Question

The half life of a radioactive substance is $20\, minutes$. The time taken between $50\%$ decay and $87.5\%$ decay of the substance will be

• A. 30 minutes
• B. 40 minutes
• C. 25 minutes
• D. 10 minutes

Answer 1

Answer: (B)

40 minutes

Answer 2

Given, $T_{1 / 2}=20 \,min$ $N_{1}=50$ $N_{2}=100-87.5=12.5$ We know that, time taken by a substance to decay, $t_{2}-t_{1} =\frac{T}{\ln 2} \ln \left(\frac{N_{1}}{N_{2}}\right)=\frac{20}{\ln 2} \ln \left[\frac{50}{12.5}\right]$ $=\frac{20}{\ln 2} \ln 4=40 \,min$