Question

The intensity of gamma radiation from a given source is $I$. On passing through $36\, mm$ 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
$\ln\left(\frac{1}{8}\right)=-k\times36$
$\ln \left(2^{-3} \right) = - k \times 36$
or $3\ln= k \times 36 \ldots\ldots\ldots\left(i\right)$
In second case, $\ln\left(\frac{1}{2}=-k\times x\right)$
or $\ln\left(2^{-1} \right) = - kx$
or $\ln2 = kx \ldots\ldots\ldots\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$3 \times \left(kx\right) = k \times 36$
or $x = 12\, mm$.