In a diffusion-controlled current transient after a potential step, the current decays proportional to which function of time?

• A. 1/√t
• B. t
• C. √t
• D. e^t

Answer: (A)

Diffusion controls how fast reactant molecules reach the electrode after a potential step, so the current is governed by the diffusion-limited transport described by the Cottrell law. In this regime, the instantaneous current declines as the inverse square root of time: i(t) ∝ t^(-1/2). The standard expression is i(t) = nFA C* sqrt(D/(π t)), showing explicitly that the current scales with 1/√t as time grows.

This happens because the diffusion layer thickness grows like √(Dt), reducing the surface concentration gradient and thus the flux over time. The other time dependences would imply the current either grows with time or changes exponentially, which isn’t what occurs under diffusion-controlled, step-potential conditions.