Q.Discuss Millikan's oil drop experiment to determine the charge of an electron.

Having established the electron's charge-to-mass ratio via Thomson's experiment, physicists still needed to measure the electron's charge $e$ itself directly - a problem solved by Robert Millikan's celebrated oil drop experiment. The apparatus consists of two horizontal circular metal plates, about 20 cm in diameter and 1.5 cm apart, enclosed in a glass chamber and connected to a high potential difference (about 10 kV) so the electric field between them points vertically; an atomizer sprays a fine mist of viscous oil (such as glycerine) through a small hole in the upper plate, and some droplets pick up a small charge from friction or exposure to X-rays as they fall. A side-mounted light source and a perpendicular microscope let an observer track a single chosen drop's motion precisely.

The measurement has two stages. First, with the electric field switched off, the chosen droplet falls under gravity, opposed by buoyancy and by Stokes' viscous drag from the air, quickly reaching a constant terminal velocity; balancing these three forces yields the droplet's radius $r=\left[\frac{9\eta v}{2g(\rho-\sigma)}\right]^{1/2}$ (where $\eta$ is air's viscosity, $\rho$ the oil's density and $\sigma$ air's density). Second, the field is switched on and carefully adjusted until the same droplet is held perfectly stationary - meaning the upward electric force $qE$ exactly balances the droplet's (buoyancy-corrected) weight, $qE=\tfrac43\pi r^3(\rho-\sigma)g$, which (using the radius found in the first stage) can be solved directly for the droplet's charge $q$.

Repeating this procedure over many different droplets, Millikan consistently found that every measured charge $q$ came out as an exact whole-number multiple of one single, smallest value: $1.6\times10^{-19}$ C. This showed conclusively that electric charge is quantised - it exists only in discrete lumps, never in arbitrary continuous amounts - and identified that smallest lump, $e=1.6\times10^{-19}$ C, as the fundamental (elementary) unit of electric charge found throughout nature, a value that combined with Thomson's $e/m$ measurement immediately yields the electron's mass.