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## Homework Statement

A proton has an energy of 2.5 × 10−10 J. What force is needed to keep it going in

a circle having a 1.0 km radius

## The Attempt at a Solution

so i tried to find v first.

total energy E = 2.5 x 10

^{-10}J =[tex]\gamma[/tex] mc

^{2}

so m = photon mass = 1.67 x 10

^{-27}

so i found [tex]\gamma[/tex] = 1.66

and v = 0.798c

so when i sub into f = mv

^{2}/R , i get f = 9.57 x 10

^{-14}

but the answer is 1.6 x 10

^{-13}

which means that the photon speed is roughly 0.9++ c

so anyone knows what's wrong?

btw why can't i use E= hf, get f, convert to T =1/f, then use circumference / T = v ?

i realize that v i get is faster than the speed of light. but which step is wrong in this attempt?

thanks!