An electron with a kinetic energy of 2 MeV is produced in a betatron. Its momentum is approximately A) 8.2 × 10^-3 kg · m/s. B) 1.31 × 10^-27 kg · m/s. C) 7.63 × 10^-22kg · m/s. D) 1.31 × 10^-21 kg · m/s. E) 7.63 × 10^-25 kg · m/s.

Question

Quizplus · Accepted Answer

The momentum of the electron can be calculated using the relativistic momentum equation:
p = sqrt((2mE)^2 + (mc^2)^2) - mc^2
Where m is the mass of the electron, E is the kinetic energy (2 MeV = 2 x 10^6 eV), and c is the speed of light.

Plugging in the values, we get:
p = sqrt((2 * 9.10938356 x 10^-31 kg * 2 x 10^6 eV * 1.602176634 x 10^-19 J/eV)^2 + (9.10938356 x 10^-31 kg * (2.998 x 10^8 m/s)^2)^2) - 9.10938356 x 10^-31 kg * (2.998 x 10^8 m/s)^2
p = 1.31 x 10^-21 kg m/s

Therefore, the correct choice is D.

An Electron with a Kinetic Energy of 2 MeV Is