Nuclear Electron Capture Accounting

When an electron is captured by a nucleus, how is the mass number and the atomic number affected?
- KECIA D. MCCRIMAGER (age 42)
jacksonville, florida. usa

  When a nucleus captures an electron, a proton changes into a neutron, and an electron-type neutrino is emitted.  The atomic number goes down by one unit, accounting for the loss of a proton, and the total number of protons plus neutrons stays unchanged, accounting for the gain of a neutron.

  The total mass of the nucleus should go down, however, as the reaction has to be energetically possible.  Energy and mass are two names for the same thing (at rest), and to gain mass in this process would violate the conservation of energy.   To lose mass allows the neutrino to carry off some energy, or for the newly-formed nucleus to decay down to its ground state by emitting one or more photons.  Paradoxically, a free neutron has more mass than a free proton (and even more than a proton’s mass plus an electron’s mass), but the total energy of a nucleus includes binding energy and kinetic energy of the pieces, in addition to all the rest masses.  If a nucleus has lots more protons than neutrons, the protons occupy states in higher-energy shells than the highest-energy neutron.  By capturing an electron, a proton can turn into a neutron and fall down to a lower energy state, thus reducing the total mass of the nucleus (but only by a tiny bit!).  The total electrostatic energy changes a bit too due to the different number of protons.

 If a nucleus is rich in neutrons, then the lowest energy level a neutron can go into will have a high energy, and the nucleus will be unable to capture an electron.

  Tom

(published on 10/22/2007)

An electron is attracted to a hydrogen proton. It stops at N1 or N0 and "orbits", but gets no closer. What stops it from proceeding to the proton, thus creating a neutron?
- mike (age 71)
athol,idaho

The view that electrons are orbiting the positively charged nucleus is not a true story (Bohr model). So instead of viewing electrons as particles, one should treat them as waves. According to quantum theory, the position of something is described by a wave function. Its amplitude gives the probability of finding your electron at different positions with respect to the nucleus. This wavefunction is governed by the Schrödinger's famous equation, to which one should supply the potential responsible for the attractive electrostatic force between the electron in the orbital and the proton in the nucleus and then solve an eigenvalue equation to obtain the energy levels and corresponding wave(s) for each of these levels. When you do the math, it turns out that the electron is mostly excluded from the nucleus (i.e. wavefunction ~0), but not with 100% certainty. As discussed in and , this is a reflection of the uncertainty principle: compaction to the nucleus would mean very high momenta. Although proton and neutron see each other, creation of a neutron is impossible in H case, because their total mass is smaller than that of a neutron. But what you suggest occasionally occurs in larger atoms which can make up for this energy gap by changes in the total nuclear energy, and this is one of the radioactive reactions. 

Tunc

(published on 11/22/2014)