Question

The activity of a radioactive material is $A_0/32$, If its halflife is 2 hours :-

• A. 10 Hr
• B. 30 Hr
• C. 20 Hr
• D. 16 Hr

Answer 1

Answer: (D)

16 Hr

Given,

$A=\frac{A_0}{32}$

$t_{1/2}=2hr$

The activity of a radioactive material,

$A=A_0{e}^{-\lambda t}=\frac{A_0}{32}$

$\lambda t=8ln\left(2\right)$

$t=\frac{8ln\left(2\right)}{\lambda }$. . . . .(1)

The half-life of the material,

$t_{1/2}=\frac{ln\left(2\right)}{\lambda }=2hr$

$\lambda =\frac{ln\left(2\right)}{2}$

Substitute in equation (1), we get

$t=\frac{8ln\left(2\right)}{ln\left(2\right)}\times 2$

$t=16hr$