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Q: Mass in Beta - Decay ( Answered,   1 Comment )
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 Subject: Mass in Beta - Decay Category: Miscellaneous Asked by: puzzledoldman-ga List Price: \$25.00 Posted: 04 Aug 2003 05:52 PDT Expires: 03 Sep 2003 05:52 PDT Question ID: 238805
 ```Using the word mass in its invariant form, rather than its relativistic form, what are the best current estimates of the masses of the neutron and of the proton, electron, and anti-neutron into which the neutron is believed sometimes to disintegrate?```
 ```Hi, puzzledoldman-ga: By "invariant form" of mass, I suspect you mean the "rest mass" of a particle, which is independent of its velocity ("relativistic form" ?). On the other hand perhaps you are asking for the mass of the particles to be given in "grams" rather than in millions of electron volts, which might be another meaning of "relativistic form". I'll try to accomodate both points. The beta-decay of a free neutron produces: - a proton - an electron (or "beta" particle) - an (electron) anti-neutrino through a "weak interaction". See here: [Decay of the Neutron] http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c4 The neutron is a baryon, like the proton, and an electron is a lepton with lepton number 1. The presence of all three particles in the "yield" provides for conservation of both baryon number (1 in, 1 out) and lepton number (because the lepton number of the electron anti-neutrino is -1). [Physical Constants and Conversion Factors] http://newton.ex.ac.uk/research/semiconductors/theory/collabs/constants.html The rest mass of the neutron is experimentally determined to be: mass of neutron = 1.6749286(10)e-24 gram The rest mass of the proton is experimentally determined to be: mass of proton = 1.6726231(10)e-24 gram The rest mass of the electron is experimentally determined to be: mass of electron = 9.1093897(54)e-28 gram Experimental determination of the rest mass of the electron anti-neutrino has proven to be a difficult and perhaps profound issue. All known experimental evidence is consistent with a zero rest mass for the electron neutrino (equiv. for the electron anti-neutrino), but a tiny mass on the order of 1eV or 1.78e-33 gram has not yet been excluded. For links to papers on measurements of neutrino masses, see here: [Neutrino Mass - Direct Measurement] http://www.to.infn.it/~giunti/NU/Neutrino_Mass/ On theoretical grounds it is believed that observations of "oscillation" between flavors of neutrinos, which are thought to be three (electron, muon, tau), show that some (presumably all) of the flavors have mass: [Neutrinos Have Mass] http://focus.aps.org/story/v2/st10 Please advise me if further clarification would be useful. regards, mathtalk-ga``` Clarification of Answer by mathtalk-ga on 04 Aug 2003 19:57 PDT ```Search Strategy Keywords: "neutron decay" ://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22neutron+decay%22&btnG=Google+Search Keywords: "mass of electron" ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=%22mass+of+electron%22&btnG=Google+Search Keywords: "mass of neutrino" ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=%22mass+of+neutrino%22&btnG=Google+Search Keywords: "mass equivalent" eV ://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22mass+equivalent%22+eV&btnG=Google+Search Keywords: "massless neutrinos" oscillation ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=%22massless+neutrinos%22+oscillation&btnG=Google+Search``` Request for Answer Clarification by puzzledoldman-ga on 04 Aug 2003 20:11 PDT ```Thanks, very helpful. But if the masses are invariant how come the sum of the resulting proton and electron masses isn't about equal to the mass of the neutron? Does invariant mean invariant only with respect to velocity?``` Clarification of Answer by mathtalk-ga on 04 Aug 2003 20:32 PDT ```Hi, puzzledoldman-ga: Yes, the mass of the proton plus the mass of the electron is "about" equal to the mass of the original neutron (note the powers of 10 involved). See the discussion on the link [Neutron Decay] given above. The difference is made more meaningful by converting the mass to the equivalent energy units (E = mc² and all that): mass of neutron --> 939.5656 MeV mass of proton --> 938.2723 MeV mass of electron --> 0.5110 MeV which, after subtractions, leaves 0.7823 MeV unaccounted for by the masses of the proton + electron. The same site goes on to explain that if only those two particles were being produced, then their kinetic energy and momentums would be very constrained. Experimental observation, however, showed that the actual distribution of energy and momentum of the electron was a smooth, continuous one, and that at the peak the electron's (relativistic) kinetic energy would account for essentially all of the "lost energy". These facts could only be explained by the presence of a third particle, without charge and (within observable limits) without mass: "The mysterious particle was called a neutrino, but it was twenty five years before unambiguous experimental observation of the neutrino was made by Cowan and Reines." Today we call that particle an electron anti-neutrino, meaning that it's in the electron family of leptons and an anti- particle so that the lepton numbers 1 for the electron and -1 for the electron anti-neutrino cancel out to conserve the total lepton number (which was 0 for the original neutron). regards, mathtalk-ga``` Request for Answer Clarification by puzzledoldman-ga on 05 Aug 2003 11:05 PDT ```For