When X-rays from a Coolidge tube pass through | vedclass

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(B) The intensity of transmitted $X$-rays through a material is given by $I = I_0 e^{-\mu x}$,where $\mu$ is the linear absorption coefficient and $x$

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$> 50\%$

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(B) The intensity of transmitted $X$-rays through a material is given by $I = I_0 e^{-\mu x}$,where $\mu$ is the linear absorption coefficient and $x$ is the thickness of the material.The absorption coefficient $\mu$ depends on the wavelength $\lambda$ of the $X$-rays. Specifically,$\mu \propto \lambda^3$.When the potential difference $V$ between the target and the cathode is increased,the energy of the electrons increases,which leads to the emission of $X$-rays with shorter wavelengths (higher frequency).Since $\lambda$ decreases as $V$ increases,the absorption coefficient $\mu$ decreases $(\mu \propto \lambda^3)$.As $\mu$ decreases,the transmission $I/I_0 = e^{-\mu x}$ increases.Therefore,the fraction of $X$-rays transmitted through the same foil will be greater than $50\%$.

When $X$-rays from a Coolidge tube pass through an aluminum foil of thickness $0.3 \, mm$,$50\%$ of the $X$-rays are transmitted. If the potential difference between the target and the cathode is increased,the fraction of $X$-rays transmitted through the same foil will be .......

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