Final answer:
High-energy protons in the Fermilab synchrotron approach the speed of light and travel around a 2.00-km diameter ring. The time taken for one trip can be calculated using the circumference and speed of light, and the frequency of passing a point is the reciprocal of this time.
Step-by-step explanation:
The student's question relates to the operation of the Fermilab synchrotron and the behavior of protons accelerated to high energies within it. When protons are accelerated to energies that are about 1000 times their rest mass energy, they approach the speed of light. The circumference of the Fermilab synchrotron, based on its 2.00-km diameter, would be π * d = 3.14159 * 2.00 km, which is approximately 6.283 km. Since speed, v, is approximately the speed of light, which is roughly 299,792 km/s, we can estimate the time for one trip, t, with the formula t = circumference / v.
To find out how many times per second a proton passes through the target area, we calculate the reciprocal of the time for one complete trip. The frequency, f, of the proton passing the target area is approximately f = 1/t.