Answer
$3.10\times 10^{-10}m$.
Work Step by Step
The accelerating voltage gives 4.00 keV of kinetic energy to the protons, which then produce the x ray photons.
$$eV=\frac{hc}{\lambda}$$
$$\lambda =\frac{hc}{ eV}=
\frac{(4.136\times10^{-15}eV \cdot s)(3.00\times10^8 m/s)}{(4000eV)}=3.10\times 10^{-10}m$$
If electrons were used instead, the answer would be the same.
X-ray tubes use electrons rather than protons because electrons are easier to extract from atoms than are protons.
