Problem

The key insight is that kinetic energy gained equals the work done by the electric field: $qV_{\text{acc}} = \frac{1}{2}mv^2$. Since each particle has charge proportional to its proton number and mass proportional to its mass number, you can rearrange to find $v \propto \sqrt{\frac{q}{m}}$ for each particle. Calculate this ratio for a proton, deuteron, and alpha particle using their actual charges and masses, then compare.

The key insight is that kinetic energy gained equals the work done by the electric field: $qV_{\text{acc}} = \frac{1}{2}mv^2$. Since each particle has charge proportional to its proton number and mass proportional to its mass number, you can rearrange to find $v \propto \sqrt{\frac{q}{m}}$ for each particle. Calculate this ratio for a proton, deuteron, and alpha particle using their actual charges and masses, then compare.