Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2018 / S26 / 2 / c / ii / Solution

Fully ionized helium supplies three particles per four hydrogen masses, so ${\mu }_{\mathrm{He}}\simeq 4/3$. The same small $Z$, but negligible hydrogen fraction, gives ${\kappa }_{0,\mathrm{He}}\propto Z$, half the hydrogen-star coefficient. The relative luminosity isConsequentlyThe very strong molecular-weight dependence outweighs the reduction in mass. Treating the two opacities as identical would miss a factor two, and using neutral-gas molecular weights would be inconsistent with the stated hot ionized stars.