Question

The half-life of a radioactive substance is 12 minutes. The time gap between 28\% decay and 82\% decay of the radioactive substance is:

• A. 6 minutes
• B. 18 minutes
• C. 12 minutes
• D. 24 minutes

Hint:

The time gap between two decay levels is determined using the exponential decay formula.

Answer 1

The Correct Option is D

Radioactive decay follows the formula: \[ N = N_0 e^{-\lambda t} \] where the decay constant is related to half-life: \[ \lambda = \frac{\ln 2}{T_{1/2}} \] Given \( T_{1/2} = 12 \) min, the fraction remaining at 28\% decay is: \[ \frac{N}{N_0} = 0.72 \] At 82\% decay: \[ \frac{N}{N_0} = 0.18 \] Solving for \( t \): \[ t = \frac{\ln(0.72)}{\ln(0.5)} \times 12 \] \[ t = \frac{\ln(0.18)}{\ln(0.5)} \times 12 \] The difference between the two times is 24 minutes.