Question

The intensity of gamma radiation from a given source is $I.$ On passing through $36mm$ of lead, it is reduced to $1/8.$The thickness of lead, which will reduce the intensity to $1/2$ will be:

• A. $6mm$
• B. $9mm$
• C. $18mm$
• D. $12mm$

Answer 1

The correct option is D $12mm$

$I=I_0{e}^{-\mu d}\text{where "d" is thickness of lead}$

$\begin{array}{cc}\frac{I}{I_0}& =e^{-\mu d}\\ & e^{\mu d}=\frac{I_0}{I}\\ \mu d& =\ln \left(\frac{I_0}{I}\right)\end{array}$

$\begin{array}{c}\text{when}d=36,I=I_0/8\\ \mu 36=\ln \left(\frac{I_0}{I_0/8}\right)=\ln \left(8\right)--\left(1\right)\\ \text{for}I=I_0/2\text{; lead thickness bed}\\ \mu d=\ln \left(2\right)--\left(2\right)\\ \text{(1)/(2)}\Rightarrow \frac{36}{d}=3\Rightarrow d=12mm\end{array}$