A beam containing both 3He+^{3}\text{He}^{+}3He+ ions (mass 3.0 u3.0\text{ u}3.0 u, charge +e+e+e) and 4He2+^{4}\text{He}^{2+}4He2+ ions (alpha particles, mass 4.0 u4.0\text{ u}4.0 u, charge +2e+2e+2e) is accelerated from rest through a constant potential difference VVV.
The ions then enter a region of uniform magnetic field of flux density B B\,B directed perpendicular to their direction of motion, where they deflect into circular paths of radii r3r_{3}r3 and r4r_{4}r4 respectively, as shown in the diagram below.
What is the ratio r4r3\displaystyle \frac{r_{4}}{r_{3}}r3r4?
23\frac{2}{3}32
23\sqrt{\frac{2}{3}}32
32\sqrt{\frac{3}{2}}23
32\frac{3}{2}23