Question

The variation of decay rate with number of active nuclei is correctly shown in graph

• A. Graph D
• B. Graph C
• C. Graph A
• D. Graph B

Hint:

In radioactive decay, the decay rate is directly proportional to the number of active nuclei, and the rate decreases over time as the number of nuclei decreases.

Answer 1

The Correct Option is C

Step 1: Understanding the decay process.
In radioactive decay, the decay rate \( \frac{dN}{dt} \) is proportional to the number of active nuclei \( N \). This means the more the active nuclei, the higher the decay rate.
Step 2: Analyzing the graphs.
- In Graph A, the decay rate increases with the number of active nuclei and then decreases, which is characteristic of the exponential decay process where the decay rate initially increases and then decreases as the number of nuclei reduces. - Graph B shows a linear relationship, which is not characteristic of the decay process. - Graph C shows a rapid increase followed by a sharp decrease, which is not correct for radioactive decay. - Graph D shows a constant decay rate, which is also not accurate.
Step 3: Conclusion.
Graph A correctly represents the variation of decay rate with the number of active nuclei. This corresponds to option (C).