An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of 6.64 × 10-27 kg. A horizontal beam of alpha particles is injected with a speed of 1.3 × 105 m/s into a region with a vertical magnetic field of magnitude 0.155 T.

(a) How much time does it take for an alpha particle to move halfway through a complete circle?

(b) If the speed of the alpha particle is doubled, does the time found in part (a) increase, decrease, or stay the same? Explain.

(c) Repeat part (a) for alpha particles with a speed of 2.6 × 105 m/s.