# Probability For A Hydrogen Atom To Be 13 Billion Years Old?

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### #1 rhertz

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Posted 10 May 2019 - 01:06 PM

Do anyone imagine how to calculate the probability that a given Hydrogen atom, either being along or as a part of the bi-atom H2, have been existing unaltered for 13 billion years?

Edited by rhertz, 18 June 2019 - 08:22 PM.

### #2 exchemist

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Posted 13 May 2019 - 03:39 PM

According to the current cosmological model, there are five cosmic components

• Dark energy
• Dark matter
• Photons (most from CBR)
• Neutrinos
• Baryons (neutrons, protons, and electrons)

After the universe cooled off enough for plasma to engage with electrons to form elementary atoms (3000 °K and less),

baryons recombined to form basic atoms H and He. And this is what is thought as happened:

• H and He atoms were formed with a ratio H/He = 12:1.
• 90% of H and He atoms remained as diffuse ionized gas surounding galaxies.
• So, 83% of them were H atoms.
• 10% of baryons are found in stars, with 2% of them forming heavier elements.
• 8% of baryons remained as H and He atoms, with 7.4% being H atoms in stars.

It took about 1.3 million years for the 83% of original H atoms to start forming stars and galaxies.

It's assumed that there are 1086 H atoms in the observable universe, with 1023 stars (here is the link)

https://www.universe...n-the-universe/

Estimations are that free Hydrogen has a density of 5/m3, what gives approximately 1059 free H atoms in the observable universe.

This is, approximately 1059 parts in a grand total of 1086  parts.

So, for this, the probability that a H atom has remained free for 13 billion years is close to one part in 1027 parts (almost zero).

What do you think about this? I've simplified a LOT of things and stuck with the observable universe only (as of today).

From your numbers, it would follow that if you consider where a randomly chosen hydrogen atom is likely to be found, it will will be more likely to be in a star than not, by a factor of 10²⁷. But since most of the stars formed quickly, the hydrogen that was not swept up into stars can have remained undisturbed ever since, can it not?  OK the fraction we are talking about is small, but it is nothing like zero. We can detect molecular clouds of hydrogen so we know they are there.

What is the purpose of this exercise?

### #3 VictorMedvil

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Posted 14 May 2019 - 12:08 AM

Basically, if I were doing this calculation I would just take the Probability of change upon a hydrogen atom over time then just take it times the time in years. So lets say that there is a 1/100 chance per year for hydrogen to change, then just take that times 1/13 billion that would give the odds of your statement, but first you would need to calculate the odds of a hydrogen atom staying the same per year to a degree of accuracy as that number in this post is wrong.

Edited by VictorMedvil, 14 May 2019 - 12:10 AM.

### #4 VictorMedvil

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Posted 14 May 2019 - 01:54 PM

Good thinking, even when there is not such a data available, and I think it's very hard to figure it out.

But, if that 83% of atoms that originally were free H atoms (didn't become condensed matter) is adopted

as a probability per Million Years, then the result would be:

P(H free 13 By) = 0.8313,000 and is almost zero.

Now that looks to be correct as it would be a very small fraction assuming it is a constant the rate of bonding but that is the best approximation you would get without being there to observe every moment in the universe. You may need to use the equivalent or approximate symbol in that calculation, but approximately it would be ‭6.3316964917734257675339216762591 * 10-106‬ chance of staying untouched Hydrogen which may I say are astronomical odds of being in the universe since the BB and not forming bonds or changing state.

Edited by VictorMedvil, 14 May 2019 - 02:15 PM.

### #5 Dubbelosix

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Posted 14 May 2019 - 02:47 PM

Approximately, but without inflation, there could be anything up to a 70 to 80 billion year expansion. Perhaps more... The universe as we have modeled it, is very rigid and does not like alternative theories, especially within academic circles.

### #6 Dubbelosix

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Posted 14 May 2019 - 02:49 PM

Einstein once argued, galaxies took far longer to form. This may have been part of his appeal to a universe where it was static.. but as Flummoxed has deduced, just because things are moving in space, does not preclude as fact that things are moving due to an expansion of space. Though, it does seem natural to think that - also, there are viable models without inflation and that certainly would add quite a few years to the true age of the universe we see around us.

### #7 VictorMedvil

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Posted 14 May 2019 - 03:34 PM

Einstein once argued, galaxies took far longer to form. This may have been part of his appeal to a universe where it was static.. but as Flummoxed has deduced, just because things are moving in space, does not preclude as fact that things are moving due to an expansion of space. Though, it does seem natural to think that - also, there are viable models without inflation and that certainly would add quite a few years to the true age of the universe we see around us.

I agree dubbel, it is very much a approximation we have no way of knowing how inflation and expansion changed this I would think the number may be higher as you would have a hydrogen atom that travels near the speed of light then also has expansive properties that keep it from bonding with another hydrogen, but in the first million years there was quite a bit of expansion as that would include parts of the inflationary epoch thus it is not negligible the effect of expansion/inflation. Does anyone know at what kinetic energy would halt bonding in hydrogen that may also may need to be calculated under a bell curve as I would think it would follow that curve as Temperature/Kinetic Energy is dispersed that way then another curve to factor in expansion via Dark Energy, but I don't know the curve for Dark Energy. There are some big factors missing but I am happy with these numbers as approximations, there is just so much that effects bonding of chemicals over large periods of time like I said, "You may have to have actually watched the entire universe for 13 billion years to get a non approximate number considering all the factors to bonding".

