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Question

(B) When an $X$-ray beam passes through a material of thickness $dx$,the decrease in intensity $dI$ is proportional to the intensity $I$ and the thick

Vedclass · Accepted Answer

$I = I_0e^{-\mu d}$

Vedclass · Answer

(B) When an $X$-ray beam passes through a material of thickness $dx$,the decrease in intensity $dI$ is proportional to the intensity $I$ and the thickness $dx$.This is given by the differential equation: $-dI = \mu I dx$.Rearranging the terms,we get: $\frac{dI}{I} = -\mu dx$.Integrating both sides from $x = 0$ (where $I = I_0$) to $x = d$ (where $I = I$):$\int_{I_0}^{I} \frac{dI}{I} = -\int_{0}^{d} \mu dx$.This results in: $\ln(\frac{I}{I_0}) = -\mu d$.Taking the exponential of both sides,we get: $I = I_0e^{-\mu d}$.

$X$-ray beam of intensity $I_0$ passes through an absorption plate of thickness $d$. If the absorption coefficient of the material of the plate is $\mu$,the correct statement regarding the transmitted intensity $I$ of the $X$-ray is:

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