 Solution

For fully ionized hydrogen with a small metal fraction, there is approximately one proton and one electron per hydrogen mass, so ${\mu }_H\simeq 1/2$. The Kramers coefficient is proportional to $Z(1+X)\simeq 2Z$. Denote this star's luminosity by $L_H$; the supplied proportionality law alone does not fix its absolute normalization.

Relative to the helium-dominated comparison star, the calculation in part ii givesIf one uses a roughly solar luminosity as an illustrative calibration for this roughly solar-mass, solar-central-temperature reference, the helium star would be of order a hundred solar luminosities. That calibration is only approximate because a mostly hydrogen composition with $\mu \simeq 1/2$ is not the actual solar composition.