Question

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

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

Answer 1

The correct option is B $12mm$

Given : Intensity of the gamma radiation from the source $I_o=l$

Intensity $I=I_o{e}^{-\mu x}$ where $x$ is the thickness of lead

Now for $x=36mm$ , intensity becomes $I=\frac{l}{8}$

$\therefore$ $\frac{l}{8}=l$ $e^{-\mu \times 36}$ ($lo{g}_{e}1/8=-2.079$)

$⟹$ $\mu =0.0578$

Now let the thickness of lead be $x$ so that the intensity becomes $I=\frac{l}{2}$

$\therefore$ $\frac{l}{2}=l$ $e^{-0.0578\times x}$ ($lo{g}_{e}1/2=-0.693$)

$-0.693=-0.0578x$ $⟹x=12$ $mm$