Hydrogen has three isotopes ¹H (m₁ = m_p), ²H (m₂ ≌ 2m_p), and ³H (m_s ≌ 3m_p), where m_p is the mass of a proton (1.67 × 10^–27 kg). You and your team are tasked with constructing an isotope separator that will separate a gas of mixed hydrogen isotopes. The gas first passes through a device that atomizes it (i.e., makes sure the atoms are separate, and do not form H₂ molecules), and then ionizes the atoms (strips off their only electron) so that they have a net charge of +e. Next, the atoms (now positive ions) are accelerated between the plates of a parallel-plate capacitor with a voltage of 2.5 kV across it, and emerge through a hole in one of the plates as a beam. 

(a) What are the speeds of the three isotopes when they emerge from the capacitor plates?

(b) The accelerated ions enter a region of uniform magnetic field oriented perpendicular to the velocity vector of the ion beam. What should be the magnitude of the magnetic field if you want the largest diameter of the three ion paths to be 20.0 cm?

(c) If you are collecting the atoms after completing a half-circle, one collector should be located 20.0 cm from the point where the beam enters the magnetic field. Where should the other two be located?