Calculating Velocities, Momenta, and Kinetic Energies of Electrons
What are the respective velocities, momenta, and kinetic energies of two oppositely travelling beams of electrons with total energies of 0.851667 MeV and 0.63875 MeV each, as observed in the lab? What is the relative speed of an electron in the inertial reference system another electron?
What are the respective velocities, momenta, and kinetic energies of the electrons?
What is the relative speed of an electron in the inertial reference system of another electron?
Answer:
The kinetic energies of the electrons can be calculated by subtracting the rest mass energy of an electron (0.511 MeV) from their total energies. As these energies are close to the rest energy, the electrons are probably relativistic and calculations of velocities and momenta will need to involve formulas from relativity.
Explanation:
The calculation of the velocities, momenta, and kinetic energies of the two electrons depends on the formulas of basic physics involving energy and velocity. To calculate these values for the electrons, we take into consideration their total energy, which in the context of particle physics, means their kinetic energy plus their rest mass energy. The rest mass energy of an electron is constant and has a value of 0.511 MeV.
For the first electron with a total energy of 0.851667 MeV, the kinetic energy can be calculated by subtracting the rest mass energy from the total energy, and is approximately 0.340667 MeV. For the second electron with a total energy of 0.63875 MeV, the kinetic energy is approximately 0.12775 MeV, calculated in the same way.
The velocities and momenta of the electrons could be calculated using the formulas commonly known in physics for non-relativistic particles, but as the energies of these electrons are very close to their rest mass energies, the velocities are close to the speed of light and the electrons are therefore relativistic. This means we would need to use the formulas involving relativistic momentum and energy to calculate these correctly.