# Effect on electron shells energy levels during nuclear decay

First thanks for this great site.

I was recently looking at photon emission from electron transitions from excited electron states in atoms. For simplicity I was using the Rutherford Bohr Model and the Rydberg equation for the transfer. I then wondered what would happen to the energy levels in the case of an atom in ground state that undergoes some kind of Nuclear decay and if any corresponding transition in electron energy level would occur and if so what kind of photon if any would be released from such a transition. I appreciate that the Rutherford Bohr model might be too simple in this case but similar changes in energy level would be expected I suppose even for more quantum mechanical models based on the scrodinger equation etc.

Is the effect nuclear decay invisible to the electrons in their specific orbital energy levels? If not what happens as the result of the change? Would a photon be released as a result of the change in energy of the orbital or shell. For example the s1 orbital or k shell energy.

For example in Beta- decay a nucleus would change by Z+1 due to a neutron change to proton. The resulting electon orbital energy levels should then be slightly different due to the change in Z. Would a photon be released due to changes in the electron orbital energy in this case or would it be transparent or absorbed elsewhere in other state reconfiguration?

In neutron emmission decay there would be no change in Z but the reduced mass of the electons will change, that would have a small effect on the energy levels of the electon orbitals. Would this result in a transition between the old and new energy level and corresponding photon emission?

Update: for an initial simple example in the case of of beta decay if we ignore the effect of reduced mass of the electron and other fine structure effects and just consider the change in Z according to the Bohr model. If we consider Tritium decay by Beta - decay to Helium 3, the Z will increase by + 1 the energy level of the k shell n = 1 will be E = -13.6 eV * (Z squared). For Tritium this would Be -13.6 eV, for Helium 3 this would be -54.4 eV.

a) Would this change be visible to the electron and cause a release of photon of 37.8 eV due to the change?

Or

b) would this change be invisible to the electron due to the orbital energy being relative to the nucleus rather than outside the atom?

If ) b is the case would there nevertheless be more subtle changes in energy in the electron that would release a low level photon due to:

I) changes in potential II) change from Hydrogen type atom to Helium type atom. III) change in reduced mass of the electons in the orbitals. IV) change in spin state of the nucleus.

This would certainly result in a change in energy levels if the nucleus changes charge; in addition, you would expect a electron ejected as well to remain overall neutral (though there are some stable ions). The simplest quantum model that would give you an idea of the energy changes for an atom are described by so-called "Hydrogen-Like" atoms. The expression for the energy levels goes like ~$Z^2$.

• Thanks anono9090 for your comment it helps put my question into context which helps alot. I'm actually more wondering about the photon emissions from the electron she'll energy change. See my reply to Bill N below. Jul 9, 2015 at 6:26

Would a photon be released due to changes in the electron orbital energy in this case or would it be transparent or absorbed elsewhere in other state reconfiguration?

If something causes a vacancy in an electron inner shell, there can be a photon emitted. Two processes related to nuclear decay in which this often happens are electron capture and internal conversion.

In electron capture, an inner shell electron is captured by the nucleus and the atomic number goes from Z to Z-1 while A stays the same. Consequently, the electron energy levels shift, and an electron from an outer shell transitions to the inner shell vacancy, usually resulting in the emission of an x-ray. The x-ray is characteristic of the daughter element.

Internal conversion is a process which happens after a radioactive decay leaves the daughter nucleus in an excited state (but the electron energies have adjusted). Instead of the usual gamma-ray emission from the nucleus, an inner shell electron is ejected with an energy equal to the gamma transition minus the electron binding energy. Then an upper shell electron transitions to the vacancy with a resulting x-ray emission.

It is even possible that instead of the x-rays mentioned above, another electron could be ejected from another shell. This is known as an Auger electron (pronounced "oh-zhay").

• Thanks Bill N for your reply, it helps put my question into context which I appreciate a lot. I'm actually more wondering about from photon emission due to to the change in a particular electron orbital resulting from the change in the Nucleus. For example the electron k shell energy level should change slightly due to the change in the nucleus. Would this small change in k shell energy for example result in low energy photon emission. Jul 9, 2015 at 6:23