Question

Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 164 v.

Answer 1

Work done in moving a proton = potential difference×Charge of a proton
                                                 = 164×1.6×10⁻¹⁹ = 2.624×10⁻¹⁷ J
This work done should be equal to change in kinetic energy.
Initial speed of proton is zero therefore K.E initial will be zero.
Work done = final kinetic energy = 2.624×10⁻¹⁷ J
K.E = mv²/2
v² = 2(2.624×10⁻¹⁷)/1.6×10⁻²⁷ = 3.28×10¹⁰ m/s
∴ v = 1.811×10⁵ m/s