How does electron capture work?
The electron combines with a proton to make a neutron and emits an electron neutrino.
The captured electron often comes from the K-shell because those electrons are closest to the nucleus. The atom stays neutral in charge, but it now exists in an excited state. The inner shell is missing an electron.
An outer shell electron then drops to a lower energy level to replace the missing electron. The excess energy leaves as an X-ray photon and a neutrino.
Many people omit the neutrino in the equation, because it has no mass or charge. All it does is carry away excess energy.
Another electron may absorb excess energy and leave the atom. We call this ejected electron an Auger electron after one of its discoverers, Pierre Victor Auger. (We pronounce the name as "oh zhay", not "aw ger).
Often the nucleus exists in an excited state as well and emits a gamma ray as it transitions to the ground state of the new nuclide.
One example of electron capture involves beryllium-7.