Answer
$2.1\times10^{-5}s$
Work Step by Step
The time for one revolution is the circumference divided by the protons’ speed. The “very high energy” protons travel at just under the speed of light.
$$T=\frac{2\pi r}{v}=\frac{2 \pi (1.0\times10^3 m)}{3.00\times10^8m/s}$$
$$T=2.1\times10^{-5}s $$