Question

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

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

Answer 1

The correct option is B

12 mm

$I^{\prime }=I{e}^{-\mu x}\Rightarrow x=\frac{1}{\mu }lo{g}_e\frac{I}{I^{\prime }}$ (where l= original intensity, I'= changed intensity)

$36=\frac{1}{\mu }lo{g}_e\frac{I}{\frac{I}{8}}=\frac{3}{\mu }lo{g}_{e}2$ ......(i)

$x=\frac{1}{\mu }lo{g}_e\frac{I}{\frac{I}{2}}=\frac{1}{\mu }lo{g}_{e}2$ ......(ii)

From equation (i) and (ii), x=12mm.