Solution
= Solution
Using $R\propto M^{1/13}$ in the <radiative diffusion in a star> scaling from part (i),
$$
L\propto M^{11/2}R^{-1/2}\propto M^{11/2-1/26}.
$$
Therefore the <mass-luminosity relation> is
$$
\boxed{L\propto M^{71/13}.}
$$
The nuclear scaling independently gives $L\propto M^6R^{-7}\propto M^{6-7/13}=M^{71/13}$, consistent with <radiative homology with proton-proton burning and Kramers opacity>.