Beta Particle Energy: Why E_max > Q? Energy Conservation Explained

[murdakah]

Why is the Emax of beta energies larger than Q? This should violate energy conservation, unless the differences in binding energies themselves are only averaged values.
What I'm actually asking, is why is Q = E_average of emitted particles?
At least, according to this page: http://www.applet-magic.com/betaemitters.htm

 

[Orodruin]

Why is the Emax of beta energies larger than Q?

It is not. The Q value is the difference between the incoming and the outgoing masses. It is always at least as big as the maximal beta energy (in fact, a bit bigger if taking the nuclear recoil into account).

The page you link to does not mention the Q value at all.

 

[murdakah]

You're right, it doesn't. But if you look at P-32. That decays into S-32, and the Q of that reaction is 0.929MeV. If you look at the table on that page, the change in binding energy, which is Q, is smaller than the max beta energy.
***EDIT***
And that's assuming all the energy is deposited in the beta particle even.

 

[Vanadium 50]

The change in binding energy is not Q.

 

[mfb]

I don't know what "Change in Binding Energy" means here (probably takes into account that we convert protons to neutrons or vice versa in beta decays), but the released energy is 1.71 MeV, which is the same as the maximal electron energy.

The table is weird, why do they have two entries for 127 Te with the same change in binding energy but different beta energies?

 

[murdakah]

Q=P-32 - S-32 = 271.781-270.852 =0.929 MeV according to my tables, and I am calling it Q, and that does take neutron/proton conversion and all other transmutations into account. What is Q according to you guys?
Now how can the energy released be any greater than that if the atoms are stationary?

The table is weird, why do they have two entries for 127 Te with the same change in binding energy but different beta energies?

That is probably because it decays into two different elements frequently?

 

[mfb]

Q is not the difference between binding energies. The number of protons and neutron changes, you have to take that into account as Q is the difference between the total energies.
Also, the table there considers the kinetic energy only, so you have to subtract the electron mass.

Now how can the energy released be any greater than that if the atoms are stationary?

It cannot.

That is probably because it decays into two different elements frequently?

Then the differences in binding energies should be different, but 127Te does beta- decay only. There is a metastable state with a longer lifetime than the ground state, but those numbers don't fit to the table.

 

[murdakah]

Thanks. Ok forget Q then.
Just tell me why the max beta energy is larger than the difference in binding energy, if you look at the table. And that is true for all the elements on there? Maybe if you can just show me an equation that would be simpler.

 

[gleem]

In the decay of P-32 a neutron is converted to a proton. the mass of the neutron is higher than that of the proton by about 1.29 Mev thus more energy is available to the beta particle above the increased BE of S32 = 0.929 MeV, Of that available energy you must subtract the energy to form the beta particle 0.511 MeV

The electron KE should be the difference between the sum of the p-n mass diff + the BE diff and the mass of the beta particle. (1.29 + .929) -.511 = 1.708 MeV making allowances for some inaccuracies in the data I used.

 

[murdakah]

I see. Thanks. I know someone mentioned it earlier, but I was under the impression that the BE takes nuclear conversion into account.
Thanks guys!