mathtalk-ga Thanks for the references. Since the missing mass after disintgration exceeds the mass of the electron I guess I'll have to remain somewhat puzzled about the meaning of invariant mass. PuzzledOldMan``` Clarification of Answer by mathtalk-ga on 05 Aug 2003 20:35 PDT ```Hi, puzzledoldman-ga: It is tempting to say that the "lost" mass of the neutron (after that of the proton, electron, and anti-neutrino are consider) is converted into "kinetic energy" of those emitted particles. This has the germ of the right idea but is not fully accurate, since there is a total combination of energy due to a particle's momentum as well as its mass equivalent. So let me drop back a bit and try to give a more complete picture. The old law of conservation of mass was replaced under Einstein's theory of special relativity by conservation of mass-energy, whose equivalence is given by the well-known formula E = mc². For background definitions, see this: [Theory of Special Relativity] http://www2.slac.stanford.edu/vvc/theory/relativity.html You will not find there any reference to "mass in its invariant form", but you will find mention of the mass of an object at rest ("rest mass") and how this is related to the "total energy" E of a freely moving particle. The formula is: E² = (mc²)² + (pc)² where m is the "rest mass", c is the speed of light, p is the momentum: p = mv/SQRT(1 - (v/c)²) taking into account the particle's relativistic mass when v is the particle's velocity. With a little algebra one more simply say that total energy is: E = Mc² where M = m/SQRT(1 - (v/c)²) is the particle's relativistic mass. Note that the first equation gave a formula for the energy squared, E². An intuitive (but incorrect) guess would be that E could be expressed simply as a sum of the particle's rest mass energy equivalent plus the particle's "kinetic energy", familiar from Newtonian mechanics as (1/2)mv². But although things are not so intuitive, the mathematics of the above is elegant in unifying the correct relativistic computations with Newtonian formulas in the limiting case of comparatively slow velocities v (i.e. compared to the speed of light). What I'm trying to say is that the missing mass from the beta decay is fully accounted for by the momentum of the particles yielded, especially that of the electron and the electron anti-neutrino. As mentioned earlier, the experimental measurement of the electron's momentum shows that it varies smoothly over a range, with a maximum equal to the entire 0.7823 MeV of missing mass energy equivalent. The smoothness of the distribution beneath this shows that the electron anti-neutrino may (randomly) carry of a certain portion of the energy release through its momentum. If the total energies of proton, electron, and electron anti-neutrino are combined, then the total energy of the original neutron is entirely accounted for. Perhaps you have doubts that a portion of the original neutron's rest mass, which I think you consider "mass in its invariant form", can be converted into energy. Yet this is precisely what happens with beta decay, as also with the fission decay of unstable isotopes. In a real sense the strong forces that bind baryons (neutrons and protons) together in the nucleus of atoms of a stable isotope inhibit the spontaneous decay of neutrons that would otherwise take place fairly quickly, were neutrons to be freed from the nucleus. regards, mathtalk-ga```
 ```What does that means in physics? Modern physics equations are formulated so that they are valid in all frames of references. We can transform the quantities from one frame of reference into another, e.g. into one which is moving with respect to the former. The laws of transformation are different in Newtonian and Relativistic physics. (Both sets of equations are invariant these days. It was not so when people were still arguing about heliocentric vs.geocentric models). In Newton's universe the masses before and after an event add up to the same number. In this sense mass is conserved, and is also truly invariant, i.e. same in all frames. Better way to say it, mass is a scalar. So is Energy . Both are conserved. Event may be collision, disintegration, etc. In Einstein's universe it is more complex. There are quantities which are conserved, and some of them are scalars, e.g. the lepton and barion numbers mathtalk is talking about. Some are vectors, and they have a complex law of transformation. Since classical physics approximates relativity in same cases, we can point out a quantity which has some properties of classical mass and energy. This, this correspondence, is source of a lot of semantic confusion you see on the Internet. Mass, or more exactly mass-energy is not a scalar in this aproximation or analogy. In the context of your question it means: there is no single-number-quantity, which you can add (for all particles in the event) and get same value, before and after the event, in any frame. In other words, there is no exact equivalent of scalar mass in relativity. There are many quotes about Internet. One cartoon says 'On Internet no one knows you are a dog' (or a hedgehog :-) I would add to the collection, the following: "On Internet, everybody understands relativity. But many understand it differently than most textbooks." If you are seriously interested, you may ask for recommended reading, to cover the area of interest at an appropriate level of complexity. This is just a free comment. It recommends a critical, skeptical approach to what you read. Particularly when it is on the Internet, and for free.```