Final answer:
The kinetic energy of an electron with a given momentum can be calculated using the relativistic energy-momentum relation. By doing the math, we can find the electron's kinetic energy, which is expected to be about 150% of its rest mass energy since the electron is traveling near the speed of light.
Step-by-step explanation:
The question asks us to calculate the kinetic energy of an electron with a given momentum in giga-electron volts (GeV). To find this, we can use the relativistic energy-momentum relation which states that the total energy E squared is equal to the rest mass energy squared plus the momentum p squared times the speed of light c squared. Therefore, we have E^2 = (m_0 * c^2)^2 + (p * c)^2, where m_0 is the rest mass of the electron (0.511 MeV/c^2) and p is the momentum (5.25 × 10⁻¹⁸ kg*m/s). Subtracting the rest mass energy squared from both sides and taking the square root gives us the kinetic energy (KE) in MeV, which then can be converted into GeV (1 GeV = 1000 MeV).
It is also noted that the kinetic energy should be approximately 150% of the rest mass energy of the electron if it is traveling close to the speed of light.