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

Answer 1

Answer: (B)

$I^{\prime }=I{e}^{-\mu x}\Rightarrow x=\frac{1}{\mu }{\log }_e\frac{I}{I^{\prime }}$
(where $I=$ original intensity, $I^{\prime }=$ changed intensity)
$36=\frac{1}{\mu }{\log }_e\frac{I}{I/8}=\frac{3}{\mu }{\log }_{e}2$ ...(i)
$x=\frac{1}{\mu }{\log }_e\frac{I}{I/2}=\frac{1}{\mu }{\log }_{e}2$ ...(ii)
From equations (i) and (ii),
$x=12mm$