Question

The activity of a sample of radioactive material is \( A_1 \) at time \( t_1 \) and \( A_2 \) at time \( t_2 \) (\( t_2>t_1 \)). Its mean life is \( T \), then:

• A. \( A_1 t_1 = A_2 t_2 \)
• B. \( \frac{A_1 - A_2}{t_2 - t_1} = \text{constant} \)
• C. \( A_2 = A_1 e^{(t_1 - t_2)/T} \)
• D. \( A_2 = A_1 e^{(t_2 - t_1)/T} \)

Hint:

Radioactive decay follows an exponential pattern where activity decreases over time.

Answer 1

The Correct Option is D

Radioactive decay follows the exponential law:
\[ A_2 = A_1 e^{-(t_2 - t_1)/T} \] Rewriting it, we get:
\[ A_2 = A_1 e^{(t_2 - t_1)/T} \]