Edited by VictorMedvil, 14 May 2019 - 04:12 PM.

### #8 Dubbelosix

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Posted 14 May 2019 - 04:30 PM

I think the top estimate for ''a possible static universe'' or a gradual release of matter over expansion, come together well in agreement. I think the largest of the galaxies would have took more longer to form, than the smaller ones we see today. We need accurate measurements on density and size of galaxies to see if it matches still to the expected values for the CMB. You said and I quote:

"You may have to have actually watched the entire universe for 13 billion years to get a non approximate number considering all the factors to bonding".

I doesn't matter whether we measure the universe for 13 billion years, the assumption here is that it has existed for 13 billion years. What we think measure and what is fact, as I once mentioned before, is speculation.

So is a pre-big bang phase, but at least such a phase (only just now supported in mainstream) seems to indicate, our ''straightforward view'' is not so straightforward as we may have contemplated.

### #9 Dubbelosix

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Posted 14 May 2019 - 04:31 PM

I have estimated, a universe, perhaps 80 billion years old... but I need to go back to what I call ''slow nucleosynthesis'' that is, a production of particles as it expands, which has given excellent models for a near homogeneous model of expanding matter and energy in a universe.

### #10 VictorMedvil

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Posted 14 May 2019 - 04:49 PM

Well, I don't know the age of the universe, I have never calculated it myself. I just always use the number that is considered to be correct under standard physics but if you are saying that the age of the universe is older than that then that number could be used too, this was just a general calculation based on the numbers given which would make the odds much lower than what is currently being displayed to answer the OP's question, the galactic formation rate would no doubt effect the number of particles that remain unchanged along with many other factors that are complex numbers of course if the age of the universe were 80 billion versus 13 billion years this probability would be subject to change which would make the probability approximately ‭1.7676247990747670107311906115191 *10-6474‬.

Edited by VictorMedvil, 14 May 2019 - 04:55 PM.

### #11 Dubbelosix

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Posted 14 May 2019 - 05:00 PM

You should give directions to how you calculated that, because its not easy. Using the CMB as an age gauge, really depends on the model.

### #12 VictorMedvil

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Posted 14 May 2019 - 05:05 PM

You should give directions to how you calculated that, because its not easy. Using the CMB as an age gauge, really depends on the model.

Well it is using exponential decay formula treating the hydrogen atom like a radioactive isotope that will create bonds unless certain conditions are met over time which causes a exponential decay of the amount of unchanged hydrogen atoms over a period of time. We have a 83/100 A value per million years then a X value of 13,000 or 80,000 in that case.

Edited by VictorMedvil, 14 May 2019 - 05:09 PM.

### #13 Dubbelosix

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Posted 14 May 2019 - 05:10 PM

A hydrogen atom, is in fact, infinitely stable in the ground state. For some strange reason, so is the proton, but be rest assured, they probably involve different physics, but along the same line as the system existing in its ground state. There will be no exponential decay for systems existing in the ground state, which is why an electron itself cannot decay.

Edited by Dubbelosix, 14 May 2019 - 05:10 PM.

### #14 VictorMedvil

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Posted 14 May 2019 - 05:12 PM

A hydrogen atom, is in fact, infinitely stable in the ground state. For some strange reason, so is the proton, but be rest assured, they probably involve different physics, but along the same line as the system existing in its ground state. There will be no exponential decay for systems existing in the ground state, which is why an electron itself cannot decay.

Well it is not decaying but rather it is the chance of it staying in its original state with the same amount of electrons and such like I said this is just a approximation, there is probably a better equation to explain this but I don't know all the complex factor's value much like trying to calculate the Drake's Equation.

Edited by VictorMedvil, 14 May 2019 - 05:13 PM.

### #15 Dubbelosix

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Posted 14 May 2019 - 05:15 PM

No, the decay is not due to an approximation ''of when it might decay'' as there are physical reasons why it cannot. Using the simplest system, an electron, the same reason holds, there is nothing the electron can decay into that is simpler. Unless of course, you argue after so many aeons it could decay into something simpler, we have yet to see direct reasons for this... though an electron is composed of smaller components, at least three if memory recollects, but this is done under different medium.

In short, a stable particle, is one that cannot decay into anything simpler in the vacuum of space.

### #16 VictorMedvil

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Posted 14 May 2019 - 05:17 PM

No, the decay is not due to an approximation ''of when it might decay'' as there are physical reasons why it cannot. Using the simplest system, an electron, the same reason holds, there is nothing the electron can decay into that is simpler. Unless of course, you argue after so many aeons it could decay into something simpler, we have yet to see direct reasons for this... though an electron is composed of smaller components, at least three if memory recollects, but this is done under different medium.

In short, a stable particle, is one that cannot decay into anything simpler in the vacuum of space.

Yes, but this is the chance of it losing or gaining an electron or becoming bonded which I just used the exponential decay formula thinking it would exponentially decay from the state given that once again I don't know the complex factors to get a better answer. I am not saying it is actually decaying like a isotope but rather from the state of having its original electrons and such.

Edited by VictorMedvil, 14 May 2019 - 05:17 PM.

### #17 Dubbelosix

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Posted 14 May 2019 - 05:23 PM

Ok.. put it this way, for a hydrogen atom to lose energy is much less in statistical significance to a ground state to gain bonds. The reason why is because ... in a loose sense of the terminology we tend to use, would take an infinite amount of energy for a ground state particle to decay.