How did Albert Einstein’s study of Brownian motion support the existence of atoms?

In 1905, Albert Einstein published a quantitative theory of Brownian motion that provided critical evidence for the existence of atoms at a time when their physical reality was still widely questioned by the scientific community.12

Einstein reasoned that if atomic theory were correct, microscopic particles suspended in a fluid would be subject to constant, random bombardment by the fluid's invisible molecules. Using statistical mechanics, he demonstrated that this uneven pressure would cause the suspended particles to exhibit a random, "wobbling" motion. He derived mathematical equations predicting that the displacement of these particles would be related to measurable properties such as temperature, fluid viscosity, and particle size.134

This work transformed atoms from useful, hypothetical constructs into observable physical entities. The French physicist Jean-Baptiste Perrin later verified Einstein’s equations through experimental observations using an ultramicroscope. Perrin’s confirmation allowed for the reliable calculation of the size and quantity of atoms, effectively ending scientific skepticism regarding their existence and earning him the Nobel Prize in 1926.314