Find the speed of an electron that has a kinetic energy of 10 MeV .

Step-by-step solution

The rest mass energy of an electron is E₀ = m₀ c^2 = 0.511 MeV . The kinetic energy is K = 10 MeV . The total energy of the electron is given by E = K + E₀ = 10 + 0.511 = 10.511 MeV . Using the relativistic energy relation E = m₀ c^2 1 - v^2 c^2 , we get: 10.511 = 0.511 1 - v^2 c^2 1 - v^2 c^2 = 0.511 10.511 0.0486 Squaring both sides: 1 - v^2 c^2 (0.0486)^2 0.00236 v^2 c^2 1 - 0.00236 = 0.99764 v c 0.99764 0.9988 Taking c = 3 10^8 m s ⁻¹ : v 0.9988 3 10^8 m s ⁻¹ = 2.996 10^8 m s ⁻¹