 Solution

Using $R\propto M^{1/13}$ in the radiative diffusion in a star scaling from part (i),Therefore the mass-luminosity relation isThe nuclear scaling independently gives $L\propto M^6{R}^{-7}\propto M^{6-7/13}=M^{71/13}$, consistent with radiative homology with proton-proton burning and Kramers opacity.