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What is the Hydrogen and Helium composition of the Sun in terms of:

Hydrogen: (1) molecular, (2) metallic and (3) ionized compositions?

and

Helium: (1) atomic, (2) metallic and (3) ionized compositions?

This seems difficult to find on the internet.

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    $\begingroup$ Somewhere above 99% of the sun’s mass is completely ionized. See this answer. $\endgroup$
    – rob
    Nov 15 at 0:08
  • $\begingroup$ @rob, thanks I'll check it out. $\endgroup$ Nov 15 at 0:12
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    $\begingroup$ This question has been cross-posted on Astronomy. $\endgroup$
    – rob
    Nov 15 at 1:50
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    $\begingroup$ It has been closed on Astronomy SE. $\endgroup$
    – ProfRob
    Nov 16 at 7:35
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Roughly speaking the hydrogen and helium in the Sun become fully ionised at depths of about $\sim 10^7$ m below the photosphere once the temperature rises above about $(2-3)\times 10^4$ K (the larger number is appropriate for helium).

Thus atomic hydrogen and helium only exists in the outer $10^7$ m of the Sun and even then, the ionisation fraction is significant below the outer $2\times 10^6$ m.

Of course the density also rapidly decreases towards the photosphere, so the fraction of the Sun's mass in atomic form is difficult to estimate without a detailed solar model. However, back of the envelope, if we assume the density in these outer layers is $<1$ kg/m$^3$ (e.g. Nordlund et al. 2009), then a fraction of $<3\times 10^{-5}$ of the Sun's mass is in atomic form.

Molecular hydrogen is dissociated at much lower temperatures and is unlikely to be present in any significant quantities anywhere in the Sun.

Metallic hydrogen is not thought to be present in the Sun, the temperatures are way too high and the electrons are not degenerate. The requirements for metallic helium are even more extreme in terms of pressure and so it should not exist either inside the Sun.

To at least three significant figures, the answers to your questions are:

Hydrogen 0.00%, 0.00%, 100%

Helium. 0.00%, 0.00%, 100%

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