The intensity of γ - radiation from a given source is I . On...

On passing through lead, the intensity of $\gamma$ - radiation decreases exponentially with the thickness traversed and is given by$</p><p>$I = {I}_{0}e^{- \mux}$, where$\mu$is the absorption coefficient of the lead.$

In the first case, when $x = 36mm$, $I = \dfrac{{I}_{0}}{8}$

$\dfrac{I0}{8} = {I}_{0}e^{- \mu \times 36}$

$⇒ \log_{\mathrm{e}}8 = 36\mu$

In the second case,$</p><p>$I = $\dfrac{I0}{2}</p><p>Let$x$be the thickness of the lead sheet, then$

$\dfrac{{I}_{0}}{2} = {I}_{0}e^{- \mux}$

$\log_{\mathrm{e}} 2 = \mux$

$\dfrac{\mux}{36\mu} = \dfrac{\log_{\mathrm{e}}2}{\log_{\mathrm{e}}8}$

$x = 36 \times \dfrac{\log_{\mathrm{e}} 2}{\log_{\mathrm{e}} {2}^{3}} = 36 \times \dfrac{\log_{\mathrm{e}} 2}{3\log_{\mathrm{e}} 2}$

$x = 12mm$