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 \( A \)? 

• A. Option a
• B. Option b
• C. Option c
• D. Option d

Hint:

Radioactivity: ( A=\lambda N \) Always linear relation.

Answer 1

The Correct Option is C

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).