A model has been constructed in order to study the effects of quantum confinement on the electron population on tapered conductive sheets. A two-dimensional rounded nanocone was considered for this study and the Schroumldinger equation was solved analytically on the entire system. The average number of electrons on the tip region was shown to be strongly influenced by the geometrical parameters of the system, such as the tip and base radius and the overall length. Field emission from such structures was also investigated using a simple one-dimensional Wentzel-Kramers-Brillouin approximation. The limitations on the electron population imposed by the strong quantum confinement at the tip region will have important consequences on the field emission current obtained from these structures.