Up to what values of kinetic energy does the period of revolution of an electron and a proton in a uniform magnetic field exceed that at non-relativistic velocities by `eta = 1.0 %`

Explanation

From (3.279),
`T = (2pi epsilon)/(c^(2) eB)` (relativistic). `T_(0) = (2pi m_(0) c^(2))/(c^(2) eVB)` (nonrelativistic),
Here, `m_(0) c^(2)//sqrt(1 - v^(2)//c^(2)) = E`
Thus, `delta T = (2pi T)/(c^(2) eB), (T = K.E.)`
Now, `(delta T)/(T_(0)) = eta = (T)/(m_(0) c^(2))`, so, `T = eta m_(0) c^(2)`