In a diffusion-controlled system following a potential step, which expression correctly represents the Cottrell current i(t)?

• A. i(t) = n F A C / sqrt(pi D t)
• B. i(t) = n F A C sqrt(pi D t)
• C. i(t) = sqrt(pi D t) / (n F A C)
• D. i(t) = n F A / (sqrt(pi D t) C

Answer: (A)

Diffusion controls the current after a potential step, so the current falls as the diffusion layer thickens. The Cottrell equation encapsulates this: i(t) = n F A C sqrt(D / (π t)). This shows the current scales with the number of electrons transferred (n), Faraday’s constant (F), the electrode area (A), and the bulk concentration (C); it increases with the diffusion coefficient (D) and decays with time as t^(-1/2). The square-root time dependence is the hallmark of diffusion-controlled transport.

The other expressions misplace either the time dependence, the diffusion coefficient, or the concentration factors, so they don’t reflect the correct diffusion-limited behavior.