The minimum wavelength, $\lambda_{\min}$, of X-rays produced by an electron can be determined using the equation derived from the energy of a photon and the energy given to an electron by an accelerating voltage, $V$.

The energy of a photon is given by $E = hc/\lambda$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the photon.

When an electron is accelerated through a potential difference of $V$ volts, it gains kinetic energy equal to $eV$, where $e$ is the electron charge.

This energy is then converted into a photon's energy when the electron collides with a target in an X-ray tube, resulting in X-rays of wavelength $\lambda$. Setting the kinetic energy equal to the photon energy gives $eV = hc/\lambda$. Solving for $\lambda$ gives $\lambda = hc/(eV)$.

Therefore, the minimum wavelength (corresponding to the maximum energy photon produced when all the kinetic energy is converted into photon energy) is inversely proportional to the voltage, $V$.

Thus, $$\lambda_{\min} \propto 1/V$$.