If the potential difference applied to an X-ray tube is doubled while keeping the separation between the filament and the target as same, what will happen to the cutoff wavelength ?

The cutoff wavelength (λ_min) of X-rays produced in a tube is governed by the Duane–Hunt law, which establishes an inverse proportionality between the minimum wavelength and the applied accelerating potential (V). According to the formula λ_min = hc / eV, where h is Planck's constant, c is the speed of light, and e is the charge of an electron, the minimum wavelength is inversely proportional to the tube voltage. This occurs because the maximum energy an X-ray photon can possess is equal to the kinetic energy of the accelerated electron (E_max = eV). When the potential difference (V) is doubled, the energy of the electrons doubles, which causes the minimum or cutoff wavelength to be reduced by half. The separation between the filament and target does not affect this fundamental quantum limit.