time interval between the stages of 33% and 67% decay is **20 minutes**.

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