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

Vedclass · Accepted Answer

$200$

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(D) The intensity of $X$-rays after 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 the intensity decreases to $36.8\%$ of its initial value,we have $\frac{I}{I_0} = 36.8\% = 0.368$.Since $e^{-1} \approx 0.368$,we can write $e^{-\mu x} = e^{-1}$.Comparing the exponents,we get $\mu x = 1$.Given $x = 5 	imes 10^{-3} \ m$,we have $\mu = \frac{1}{x} = \frac{1}{5 	imes 10^{-3} \ m}$.$\mu = \frac{1000}{5} \ m^{-1} = 200 \ m^{-1}$.

After passing through a gold film of thickness $5 \times 10^{-3} \ m$,the intensity of an $X$-ray beam decreases to $36.8\%$ of its initial intensity. The absorption coefficient is ....... $m^{-1}$.

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