91Ó°ÊÓ

$\mathit{E}\mathbf{=}\mathit{h}\mathit{f}\mathbf{=}\frac{\mathbf{h}\mathbf{c}}{\mathbf{λ}}$

When the photon is accelerated through the potential , it gains kinetic energy equals

$\mathit{K}\mathbf{=}\mathit{e}\mathit{V}\mathbf{=}\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{*}{\mathbf{10}}^{\mathbf{-}\mathbf{19}}\mathbf{C}\mathbf{)}\mathbf{(}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{*}{\mathbf{10}}^{\mathbf{3}}\mathit{V}\mathbf{)}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{40}\mathbf{*}{\mathbf{10}}^{\mathbf{-}\mathbf{16}}\mathit{J}$

The most energetic photon is produced if the photons is braked to a stop, so that all its kinetic energy goes to produce one photon.

Plug the values in equation (1),

$$\begin{gathered} \mathbf{6}\mathbf{.}\mathbf{40}\mathbf{*}{\mathbf{10}}^{\mathbf{-}\mathbf{16}}\mathit{J}\mathbf{=}\frac{\left(6.626*Js\right)\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{*}{\mathbf{10}}^{\mathbf{8}}\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{)}}{\mathbf{λ}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{⇒}\mathit{λ}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{11}\mathbf{*}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathit{m}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{311}\mathit{n}\mathit{m} \end{gathered}$$

Thus, the minimum wavelength of the resulting x rays is 0.311nm. The wavelength of the resulting photon is the same in both cases since both the electrons and protons have the same kinetic energy. X-ray tubes use electrons rather than protons to produce x-rays because it is easier to accelerate electrons than protons.