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

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