Why viscosity changes the spread
Combining ideal osmotic pressure with mobility and diffusive balance relates diffusivity to temperature, viscosity and radius.
Read · Brownian motion: from wandering to a measurable law · Results
§5 · From displacement to molecular scale
Read the displacement argument, ask for its missing steps, and investigate the same relationships in three working laboratories.
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What would let us count molecules?
Displacement constrains diffusivity; independent radius, viscosity, temperature and gas-constant information are needed to infer molecular number.