Moseley's Law Conceptual Question From Young & Freedman, Univ. Phys. p. 1394 about Moseley's law:

Suppose one electron is knocked out of the K shell. This process leaves a vacancy, which we’ll call a hole. (One electron remains in the K shell.) The hole can then be filled by an electron falling in from one of the outer shells, such as the L, M, N, ... shell. This transition is accompanied by a decrease in the energy of the atom (because less energy would be needed to remove an electron from an L, M, N, Á shell).

I don't quite get why there is a decrease in the energy of the atom. Can someone explain to me please? 
 A: Morsley's experiment was based on Bohr's atom model, it showed that the value of the nuclear charge increased by one, as the atom's place increases across the periodic table.  
The method was to knock out an electron, and look for the emmission-spectrum as another electron fell from the outer shell to the inner one.  This would produce a hydrogen-like spectrum.
The incoming x-ray is converted into kinetic energy as it knocks the electron out of the K shell.  You don't see this in the emmission spectrum,  the energy is variously lost as heat.
What you do see is the outer electron falling into the inner shell, producing a outbound photon.  These photons has a characteristic hydrogen-like spectrum, based on the departing orbit and the arriving orbit.  This is because it requires more energy to keep an electron in an outer shell, than an inner one.  
But the outer shells are occupied, because electrons obey the fermi-dirac statistics, which means there can only be one electron in any given state.  This is why, for example, all orbitals fill up with exactly two (one spin-up and one spin-down) electrons.  The fall of the electron from an outer shell to an inner shell, releases a photon, which shows in the emission spectrum.
A: The transition of an outer shell electron to the K shell is accompanied by a decrease in the energy of the atom because the process brings opposite charges (the electron and nucleus) closer together. The system has lower electric potential energy. There is also a change (an increase) in the kinetic energy of the electron, but overall the system decreases in energy.
