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Suppose we want to accelerate a proton (charge = +1.6×10⁻¹⁹ C, mass = 1.67×10⁻²⁷ kg) in a cyclotron with a magnetic field of 0.5 T and a voltage difference of 10 kV between the dees. How much kinetic energy will the proton have after it has crossed the gap 5 times? Step 1: Calculate the energy gained per crossing. Energy per crossing = q × V = (1.6×10⁻¹⁹ C) × (10,000 V) = 1.6×10⁻¹⁵ J. Step 2: Multiply by the number of crossings. Total kinetic energy = 5 × 1.6×10⁻¹⁵ J = 8.0×10⁻¹⁵ J. Step 3: Convert to electron‑volts (1 eV = 1.6×10⁻¹⁹ J). Kinetic energy (eV) = (8.0×10⁻¹⁵ J) / (1.6×10⁻¹⁹ J/eV) = 5.0×10⁴ eV = 50 keV. So after 5 crossings the proton has 50 keV of kinetic energy.