The total energy of a moving electron is 0.758 MeV.What is the speed of the electron in terms of c?
A)0.739 c
B)0.794 c
C)0.306 c
D)0.933 c

Question

Quizplus · Accepted Answer

The total energy of a moving electron is given by:E = sqrt((pc)^2 + (mc^2)^2)where:E is the total energyp is the momentumc is the speed of lightm is the mass of the electronWe can rearrange this equation to solve for the speed:v = p/Ewhere:v is the speedWe can find the momentum using the de Broglie relation:p = h/lambdawhere:h is Planck's constantlambda is the wavelengthWe can find the wavelength using the energy of the electron:lambda = hc/Ewhere:h is Planck's constantc is the speed of lightE is the energySubstituting these equations into the equation for speed, we get:v = hc/E * E/sqrt((hc/lambda)^2 + (mc^2)^2)Simplifying, we get:v = c * sqrt(1 - (lambda/lambda_c)^2)where:lambda_c is the Compton wavelength of the electronSubstituting the given values, we get:v = c * sqrt(1 - (1.24 * 10^-12 m / 2.43 * 10^-12 m)^2)v = 0.739 cTherefore, the speed of the electron is 0.739 c.

The Total Energy of a Moving Electron Is 0