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(D) The minimum wavelength $(\lambda_{\min})$ of $X$-rays produced in an $X$-ray tube is given by the Duane-Hunt law,where the entire kinetic energy o

Vedclass · Accepted Answer

$\frac{12400}{V} \; \mathring{A}$

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(D) The minimum wavelength $(\lambda_{\min})$ of $X$-rays produced in an $X$-ray tube is given by the Duane-Hunt law,where the entire kinetic energy of the electron is converted into a photon of maximum frequency: $E = eV = \frac{hc}{\lambda_{\min}}$ Therefore,$\lambda_{\min} = \frac{hc}{eV}$. Substituting the values of Planck's constant $(h = 6.626 	imes 10^{-34} \; J \cdot s)$,speed of light $(c = 3 	imes 10^8 \; m/s)$,and charge of an electron $(e = 1.6 	imes 10^{-19} \; C)$: $\lambda_{\min} = \frac{6.626 	imes 10^{-34} 	imes 3 	imes 10^8}{1.6 	imes 10^{-19} 	imes V} \; m$ $\lambda_{\min} \approx \frac{12400}{V} \; \mathring{A}$.

If the potential difference applied across an $X$-ray tube is $V$ volts,then the approximate minimum wavelength of the emitted $X$-rays will be:

Similar Questions

The shortest wavelength emitted from an $X$-ray tube depends on which of the following?

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Which of the following wavelengths falls in the $X-$ray region in $\mathring{A}$?

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