Final answer:
For an electron with a kinetic energy of 0.100 MeV, the classical speed would be 2.15× 10⁸ m/s, while the relativistic speed would be 1.19× 10⁸ m/s, indicating option (b) is correct. Relativistic effects make the speed lower than the classical calculation when the kinetic energy is a significant fraction of the rest mass energy.
Step-by-step explanation:
To find the speed of an electron with a kinetic energy of 0.100 MeV, we need to consider both classical and relativistic mechanics. In classical mechanics, kinetic energy (KE) is given by the formula KE = 1/2 mv², where m is the mass of the electron and v is its velocity. The mass of an electron is 9.11 × 10⁻³¹ kg. Using this formula and converting the kinetic energy into joules (1 eV = 1.602 × 10⁻¹⁹ Joules), we can solve for v to find the classical speed of the electron. However, this approach does not take into account relativistic effects, which are significant for velocities close to the speed of light (c). In relativistic mechanics, the kinetic energy is given by KE = (γ - 1)mc², where γ is the relativistic factor. For an electron with a kinetic energy that is approximately 150% of the rest mass energy (0.511 MeV), it should be travelling close to the speed of light. Given these considerations, the correct speeds for an electron with 0.100 MeV kinetic energy would be lower in relativistic mechanics, indicating option (b) as the correct answer, with the classical speed being 2.15× 10⁸ m/s and the relativistic speed being 1.19× 10⁸ m/s.