How long does it take for two hydrogen atoms to fuse?

[OneOnOne1162]

This may be kind of an odd question, but provided that two hydrogen atoms are in a position where they are about to fuse, how long does this process actually take?

 

As an extra question, how long would it take to fuse every atom in 1 gram of hydrogen, assuming you had conditions that allowed for this to happen?

[swansont]

As an extra question, how long would it take to fuse every atom in 1 gram of hydrogen, assuming you had conditions that allowed for this to happen?

 

 

The mean time for proton fusion in the sun is estimated to be about a billion years. Fortunately a gram of H-1 has 6.02 x 10^14 billion atoms in it. But the rate would slow as you ran out, because the reaction rate will depend on the number of available atoms per unit volume (N) (and since the protons are fusing with other protons, it should end up depending on N^2) . So this would end up being some sort of an exponentially decreasing rate.

 

If you had the other isotopes the situation changes a little, but I expect not a lot.

[Strange]

The mean time for proton fusion in the sun is estimated to be about a billion years.

 

Wow. That certainly gives an idea of scale.

[swansont]

 

Wow. That certainly gives an idea of scale.

 

 

Proton-proton fusion is tough, because one of the has to beta-plus decay almost immediately. That's endothermic, so there's an activation energy involved. One of the main reasons deuterium and tritium are preferred — you can form He-4 directly, which is exothermic. The p-p fusion actually acts to cool the core of the sun.

[Enthalpy]

But was that the original question?

 

Several billion years is the mean time it takes for nuclei to have a chance to come to the conditions permitting the fusion. Once they're at the proper distance, the beta decay and other operations must be snappy. Everything has to be quick, faster than the protons need to come apart if the fusion doesn't proceed.

[OneOnOne1162]

But was that the original question?

 

Several billion years is the mean time it takes for nuclei to have a chance to come to the conditions permitting the fusion. Once they're at the proper distance, the beta decay and other operations must be snappy. Everything has to be quick, faster than the protons need to come apart if the fusion doesn't proceed.

 

It was not in fact the original question. I was personally looking for more of an answer in femtoseconds or something. You know, the time it takes for two hydrogen atoms to fuse together from the moment it becomes possible for them to do so.

Or alternatively what the timetable would be for 1 gram of hydrogen to become fully fused. Alternatively the equivalent of "half-life" would also be a fine answer (since it may in fact be the case that the rate slows down).

Edited April 27, 2016 by OneOnOne1162

[swansont]

But was that the original question?

No, it was the second question.

[John Cuthber]

 

Wow. That certainly gives an idea of scale.

On a weight for weight basis the sun produces roughly as much heat as a compost heap.

This is jut as well. if it was ten times faster the Sun would be have pretty much gone out before we evolved. (Well, we would have had to evolve on a planet in orbit round a smaller star)

Edited April 27, 2016 by John Cuthber

[swansont]

 

It was not in fact the original question. I was personally looking for more of an answer in femtoseconds or something. You know, the time it takes for two hydrogen atoms to fuse together from the moment it becomes possible for them to do so.

Or alternatively what the timetable would be for 1 gram of hydrogen to become fully fused. Alternatively the equivalent of "half-life" would also be a fine answer (since it may in fact be the case that the rate slows down).

 

 

It's probably much shorter than even femtoseconds. Reactions with diprotons may have been observed in the lab, but not to the extent that a lifetime could be measured. And the reaction has to occur on the scale of the diproton lifetime. Possibly faster than 10^21 seconds.

 

The initial rate is going to be related to the time I mentioned. If it's a billion years for a fusion reaction, the rate is about 20 million reactions per second for 1 mole (i.e.1 gram). But that only works under the conditions of our sun, because it depends on N^2, and has two dependencies on temperature — the speed, which dictates how often collisions occur, and the fraction of collisions that will have enough energy to allow the reaction to occur.

[OneOnOne1162]

 

 

It's probably much shorter than even femtoseconds. Reactions with diprotons may have been observed in the lab, but not to the extent that a lifetime could be measured. And the reaction has to occur on the scale of the diproton lifetime. Possibly faster than 10^21 seconds.

 

The initial rate is going to be related to the time I mentioned. If it's a billion years for a fusion reaction, the rate is about 20 million reactions per second for 1 mole (i.e.1 gram). But that only works under the conditions of our sun, because it depends on N^2, and has two dependencies on temperature — the speed, which dictates how often collisions occur, and the fraction of collisions that will have enough energy to allow the reaction to occur.

 

I think that answers my question pretty fully now, thanks.

 

Though a side question: Is there any sort of graph which shows how the rate would change depending on those last factors you mentioned?

[Sensei]

Proton-proton fusion is tough, because one of the has to beta-plus decay almost immediately. That's endothermic, so there's an activation energy involved. One of the main reasons deuterium and tritium are preferred you can form He-4 directly, which is exothermic. The p-p fusion actually acts to cool the core of the sun.

What do you mean by that?

Decay plus is exothermic process. If Decay Energy is negative value Decay Plus is prohibited decay mode.

proton-proton fusion release 0.42 MeV energy:

[math]p^+ + p^+ \rightarrow D^+ + e^+ + V_e + 0.42 MeV[/math]

From 420,000 eV there is part taken by neutrino, and immediately escape core.

But even then it's 210,000 eV, energy released from reaction and remaining there.

Additionally newly created positron annihilates with electron, giving 1.022 MeV energy.

[math]e^+ + e^- \rightarrow \gamma + \gamma + 1.022 MeV[/math]

So it releases ~1.232 MeV energy per reaction average.

 

Fusion of heavier elements than Iron is indeed endothermic, as their Decay Energy is negative value.

 

The problem with pp fusion is that the most often it decays back to two protons.

"In the Sun, deuterium-producing events are rare because diprotons, the much more common result of nuclear reactions within the star, immediately decay back into two protons."

https://en.wikipedia.org/wiki/Proton-proton_chain_reaction

Slow rate of reaction means star surface will have plentiful of time to release energy.

 

One of the main reasons deuterium and tritium are preferred you can form He-4 directly, which is exothermic.

It's preferred because it releases 17.6 MeV (DT), instead of 1.232 MeV. That's 14x more per reaction.

Edited May 9, 2016 by Sensei

[swansont]

 

What do you mean by that?

Decay plus is exothermic process. If Decay Energy is negative value Decay Plus is prohibited decay mode.

proton-proton fusion release 0.42 MeV energy:

[math]p^+ + p^+ \rightarrow D^+ + e^+ + V_e + 0.42 MeV[/math]

 

 

 

You're missing a step (and I stated this poorly). The two protons first form a diproton (He-2). The decay of that to H-2 is endothermic, while the overall result is exothermic

https://en.wikipedia.org/wiki/Proton–proton_chain_reaction#The_pp_chain_reaction

[BearOfNH]

swansont Evil Liar (or so I'm told) posted 27 April 2016 - 03:06 PM:

 

... And the reaction has to occur on the scale of the diproton lifetime. Possibly faster than 10^21 seconds. ...

 

Of course 10^21 seconds (3.17e+13 years) is greater than the accepted lifetime of the universe. Evil liar, indeed.

[swansont]

Someone stole the - sign in the exponent