The diffusion coefficient D has been measured for $^{133}\mathrm{Xe}$ atoms diffusing through 12 liquid n-alkanes, n-pentane through n-hexadecane, at 20.0 \ifmmode^\circ\else\textdegree\fi{}C. The dependence of D (${\mathrm{cm}}^{2}$/sec) on the viscosity \ensuremath{\eta} (P) was found to be D=(1.26\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$${\ensuremath{\eta}}^{\mathrm{\ensuremath{-}}0}$ $^{686\ifmmode\pm\else\textpm\fi{}0.011}$ where ${\ensuremath{\eta}}_{20.0}$ $_{\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}}$ varies monotonically in these solvents from 0.235 cP (for n-${\mathrm{C}}_{5}$${\mathrm{H}}_{12}$) to 3.48 cP (for n-${\mathrm{C}}_{16}$${\mathrm{H}}_{34}$). The observation that D is proportional to \ensuremath{\eta} to a negative power of magnitude near (2/3) is in agreement with other work on several different solute-solvent systems. Some ramifications of this dependence are suggested.