An electron is accelerated from rest through a potential difference V and strikes a target to produce continuous X-rays. If _ d is the de Broglie wavelength of the incident electron and _ min is the minimum wavelength of the emitted X-rays, then the ratio _ d _ min is proportional to:

Step-by-step solution

The de Broglie wavelength of an electron accelerated through a potential difference V is given by: _ d = h 2meV The minimum wavelength of the continuous X-rays produced is given by equating the maximum photon energy to the electron's kinetic energy: _ min = hc eV Taking the ratio of the two wavelengths: _ d _ min = h 2meV hc eV _ d _ min = h 2meV eV hc = 1 c eV 2m Since h , c , e , and m are constants, the ratio _ d _ min is directly proportional to V . Answer: V