Total energy: A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, m_proton = 1.67 × 10^-27 kg) A) 2.51 × 10^-19 kg ∙ m/s B) 2.89 × 10^-19 kg ∙ m/s C) 4.34 × 10^-19 kg ∙ m/s D) 5.01 × 10^-19 kg ∙ m/s E) 8.68 × 10^-19 kg ∙ m/s

Question

Quizplus · Accepted Answer

When the kinetic energy equals the rest energy, the total energy is twice the rest energy. Using the relativistic energy-momentum relation, the momentum p = sqrt((E/c)^2 - (m_0c)^2), where E = 2m_0c^2. Solving gives p = sqrt(3)m_0c, which calculates to approximately 8.68 × 10^-19 kg∙m/s.

Total Energy: a Proton in a Certain Particle Accelerator Has