Question

The intensity of gamma radiation from a given source is $I$ on passing through $36\text{mm}$ 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. $6\text{mm}$
• B. $9\text{mm}$
• C. $18\text{mm}$
• D. $12\text{mm}$

Answer 1

The correct option is D $12\text{mm}$

Given,

For, thickness $36\text{mm}\to \frac{I}{8}{x}^{{}^{\prime }}\text{mm}\to \frac{I}{2}$

Intensity attenuation is given by,

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

$\Rightarrow -\mu x=\ln \frac{I^{\prime }}{I}$

$\Rightarrow -\mu \times 36=\ln \frac{I}{8I}.........\left(1\right)$

$\Rightarrow -\mu x^{{}^{\prime }}=\ln \frac{I}{2I}.......\left(2\right)$

From (1) and (2)

$\frac{36}{x^{{}^{\prime }}}=\frac{3\ln \left(\frac{1}{2}\right)}{\ln \frac{1}{2}}$

$\therefore x^{\prime }=12\text{mm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.