Question

The intensity of gamma radiation from a given source is $I$. If on passing through $36mm$ of lead its intensity is reduced to $\frac{I}{8}$, then what will be the thickness of lead which reduces its intensity to $\frac{I}{2}$?

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

Answer 1

Answer: (C)

$12mm$

We have, $I=I_0{e}^{-\mu x}$
$\therefore \frac{1}{8}=e^{-4.36}$
$\Rightarrow {\left(\frac{1}{2}\right)}^3=e^{-4.36}=(e^{-\mu x}{)}^3$
or $-3\mu x=-36\mu$
$\Rightarrow x=12mm$.