When the Sun entered the main sequence, its core was approximately 75 percent hydrogen and 25 percent helium, by mass. What was the ratio of hydrogen nuclei to helium nuclei?

Question

Quizplus · Accepted Answer

The mass of a hydrogen nucleus (proton) is roughly 1 atomic mass unit (amu), while the mass of a helium nucleus (alpha particle) is roughly 4 amu. Given the Sun's core composition of 75% hydrogen and 25% helium by mass, for every 4 amu of helium, there are 3 amu of hydrogen. Therefore, for every helium nucleus, there are $ \frac{3}{1} \times \frac{1}{4} = \frac{3}{4} $ hydrogen nuclei, which simplifies to 3 hydrogen nuclei for every 4 amu of mass. Since helium is 4 times heavier than hydrogen, you get 3 hydrogen nuclei for every 1 helium nucleus by mass, but considering the mass proportions (75% H, 25% He), you actually have 3 times as much hydrogen by mass, which translates to 3 times 4, or 12 hydrogen nuclei for every helium nucleus, making the ratio 12:1.

When the Sun Entered the Main Sequence, Its Core Was