# Can an electron in an atom have insufficient energy to achieve an energy level, or orbital, and what happens to this electron when this occurs?

If a nucleus undergoes a change in Z or Mass due decay or absorption, could this disrupt the electrons from their orbital/shell energy levels?

If so, could the electrons that were previously in the original orbitals have insufficient energy for the new orbitals?

What would happen to these electrons if this occurs?

For example:

• Could the electrons formerly in the k shell or s1 orbitals have insufficient energy to remain in those orbitals after a change in the nucleus?
• What happens to them if this occurs since there is no lower energy orbital for them to enter but they remain trapped in the potential well?
• Would they remain in an unstable state (i.e. not in a stable orbital) or reacquire the energy level due to rearrangement of other atomic states?
• I suppose higher energy level electrons would also not move to the new energy level due to shielding of the lower ones, even if they were not in a stable orbital?
• If these electrons are in an unstable state, would they remain paired as in the original orbitals?
• The reaction can't proceed if there is zero phase space for the final state... – dmckee --- ex-moderator kitten Jul 15 '15 at 23:15

You can also easily show this by considering the energy functional under the sudden approximation. We have a Hamiltonian $H_0$ and a Hamiltonian $H_1$ with changed parameters, correspondingly we have two functionals $E_0$ and $E_1$. The electrons be in a state $\left|\psi\right>$ prior to the change of parameters. The sudden approximation says, that the electronic configuration remains $\left|\psi\right>$ during the decay/capture, so the energy afterwards will be $E_1[\left|\psi\right>] \ge E_1^\text{ground}$ which is greater than the ground state energy after the parameter change, so the energy of the electron configuration will be greater than the lower bound in all cases.