Physics - EM Waves Question with Solution | TestHub

On passing through lead, the intensity of $\gamma$ - radiation decreases exponentially with the thickness traversed and is given by

$I=I_0{e}^{-\mu x}$ , where $\mu$ is the absorption coefficient of the lead.

In the first case, when $x=36 \mathrm{mm}$, $I=\frac{I_0}{8}$

 $\frac{I_0}{8}=I_0 e^{-\mu \times 36}$

$\Rightarrow {\log }_{e}8=36\mu$

In the second case,

$I=\frac{I_0}{2}$

Let $x$ be the thickness of the lead sheet, then

$\frac{I_0}{2}=I_0 e^{-\mu x}$

${\log }_{e}2=\mu x$

$\frac{\mu x}{36\mu }=\frac{{\log }_{e}2}{{\log }_{e}8}$

$x=36\times \frac{{\log }_{e}2}{{\log }_e{2}^3}=36\times \frac{{\log }_{e}2}{3{\log }_{e}2}$

$x=12\mathrm{ }\mathrm{mm}$