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

Answer 1

The correct option is B $40minutes$

GIven : $T_{1/2}=20$ minutes

Time taken in $50$ % decay $t_1=T_{1/2}=20$ minutes

Time taken in $87.5$ % decay $t_2=3T_{1/2}=60$ minutes

Thus time interval between $50$ % and $87.5$ % decay $\Delta t=t_2-t_1$

$\therefore$ $\Delta t=60-20=40$ minutes