Question

The rate of disintegration of a radioactive substance falls from $800dpm$ to $100dpm$ in $6$ hours. The half-life of the radioactive substance is

• A. $6/7hrs$
• B. $2hrs$
• C. $3hrs$
• D. $1hr$

Answer 1

Answer: (B)

$2hrs$

$A=A_0{e}^{-\lambda t}$
$\Rightarrow 100=800e^{-\lambda (6\times 60)}$

$\Rightarrow e^{-360\lambda }=\frac{1}{8}$
$\Rightarrow -360\lambda =ln\frac{1}{8}=-In8\Rightarrow \lambda =\frac{ln{2}^3}{360}=$$\frac{ln2}{120}$

$\therefore T_{1/2}=\frac{ln2}{\lambda }=\frac{ln2}{\left(ln2/120\right)}=120$ min.

$T_{1/2}=2$ hrs