An electron is limited to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is the upper limit? If not, explain.
Yes, the fact that an electron cannot travel faster than the speed of light (c) puts an upper limit on its momentum. This limit is known as the relativistic momentum limit and it is given by:
p = γmv
where:
p = relativistic momentum
γ = Lorentz factor (1/√(1-v^2/c^2))
m = rest mass of the electron
v = velocity of the electron
As v approaches c, the Lorentz factor approaches infinity and the relativistic momentum becomes unbounded. However, since the electron cannot travel faster than c, its relativistic momentum is always finite. The maximum value of the relativistic momentum is given by:
p_max = γ_max m c
where γ_max is the Lorentz factor at v=c, which is infinite. Therefore, the upper limit on the momentum of an electron is given by:
p_max = ∞
This means that there is no absolute upper limit on the momentum of an electron, but the maximum momentum that can be achieved is always finite due to the finite speed of light.