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How many atoms in the Universe?

Answer from in the UK. The universe may perhaps be infinite, but we have no way of knowing if that is so, and so we can only sensibly discuss "the observable universe", i.e. what we can see. Then your question becomes meaningful.

To answer "innumerable" atoms exist in an infinite universe doesn't really tell us anything new. It is a tautology, saying the same thing twice.

When I was 11, I wondered about space and asked the same question, and the answer I was given was "about 10^78", accompanied with the thought that that might seem like a very big number but the number of possible 40-move chess games has been estimated as being "about 10^120".

The person who answered 10^80 above is in the same league, as what I was told was the case. Let's try to re-examine the figures and see if they look right.

Obviously 10^78 is just an estimate, but it sounds about right if the number of stars in the observable universe is estimated to be 70 sextillion (7 x 10^22) That would mean about 1.5 x 10^55 atoms in the average star and stellar system (planets, asteroids, comets etc.

The Sun's mass is 2 x 10^30 kgs.

About 3.4×10^38 protons (hydrogen nuclei) are converted into helium nuclei every second (out of about ~8.9×10^56 total amount of free protons in the Sun),

So that sounds like an argument for 10^80 (10^23 stars x 10^57 hydrogen nuclei) if the Sun is typical of all other stars, But 78% of stars are low-mass red dwarfs so it looks like the Sun is probably above average in its mass and the number of atoms it contains and in which case the number of atoms in the universe may be nearer to 10^78 than it is to 10^80.

However, 10^78 might have to be revised upwards to take account of dark matter. So as you can see, there are a number of issues involved in a reliable guestimate being made.

The following features emerge from this analysis so far:

(a) the vast majority (99%+) of atoms are in stars not in planets

(b) matter in stars is a plasma of free protons rather than separate hydrogen atoms, because of the high temperature and pressure inside stars.

(c) nuclear fusion in stars creates helium from hydrogen as a raw material. In the process the number of protons remains the same but the number of atoms decreases as two hydrogen nuclei are needed to make 1 helium nucleus.

(d) the abundance of the most abundant elements in the universe is:

Element Parts per million by mass
Hydrogen 739,000
Helium 240,000
Oxygen 10,700
Carbon 4,600
Neon 1,340
Iron 1,090
Nitrogen 950
Silicon 650
Magnesium 580
Sulfur 440
All Others 650

so plainly the vast majority of atoms in the universe are hydrogen and the vast majority of hydrogen is the universe exists in stars and exists as a plasma of protons.

So it is quite a complex can of worms you have opened up here, and I hope I have said enough to stimulare you to read further about it.