What is the mean moleculer weight of the gas at the solar core?

[Thomas Smith]

Homework Statement

A crude model of the sun has uniform density. The perfect gas law applies and the core is completely ionised and made up by 75% hydrogen and 25% helium by mass. In terms of mass of the hydrogen atom, find the mean molecular weight of the gas at the stellar core.

Relevant Equations

u=(2X+3/4Y+1/2Z)^-1

Here, i have provided the description of the mean molecular weight from my course notes as well as my workings.

I'm not sure about my values for X and Y. It states that X=1 if all of the hydrogen is ionised which i think the 1 represents 100% hydrogen but the core is also made up of ionised helium to, not only hydrogen which is why I have included the 75%= 0.75 of hydrogen as the abundance and the 25% = 0.25 of helium as the abundance.

I know the weight of the hydrogen atom is 1.67 x 10^-27 kg but not sure how the supposed answer of the mean molecular weight is converted to in terms of the weight of the hydrogen atom.

 

[haruspex]

It states that X=1 if all of the hydrogen is ionised

No, X=1 if all of the gas is ionised hydrogen.

I know the weight of the hydrogen atom is 1.67 x 10^-27 kg

Not relevant.

I believe your calculation is correct.

 

[Thomas Smith]

No, X=1 if all of the gas is ionised hydrogen.

Not relevant.

I believe your calculation is correct.

Thank you for your reply, what units is my answer in? mH ?

 

[haruspex]

Thank you for your reply, what units is my answer in? mH ?

All I know of this subject is from a little online research to answer your question. As far as I can make out, it is dimensionless.