Question

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

• A. 40 minutes
• B. 60 minutes
• C. 13 minutes
• D. 20 minutes

Hint:

33% decay leaves 67% undecayed and 67% decay leaves 33%; the remaining amount halves (roughly) in between.

Answer 1

The Correct Option is D

At 33% decay, \(N_1 = 0.67N_0\); at 67% decay, \(N_2 = 0.33N_0\).
\(N = N_0 e^{-\lambda t}\), so \(t_2 - t_1 = \frac{1}{\lambda}\ln\frac{N_1}{N_2} = \frac{T_{1/2}}{\ln 2}\ln\frac{0.67}{0.33}\).
\(\ln\frac{0.67}{0.33} = \ln 2.03 = 0.708\), so \(t_2 - t_1 = 20\times\frac{0.708}{0.693} = 20.4\ \mathrm{min}\approx 20\ \mathrm{min}\).

Answer: (4) 20 minutes