Question

A radioactive substance decays with decay constant 0.5s⁻1 and is being produced at a constant rate of 50 nuclei per second. If there are no nuclei present initially, the time (in s) after which 25 nuclei will be present is:

• A. 1
• B. \(\ln 2\)
• C. \(\ln(4/3)\)
• D. 2ln(4/3)

Hint:

Use production–decay equilibrium equations carefully.

Answer 1

The Correct Option is D

Step 1: Number of nuclei at time t: N=(R)/(λ)(1-e⁻λ t)
Step 2: 25=(50)/(0.5)(1-e⁻0.5t) ⟹ 1-e⁻0.5t=(1)/(4)
Step 3: e⁻0.5t=(3)/(4) ⟹ t=2ln((4)/(3))