The half - life of a radioactive substance is 50 days. The substance will disintegrate completely in

Options

A. 50 days
B. 500 days
C. 5000 days
D. infinite time

Answer

To solve the problem of how long it will take for a radioactive substance to completely disintegrate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life (t_half) of a radioactive substance is the time taken for half of the substance to decay. In this case, the half-life is given as 50 days.

2. **Decay Process**: After each half-life, the amount of substance remaining is halved:
- After 1 half-life (50 days): 1/2 of the original amount remains.
- After 2 half-lives (100 days): 1/4 of the original amount remains.
- After 3 half-lives (150 days): 1/8 of the original amount remains.
- After 4 half-lives (200 days): 1/16 of the original amount remains.
- This process continues indefinitely.

3. **Complete Disintegration**: Theoretically, a radioactive substance never completely disintegrates in a finite amount of time. It approaches zero but never actually reaches it. Thus, we can say that it will take an infinite amount of time for the substance to completely disintegrate.

4. **Conclusion**: Therefore, the substance will disintegrate completely in an infinite amount of time.

### Final Answer:
The substance will disintegrate completely in an infinite amount of time.