Special relativity is a theory proposed by Albert Einstein in 1905 that explains the behavior of objects traveling at high speeds. It states that the laws of physics are the same for all observers in uniform motion and that the speed of light is constant for all observers, regardless of their relative motion. In this problem, special relativity applies because the electron is traveling at a high speed, which requires us to use this theory to accurately describe its behavior.
The "c" in this problem represents the speed of light in a vacuum, which is approximately 299,792,458 meters per second. Therefore, an electron traveling at 0.422c means that it is moving at 0.422 times the speed of light, or about 126,646,100 meters per second.
The relativistic momentum of an object is given by the equation p = γmv, where γ is the Lorentz factor, m is the mass of the object, and v is its velocity. In this problem, we can calculate the relativistic momentum of the electron by substituting its mass and velocity into this equation.
Other effects of special relativity that may be observed in this problem include time dilation, length contraction, and mass-energy equivalence. Time dilation refers to the slowing down of time for an object moving at high speeds, while length contraction refers to the shortening of an object's length in the direction of its motion. Lastly, mass-energy equivalence states that mass and energy are equivalent and can be converted into one another according to the famous equation E=mc².
Special relativity plays a crucial role in our understanding of the behavior of high-speed particles, as it allows us to accurately describe and predict their behavior. It also shows that our traditional ideas of time, space, and mass are not absolute and can change depending on an observer's frame of reference. This theory has been extensively tested and has been proven to be accurate in many experiments, further solidifying its importance in our understanding of the universe.