Question

The half life of a radioactive substance is 30 minutes. The time taken between 40% decay and 85% decay of the same radioactive substance in minutes is:

• A. 60
• B. 15
• C. 30
• D. 45

Answer 1

The correct option is A 60

$t_{1/2}=30min$
$N_1=N_0{\left(\frac{1}{2}\right)}^{\frac{T_1}{30}}{N}_2=N_0{\left(\frac{1}{2}\right)}^{\frac{T_2}{30}}$
$N_1=100-40=60$
$N_1$ = Atom remains undecay
$N_2$ = 100-85
$N_2$ = Atom remains undecay
$60=N_0{\left(\frac{1}{2}\right)}^{\frac{T_1}{30}}$ $\cdots \left(1\right)$
$15=N_0{\left(\frac{1}{2}\right)}^{\frac{T_1}{30}}$ $\cdots \left(2\right)$
By (1) and (2)
$4={\left(\frac{1}{2}\right)}^{\frac{T_1-T_2}{30}}$
$4=2^{-\frac{(T_1-t_2)}{30}}$
$(2{)}^2=(2{)}^{\frac{30}{T_1-T_2}}$
$2=\frac{T_1-T_2}{30}$
$T_2-T_1=60min$