The one-dimensional particle-in-a-box model used to introduce quantum mechanics to students suffers from a tenuous connection to a real physical system. This article presents a two-dimensional model, the particle confined within a ring, that directly corresponds to observations of surface electrons in a metal trapped inside a circular barrier. This model involves the solution of the Schrodinger equation in two dimensions, separation of variables, and known solutions to an established differential equation. Because of the striking visual nature of the probability distributions arising from this model, it is likely to captivate student interest. Close agreement between experimental data and this model provides further support for the wave nature of matter and establishes the accuracy of the model. (Contains 8 figures and 2 tables.)