If an electron (rest mass = 0.511 MeV/c²)has a speed of 99% of that of light,what is its total energy? A)0.511 MeV B)0.750 MeV C)3.62 MeV D)7.33 MeV E)19.2 MeV

Question

Quizplus · Accepted Answer

When an object moves at a speed close to the speed of light, we cannot use classical mechanics to calculate its energy. Instead, we need to use relativistic mechanics. The formula to calculate the total energy of a particle with mass m and speed v is:
E = (gamma) * mc^2
where gamma is the Lorentz factor, given by:
gamma = 1 / sqrt(1 - v^2/c^2)

In this problem, we have:
m = 0.511 MeV/c^2 (rest mass of electron)
v = 0.99c (99% of the speed of light)

Using the above formulas, we get:
gamma = 1 / sqrt(1 - 0.99^2) = 7.09
E = gamma * mc^2 = 7.09 * 0.511 MeV = 3.62 MeV

Therefore, the best choice is C.

If an Electron (Rest Mass = 0