# [Astro] Proton-Proton Chain Energy

1. Oct 21, 2012

### tylerc1991

1. The problem statement, all variables and given/known data

Find the energy released for the reactions in the Proton-Proton chain.

2. Relevant equations

Proton-Proton Chain:
1H + 1H -> 2H + e+ + v
e+ + e- -> γ + γ
2H + 1H -> 3He + γ
3He + 3He -> 4He + 2 1H

3. The attempt at a solution

To find the energy released in each of these reactions, I am calculating the mass deficit.

For the first reaction, I am finding a mass deficit of
2(1.007825 u) - 2.014102 u - 0.0005486 = 0.0009994 u
because v (neutrino) is massless.

Then the energy in MeV of this reaction is 0.0009994 u x 931.5 MeV/u = 0.9309411 MeV.

However, I checked http://en.wikipedia.org/wiki/Proton–proton_chain_reaction#The_proton.E2.80.93proton_chain_reaction, and it looks like the energy released is 0.42 MeV.

Did I do the calculation correctly?

Thank you for any help!

2. Oct 21, 2012

### TSny

Looks like you're using atomic masses (which include the mass of the electrons in the atom as well as the mass of the nucleus.) So, you'll need to take account of those atomic electrons.

3. Oct 21, 2012

### tylerc1991

I'm not exactly sure what you mean by this. I've calculated the energies of the other reactions and they seem to correspond to the correct values. It is only the first reaction that is getting me confused.

That is, I found a mass deficit of 2(0.0005486 u) = 0.0010972 u for the second reaction, which corresponds to a release of 1.0220418 MeV of energy (that matches the result online), and I used atomic masses here too.

4. Oct 21, 2012

### TSny

For the second reaction you are just using the mass of the electron rather than an atomic mass.

If you go to the third reaction, you would get the correct answer using atomic masses. That's because the atomic masses of 2H and 1H each contain the mass of one electron. So, together the two atomic masses include two electron masses. In the 3He product, the atomic mass will include two electrons. Since you end up subtracting the initial and final masses, the 2 electron masses in the hydrogen atomic masses are cancelled out by the two electrons in the helium atomic mass. So, you "luck out".

But if you look at your first reaction, you are starting with two 1H's (1 electron in each atomic mass) and going to one 2H (1 electron in its atomic mass). So, now when you subtract the initial and final atomic masses, the electrons do not cancel. You'll need to take care of that.

Last edited: Oct 21, 2012
5. Oct 21, 2012

### tylerc1991

I see. So there is an electron left over in the first reaction. Now if I calculate the mass deficit using the atomic masses I find

2(1.007825 u) - 2.014102 u - 2(0.0005486 u) = 0.0004508 u,

which corresponds to an energy release of 0.4199 MeV. Thank you for your help!!

6. Oct 21, 2012

Nice going!