Question

The masses of the neutrinos are still not precisely determined. Let us assume that the mass of an electron neutrino is one millionth the mass of an electron. What is the kinetic energy, in eV, of an electron neutrino moving at 0.951c?

A. 0.5 eV
B. 1.0 eV
C. 2.0 eV
D. 3.0 eV

Answer 1

The kinetic energy of an electron neutrino moving at 0.951c is approximately 2.910 MeV.

Step-by-step explanation:

To calculate the kinetic energy of an electron neutrino moving at 0.951c, we need to use the relativistic equation for kinetic energy:

Kinetic Energy (KE) = (gamma - 1) * rest mass energy

Where gamma is the Lorentz factor given by gamma = 1 / sqrt(1 - (v/c)^2), and c is the speed of light.

Given the rest mass energy of an electron is 0.511 MeV, the Lorentz factor gamma for the neutrino can be calculated using its speed:

gamma = 1 / sqrt(1 - (0.951c/c)^2) = 1 / sqrt(1 - 0.9048) = 1 / 0.2935 ≈ 3.4107

Substituting the values into the formula, we get:

KE = (3.4107 - 1) * 0.511 MeV = 2.910 MeV (approximately)

Therefore, the kinetic energy of the electron neutrino is approximately 2.910 MeV.