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(A) The minimum accelerating voltage $V$ required to produce $X$-rays of a given wavelength $\lambda$ is determined by the Duane-Hunt law,where the ki

Vedclass · Accepted Answer

$8280$

Vedclass · Answer

(A) The minimum accelerating voltage $V$ required to produce $X$-rays of a given wavelength $\lambda$ is determined by the Duane-Hunt law,where the kinetic energy of the electron is converted into the energy of the photon: $eV = \frac{hc}{\lambda}$.Given:$h = 6.63 	imes 10^{-34} \ 	ext{J}\cdot	ext{s}$$c = 3 	imes 10^8 \ 	ext{m/s}$$\lambda = 1.50 \ \mathring{A} = 1.50 	imes 10^{-10} \ 	ext{m}$$e = 1.6 	imes 10^{-19} \ 	ext{C}$Substituting the values:$V = \frac{hc}{e\lambda} = \frac{6.63 	imes 10^{-34} 	imes 3 	imes 10^8}{1.6 	imes 10^{-19} 	imes 1.50 	imes 10^{-10}}$$V = \frac{19.89 	imes 10^{-26}}{2.4 	imes 10^{-29}}$$V = 8.2875 	imes 10^3 \ 	ext{V} \approx 8280 \ 	ext{V}$.

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