Final answer:
The potential difference across an X-ray tube for accelerating electrons could be 50 kV, 100 kV, 150 kV, or 200 kV. It is determined by the specific energy needs for electron acceleration or X-ray production. Without further context, it is not possible to select a definitive answer among the provided options.
Step-by-step explanation:
The question pertains to the potential differences used in devices like a tube in an X-ray machine or a Van de Graaff accelerator to accelerate electrons. In such devices, specific voltage levels are set to accelerate charged particles, including electrons, to high velocities. When an electron is accelerated through a potential difference, it gains energy equal to the charge of the electron times the potential difference. Therefore, an electron accelerated through a potential difference of 1 V is given an energy of 1 electron volt (eV).
In the case of an X-ray tube, the potential difference used for accelerating electrons to the anode can vary based on the application. For generating X-rays, potential differences of 50 kV (50,000 V) and above are common. A 100-kV potential difference, for instance, gives an electron an energy of 100 keV. The option of adjustable voltages in X-ray tubes allows for the production of X-rays with varying energies, affecting their ability to penetrate different materials.
Given these points, the potential difference maintained across the tube can be either 50 kV, 100 kV, 150 kV, or 200 kV, but without additional context stating the specific requirements of the electron acceleration or X-ray production in question, it is not possible to definitively select one of the provided options a, b, c, or d as the correct answer.