Rutherford backscattering spectrometry (RBS) is a technique used to determine the structure and composition of materials. A beam of ions (typically helium ions) is accelerated to high energy and aimed at a sample. By analyzing the distribution and energy of the ions that are scattered from (that is, deflected by collisions with) the atoms in the sample, researchers can determine the sample's composition. To accelerate the ions to high energies, a tandem electrostatic accelerator may be used. In this device, negative ions (HeHe) start at a potential VV = 0 and are accelerated by a high positive voltage at the midpoint of the accelerator. The high voltage produces a constant electric field in the acceleration tube through which the ions move. When accelerated ions reach the midpoint, the electrons are stripped off, turning the negative ions into doubly positively charged ions (He++He++). These positive ions are then repelled from the midpoint by the high positive voltage there and continue to accelerate to the far end of the accelerator, where again VV = 0.

For a particular experiment, helium ions are to be given a kinetic energy of 4.2 MeV . What should the voltage at the center of the accelerator be, assuming that the ions start essentially at rest? 4.2 MV + 4.2 MV + 2.1 MV + 1.4 MV