A paper by this scientist proposed a new calculation for the mean squared displacement of particles, a concept in diffusion and Brownian motion. Which scientist is credited?

• A. Louis de Broglie
• B. Albert Einstein
• C. James Clerk Maxwell
• D. Niels Bohr

Answer: (B)

Mean squared displacement. In diffusion problems, you look at how far particles wander over time due to random collisions, and the average of the squared displacement grows with time. Einstein showed how this random motion could be described quantitatively, linking microscopic jitter to a measurable diffusion process. He demonstrated that the mean squared displacement increases linearly with time (in three dimensions, ⟨Δr^2⟩ = 6Dt), where D is the diffusion coefficient that depends on temperature, viscosity, and particle size. This work provided the first solid bridge between molecular motion and observable diffusion and gave a concrete way to relate microscopic behavior to macroscopic measurements. Other scientists listed contributed to related ideas—de Broglie to matter waves, Maxwell to kinetic theory, Bohr to atomic structure—but it was Einstein who formalized the calculation for Brownian motion’s mean squared displacement.