Final answer:
For an electron moving near the speed of light, relativistic mechanics is used to calculate kinetic energy, momentum, and total energy. Photon momentum is calculated using Planck's equation, and comparing energies of electrons and photons involves considering their wave-particle duality and relativistic effects.
Step-by-step explanation:
When calculating the momentum, kinetic energy, and total energy of an electron moving at a high velocity such as 0.990c (where c is the speed of light), it is important to use relativistic mechanics, as classical mechanics does not provide accurate results at such speeds. The mass of an electron is 9.11×10−7 kg, and the speed given is 0.990c. When dealing with photons, we often use the equation p = h/λ, where p is momentum, h is Planck's constant, and λ is the wavelength of the photon.
To calculate the momentum of a photon, you first convert the wavelength from micrometers to meters and then apply the aforementioned equation. To compare the kinetic energy of an electron and a photon, you need to calculate each separately, considering that for an electron, the kinetic energy can be found using the relativistic equation KE = (−1 - 1)m0c2, where −1 = 1/√(1-v2/c2) is the Lorentz factor, and m0 is the rest mass of the electron. The velocity of an electron with the same momentum as a photon can be found by equating their relativistic momenta and solving for velocity.
For example, the question mentions an electron with kinetic energy approximately 150% of the rest mass energy, which implies that the electron is traveling at relativistic speeds, and the classical formula for kinetic energy (KE = 1/2 m v2) would not be accurate. Instead, the relativistic formula for kinetic energy would be applicable. In cases where you are asked to compare energies or momenta of particles like photons and electrons, it is crucial to take into account both their relativistic effects and the distinct properties of particles and waves (dual nature of matter and radiation).