Numerator: RT

The passage around this formula

with the diffusion constant D fixed by measurable quantities. Einstein derived it explicitly, from the balance between the drag on a sphere of radius P in a fluid of viscosity k and the osmotic pressure driving diffusion, as $D = \frac{RT}{N}\cdot\frac{1}{6\pi k P}$. where R is the gas constant, T the absolute temperature, and N Avogadro’s number [ 1 ] . That last dependency was the trap door: if D could be read off a microscope by timing how far a particle wandered, and every other term in the equation was already known independently, then watching one particle jiggle became a way to count atoms.

Read this part in the article →