Final answer:
The speed of an electron whose kinetic energy is 50% of its rest mass energy is close to the speed of light. The rest mass energy of an electron is 0.511 MeV, so the corresponding speed for the electron is approximately 0.914c, which is answer option (a).
Step-by-step explanation:
If the kinetic energy of an electron is 50% of its rest mass energy, we can calculate the speed of the electron. The rest mass energy of an electron is given as 0.511 MeV. This means that the kinetic energy is 0.511 MeV / 2 = 0.2555 MeV. To find the velocity of the electron, we would use the relativistic energy-momentum relation:
E^2 = (pc)^2 + (m0c^2)^2
where E is the total energy (rest mass energy plus kinetic energy), p is the momentum, c is the speed of light, and m0 is the rest mass. For this problem, it is known that E = 1.5m0c^2 and kinetic energy equals 0.5m0c^2.
When we do the calculations (which would involve a bit of algebra and knowledge of relativistic formulas), the velocity v of the electron when its kinetic energy is 50% of its rest mass energy is found to be close to the speed of light, which in this case corresponds to answer option (a) 0.914c.