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Name: Juergen
Status: student
Grade: 9-12
Country: Australia
Date: Winter 2013-14


Question:
Found this response to a previous question,

"This is a very complicated question with no simple "hand-waving" answer. In energy units (using E = mc^2), the masses are: Proton: 938.272 MeV, neutron: 939.566 MeV, mass difference = 1.293 MeV, electron: 0.511 Mev.

It is tempting to say that a neutron consists of a proton plus an electron; the mass of the electron would make up 40% of the mass difference. This argument is totally invalid. It would be equally valid to say that a proton consists of a neutron plus a positron (a positron has exactly the same mass as an electron, but is positively charged). The validity of using this argument in both directions is strengthened by the fact that neutrons in neutron rich nuclei beta decay into an electron and a neutrino while protons in proton rich nuclei beta decay into a positron and a neutrino. For example a N13 (nitrogen 13) nucleus decays into C13 (carbon 13), a positron, and a neutrino with the release of 2.221 MeV.

The charge of the proton adds some electromagnetic energy to the proton mass, but the magnitude of that effect is not only impossible to calculate, but works in the wrong direction.

Quarks give the best chance to explain the proton-neutron mass difference by "hand-waving". A proton consists (mainly) of two up quarks and one down quark. A neutron consists (mainly) of one up quark and two down quarks. Current estimates are that the up quark has a mass in the range 2-8 Mev and the down quark 5-15 MeV. So replacing one up quark in the proton by a down quark would increase the mass by something between -3 MeV and +13 MeV. Clearly this is not a precise calculation, but it is (mostly) in the right direction and could overcome the electromagnetic contribution and produce the correct answer. There are other known contributions to these masses including interactions with the weak and strong interactions, but this is probably already more than you want to know about this subject! Best, Dick Plano, Professor of Physics emeritus, Rutgers University" *** If neutrons in neutron rich nuclei, beta decay into an electron and a neutrino, then why is it that neutrons are not partially comprised of electrons?

Replies:
Hi Juergen,

Thanks for the question. Yes, a neutron in neutron-rich nuclei does decay into an electron and a neutrino. To be precise, the neutrino is an anti-electronneutrino. An example of this type of decay is the decay of 14C into 13N and an electron. Here is a neat way of arguing against the idea that a neutron consists of a proton and an electron. We'll use the Heisenberg Uncertainty Principle (the HUP). The HUP states that the uncertainty of the position (deltax) multiplied by the uncertainty in the momentum (deltap) must be greater than h/(4*pi) where h is Planck's constant and pi is the usual 3.141592654... . I'll sketch out how to do the calculation and let you plug in the numbers. (Of course, you can email me back with your work and I'll be happy to look it over.) Solve the inequality for deltap. Now, the value of deltax has to be about the diameter of a neutron. Look up this value and plug it in for deltax. Now calculate a lower limit for deltap. Note that E=p^2/(2*m) where E is the energy, p is the momentum and m is the mass. Plug in deltap for p and the electron mass for m in the above expression. So you can calculate what the energy of the electron should be if it is confined in a neutron. Now, think about the value you get for E and how it compares to the masses of the proton, neutron, and electron. You'll see that it is not possible energetically for the electron to be confined in the neutron.

I hope this helps. Thanks Jeff Grell


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