We have performed a high field magneto-absorption on silicon doped with a variety of single and double donor species. The magnetic field provides access to an experimental magnetic length, and the quadratic Zeeman effect in particular may be used to extract the wavefunction radius without reliance on previously determined effective mass parameters. We were therefore able to determine the limits of validity for the standard one-band anisotropic effective mass model. We also provide improved parameters and use them for an independent check on the accuracy of effective mass theory. Finally, we show that the optically accessible excited state wavefunctions have the attractive property that interactions with neighbours are far more forgiving of position errors than (say) the ground state.