(a) Find the maximum values of velocity and if the non-relativistic approximation for energy, E mc 2 + p 2 /2m, is

(a) Find the maximum values of velocity υ and γ if the non-relativistic approximation for energy, E ≈ mc² + p²/2m, is to be used with an error less than εp²/2m. Hence show that for an error of 1%, the momentum satisfies p ≈ 0.2mc.

(b) Find the minimum values of velocity υ and γ if the relativistic approximation for energy, E ≈ pc, is to be used with an error of less than εpc. Hence show that for an error of 1%, the momentum satisfies p ≈ 7mc.