Chapter 32, Problem 4P

To determine

The time for one complete revolution for a very high-energy proton in the 1.0-km-radius Fermilab accelerator?

Answer to Problem 4P

Solution:

The time ($T$)for one complete revolution is $\text{2}.\text{1}\times \text{1}{0}^{-\text{5}}\text{s}$.

Explanation of Solution

Given info:

The radius $\left(R\right)$ of the accelerator is 1.0-km.

Formula used:

The time for one complete revolution is called Period $\left(T\right)$, and can be defined as:

$T=\frac{2\pi R}{v}$

Where:

• $R$ radius of circumference

• $v$ speed of proton. In this case, proton has moving with a very high energy, therefore, the speed can be taken as:

Calculation:

Replacing given data into equation (2)we get:

Solving (3)we obtain: