Question

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

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

Answer 1

Answer: (B)

$\because I=I_0{e}^{-kx}\Rightarrow \frac{I}{I_0}=e^{-kx}$
$\therefore In\left(\frac{I}{I_0}\right)=-kx$
In first case
$\ln \left(\frac{1}{8}\right)=-k\times 36$
$\ln \left(2^{-3}\right)=-k\times 36$
or $3\ln =k\times 36\dots \dots \dots \left(i\right)$
In second case, $\ln \left(\frac{1}{2}=-k\times x\right)$
or $\ln \left(2^{-1}\right)=-kx$
or $\ln 2=kx\dots \dots \dots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$3\times \left(kx\right)=k\times 36$
or $x=12mm$.