Question

A radioactive sample contains two different types of radioactive nuclei : A with half-life 5 days and B-with half-life 30 days. Initially the decay rate of the A-type nuclie is 64 times that of B-type nuclei. Find the time after which their decay rates will be equal.

• A. 18 days
• B. 60 days
• C. 9 days
• D. 36 days

Answer 1

The correct option is D 36 days

At t = 0, activities are $A_{01}\&A_{02}$ respectively.

At t = t, activities become equal.

$A_1=A_2$

$A_{01}{e}^{-{\lambda }_{1}t}=A_{02}{e}^{-{\lambda }_{2}t}$

$64=e^{(}{\lambda }_1-{\lambda }_2)t\because A_{01}=16A_{02}$

$6ln2=ln2[\frac{1}{T_1}-\frac{1}{T_2}]t$

$6=[\frac{1}{5}-\frac{1}{30}]t\Rightarrow$ t=36 days