Question

The intensity of gamma radiation from a given source is $I_0$. On passing through 37.5 mm of lead it is reduced to $I_0/8$. The thickness of lead which will reduce it to $I_0/2$ is

• A. ${\left(37.5\right)}^{1/3}mm$
• B. ${\left(37.5\right)}^{1/4}mm$
• C. $37.5/3mm$
• D. $\left(37.5/4\right)mm$

Answer 1

The correct option is C $37.5/3mm$

$I=I_0{e}^{-\mu x}$

$\frac{I_o}{8}=I_o{e}^{-\mu \times 37.5}$

$ln8=\mu \times 37.5$..........(I)

$\frac{I_o}{2}=I_o{e}^{-\mu x}$

$ln2=\mu \times x$ ..........(II)

divide (I) and (II)

we get $\frac{ln8}{ln2}=\frac{37.5}{x}$

$x=\frac{37.5}{3}mm$