Question:
The number of undecayed nuclei \( N \) in a sample of radioactive material as a function of time \( t \) is shown in the figure. Which of the following graphs correctly shows the relationship between \( N \) and the activity \( A \)?
The number of undecayed nuclei \( N \) in a sample of radioactive material as a function of time \( t \) is shown in the figure. Which of the following graphs correctly shows the relationship between \( N \) and the activity \( A \)?
Show Hint
Radioactivity:
( A=\lambda N \)
Always linear relation.
Updated On: Mar 2, 2026
- Option a
- Option b
- Option c
- Option d
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Activity of radioactive material:
\[
A = \lambda N
\]
where \( \lambda \) is decay constant.
Step 1: {\color{red}Relationship between \( A \) and \( N \).}
\[
A \propto N
\]
So:
\[
N = \frac{A}{\lambda}
\]
Step 2: {\color{red}Graph interpretation.}
This is a linear relation passing through origin.
But plotted with \( N \) vs \( A \) gives straight line.
Step 3: {\color{red}Slope direction.}
As activity decreases, nuclei decrease proportionally ⇒ straight decreasing line in plotted orientation.
Correct graph: (C).
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