A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy.What is the TOTAL energy 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) 5.69 × 10^-11 J B) 1.50 × 10^-10 J C) 2.07 × 10^-10 J D) 3.01 × 10^-10 J E) 8.77 × 10^-10 J

Question

Quizplus · Accepted Answer

The total energy of a particle is given by the equation E = sqrt((pc)^2 + (mc^2)^2), where p is the momentum of the particle, m is the mass of the particle, and c is the speed of light. In this case, the kinetic energy of the proton is equal to its rest energy, so we have:1/2 mv^2 = mc^2Solving for v, we get:v = cSubstituting this into the equation for total energy, we get:E = sqrt((pc)^2 + (mc^2)^2)= sqrt((mc)^2 + (mc^2)^2)= sqrt(2) mc^2= 2.07 × 10^-10 J

A Proton in a Certain Particle Accelerator Has a Kinetic