Question

When X-rays of wavelength $0.5\mathring{A}$ would be trasmitted by an aluminium tube of thickness 7 mm, its intensity remains one-fourth. The attenuation coefficient of aluminium for these X-rays is

• A. $0.188m{m}^{-1}$
• B. $0.189m{m}^{-1}$
• C. $0.198m{m}^{-1}$
• D. None of these

Answer 1

The correct option is C $0.198m{m}^{-1}$

The coefficient of attenuation $\mu$ is related with the initial intensity $I_0$ of ray and final intensity (after crossing the material) $I$ by the following relation.

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

or $e^{\mu x}=I_0/I$

or $\mu x=2.303lo{g}_{10}\left(I_0/I\right)$

or $\mu =\left[2.303lo{g}_{10}\right(I_0/I\left)\right]/x$

where $x=$ thickness of material.

Given - $x=7mm,I=I_0/4$

by using above relation

or $\mu =\frac{2.303lo{g}_{10}\left(4I_0/I_0\right)}{7}$

or $\mu =\frac{2.302\times 0.6020}{7}=0.198m{m}^{-1}$