Beta Decay Accounting

In beta decay, if a neutron spilts into a proton and an electron, why doen’t the mass number decrease? (because there is one less neutron). But the atomic number increases due. What happens to the electrons?
- carol (age 16)
singapore

  Hi Carol,

  The mass of the decaying nucleus does in fact decrease, but only by just a bit.  A neutron decays into a proton and an electron and an electron-type antineutrino, and the mass of a neutron is just a bit more than the mass of the proton plus the mass of an electron.  The total number of nucleons (neutrons+protons) remains the same in the interaction, and so the atomic mass remains close to what it was before.  The electron and the antineutrino carry off energy, and this is reflected in the decreased energy (and therefore mass) of what’s left.

  Not only did the neutron lose mass when decaying, but it may then be able to fall into a lower-energy state inside the nucleus.  Protons and neutrons separately obey the Pauli Exclusion Principle inside the nucleus -- you cannot put two neutrons in the same quantum state, or two protons, but you can get neutrons and protons together to fill  up their own lowest-lying energy shells.  Change one into the other and it may be able to drop down into a lower-energy state, emitting photons in the process, losing a bit more energy, and further reducing the mass of the nucleus that’s left (but only by a small fraction of its total mass). On the other hand, converting a neutron to a proton raises the electrostatic potential energy of the positively charged nucleus. The total energy involves a balance of all these effects.

A second kind of beta decay, called positron beta decay, involves emission of the antiparticle of an electron and an electron-type neutrino.  In this case, the atomic number would go up by one unit, and the mass would go down by a tiny amount.  A proton would have to turn into a neutron, which by itself would be a bit heavier, but due to the energy-level argument above, the total energy of the nucleus would be less after the decay, but only for proton-rich nuclei.  An example of an atom that does this is Na²².

The electron emitted in beta decay (not the positron kind) flies away until it crashes into something.  Sometimes this is used for pracitcal purposes.  Tritium decays via beta decay, and a tritium illumination device will have a small container of it coated on the inside with a phosphor.  The electron crashes into the phosphor and makes a little flash of light (much the way a cathode-ray television screen works).  The remaining nucleus has gained +1 unit of electric charge, and must capture an electron from somewhere.  In most circumstances, electrons can drift freely through the air and positive ions don’t last very long.  You can keep these atoms embedded in insulators (like most plastics or glass or teflon or something like that) and they will  remain positively charged for a very, very long time.

  If the nucleus of an atom changes charge in this way by beta-decaying, the electrons surrounding it change configuration.  The average radius of the orbits decreases if the charge increases, and photons are emitted as the energies shift.  When the atom captures a new electron, one or more photons are emitted as the electron fills its new state.

In positron beta decay, the positron will usually annihilate with an electron in some other atom close by, if there are any, emitting two photons of energy close to 511 KeV.  The rest of the electrons in the atom undergo a similar process -- one is lost and the orbit sizes increase.  Energy must be input in order to do this, and the energy must come out of the change in energy of the nuclear levels, which is usually much greater than the energy required to shuffle around the atomic electrons.

Tom

(published on 10/22/2007)