Force to keep photon in circular motion

quietrain

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 =$$\gamma$$ mc2

so m = photon mass = 1.67 x 10-27

so i found $$\gamma$$ = 1.66
and v = 0.798c

so when i sub into f = mv2/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 whats wrong?

btw why can't i use E= hf, get f, convert to T =1/f, then use circumference / T = v ?
i realise that v i get is faster than the speed of light. but which step is wrong in this attempt?

thanks!