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

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Discussion Overview

The discussion revolves around the relationship between the maximum energy of beta particles (Emax) and the Q value in beta decay processes. Participants explore the implications of energy conservation, the definitions of binding energy, and the calculations involved in determining these values, with a focus on specific isotopes like P-32 and Te-127.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants question why Emax appears larger than Q, suggesting this could imply a violation of energy conservation unless binding energies are averaged values.
  • Others argue that the Q value is defined as the difference between incoming and outgoing masses, and it should be at least equal to the maximum beta energy, factoring in nuclear recoil.
  • One participant points out that for the decay of P-32 to S-32, the Q value is 0.929 MeV, while the maximum beta energy is reported as higher, raising questions about the interpretation of binding energy changes.
  • There is a discussion about the meaning of "change in binding energy," with some suggesting it relates to the conversion of protons to neutrons in beta decay.
  • Another participant emphasizes that Q should be considered as the difference between total energies, not just binding energies, and notes the need to account for the kinetic energy of emitted particles.
  • One participant provides a calculation involving the mass difference between neutrons and protons, suggesting that the energy available to the beta particle exceeds the binding energy difference.
  • There are inquiries about the discrepancies in a referenced table regarding binding energies and beta energies for certain isotopes.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of Q and binding energy, with no consensus reached on the relationship between Emax and Q or the interpretation of the data presented.

Contextual Notes

Participants highlight potential ambiguities in definitions and calculations, particularly regarding the treatment of binding energies and the kinetic energy of beta particles. The discussion reflects varying interpretations of the same data and concepts.

murdakah
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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
 
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murdakah said:
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.
 
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.
 
The change in binding energy is not Q.
 
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?
 
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?

mfb said:
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?
 
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.
murdakah said:
Now how can the energy released be any greater than that if the atoms are stationary?
It cannot.
murdakah said:
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.
 
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.
 
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.
 
  • #10
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!
 

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