Particle accelerators: The voltage across the dees of a cyclotron is 30,000 V. How many revolutions do the protons go through in reaching a kinetic energy of 21 MeV? (1 eV = 1.60 × 10^-19 J, e = 1.60 × 10^-19 C, m_proton = 1.67 × 10^-27 kg) A) 2.0 million B) 1400 C) 700 D) 350 E) 35

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Quizplus · Accepted Answer

Each time a proton completes a revolution in the cyclotron, it is accelerated by the voltage across the dees, gaining kinetic energy equal to the charge of the proton times the voltage (eV). To find the total number of revolutions to reach 21 MeV, divide the total desired kinetic energy (21 MeV) by the energy gained per revolution (30,000 V or 30 keV, since 1eV = 1.60 × 10^-19 J and the charge of a proton e = 1.60 × 10^-19 C). Thus, 21 MeV / 30 keV = 700,000 keV / 30 keV = 700 revolutions.

Particle Accelerators: the Voltage Across the Dees of a Cyclotron