Final answer:
To calculate the group velocity and de Broglie wavelength of an electron with kinetic energy 500 KeV in vacuum, you can use equations involving velocity, kinetic energy, mass, speed of light, Planck's constant, and momentum.
Step-by-step explanation:
The group velocity of an electron can be calculated using the equation:
Vg = v(1 + (2KE/m0c2))
where v is the velocity of the electron, KE is the kinetic energy, m0 is the rest mass of the electron, and c is the speed of light. In this case, the velocity is close to the speed of light, so we can assume v ≈ c.
Therefore, Vg ≈ c(1 + (2KE/m0c2)).
The de Broglie wavelength of an electron can be calculated using the equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum. The momentum can be calculated using the equation:
p = mv
where m is the mass of the electron and v is the velocity.
Using the given values, we can calculate the group velocity and de Broglie wavelength of the electron.