When X-rays of wavelength 0.5 , Å pass throug | vedclass

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(D) The intensity of $X$-rays passing through a material is given by the formula $I = I_0 e^{-\mu x}$, where $I$ is the final intensity, $I_0$ is the

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$0.179$

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(D) The intensity of $X$-rays passing through a material is given by the formula $I = I_0 e^{-\mu x}$, where $I$ is the final intensity, $I_0$ is the initial intensity, $\mu$ is the absorption coefficient, and $x$ is the thickness of the material.Given that $I = \frac{I_0}{6}$ and $x = 10 \, mm$.Substituting these values: $\frac{I_0}{6} = I_0 e^{-\mu (10)}$.Taking the natural logarithm on both sides: $\ln(6) = \mu 	imes 10$.$\mu = \frac{\ln(6)}{10} = \frac{1.7917}{10} = 0.17917 \, mm^{-1}$.Rounding to three decimal places, we get $\mu = 0.179 \, mm^{-1}$.

When $X$-rays of wavelength $0.5 \, Å$ pass through an $Al$ sheet of thickness $10 \, mm$, their intensity is reduced to one-sixth of its initial value. The absorption coefficient for aluminum is ............. $mm^{-1}$.

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