Estimating Temperature of Universe at Deuteron Disassociation?

[freefallin38]

Ok, I have this homework problem that is driving me nuts, and I only have a short period of time to get it. The question is, Estimate the temperature of the universe when it has cooled enough that photons no longer disassociate the deuteron. There was another part that asked for the temperature when the hydrogen atom is no longer dissociated. For that problem I used the Ionization Energy of the ground state of electron(13.6 eV), and used the following approach:
13.6eV=kT, where k=8.62e-5eV/K.
I got that part right, so I figured that I could use the Ionization energy of deuterium (14.9eV) for the 2nd part, but this doesn't give me the right answer. Does anyone know why this is so and if there's another approach to the problem?

 

[Dick]

Dissociating the deuteron is not splitting an electron from a deuterium nucleus, it's splitting the proton from the neutron in the deuterium nucleus. That's an energy that should be measured in MeV, not eV. Where did you get 14.9eV??

 

[freefallin38]

I got it somewhere online, and it didn't seem right. I can't think of any other way of going about the problem though, and I can't find any other value for that ionization energy.

 

[Avodyne]

The relevant energy is the binding energy of the proton and neutron that form the deuteron, not the binding energy of the electron in a deuterium atom.

 

[Dick]

What's the mass difference between a free proton and neutron and the deuterium bound state? Times c^2. That's that's the 'ionization' energy you are looking for.

 

[freefallin38]

Ok, so calculating that would give me 1875.6 MeV for he 'ionization energy' of the deuteron. Then, when I set it equal to kT, I get 2.177e13K, which still isn't the right answer. Am I on the right track at least?

 

[Dick]

Ok, so calculating that would give me 1875.6 MeV for he 'ionization energy' of the deuteron. Then, when I set it equal to kT, I get 2.177e13K, which still isn't the right answer. Am I on the right track at least?

That number is really way wrong. That's about the total mass of deuterium.

 

[freefallin38]

ohh ok, i got it now. i just had some trouble with using the right masses haha. thank you so much!