Question

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

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

Answer 1

The correct option is D $12mm$

$\begin{array}{c}\text{Given - * on passing through}36mm\text{thick lead}\\ \text{Intensity reduces to}\frac{I}{8}\end{array}$

$\begin{array}{c}\text{We know}\\ \begin{array}{cc}I=[I_0\cdot e^{-\mu t}]& \text{where}t=\text{thickness}\\ \mu & =\text{material constt}\\ I& =\text{Intensity}\end{array}\end{array}$

$\begin{array}{c}\Rightarrow \text{for}36mm\text{lead}\to \frac{I_0}{8}=I_0{e}^{-\mu t}\Rightarrow e^{\mu t}=8\\ \Rightarrow \mu \times 36=\log 8\\ \mu =\frac{\log 2}{12}{cm}^{-1}\\ \Rightarrow \text{for}12\text{Intensity}\frac{I_0}{2}\to \frac{I_0}{2}=I_0{e}^{-\frac{\log 2}{12}\times t}\\ \Rightarrow \frac{t}{12}\times \log 2=\log 2\Rightarrow \text{Thickness}=12mm\end{array}$