Therefore in this scenario, the ease at which an electron is removed is just a question of energetics. To determine, which electron requires the most energy for its removal, we must consider the forces acting on it. The repulsive forces that prevent an electron from collapsing into the nucleus originate from quantum mechanics, and it is they that are responsible for the energy levels in atoms. However it is the attractive forces that have to be overcome and these are purely electrostatic, arising from the opposite charges of the nucleus (positive) and the electron (negative). An electron in a lower energy level is both closer to the nucleus and has fewer electrons between itself and the nucleus. The former is important because the force between two charged particles is proportional to 1/r^2 where r is the distance between then. The latter is important because the negative charges of the electrons shield (or partially cancel out) the positive charge of the nucleus.
The energy required to remove an electron is the net attractive force integrated with respect to the distance from the nucleus. For a second level electron as compared to a third level electron, the average force experienced and also the distance for which the electron has to move against that force (until the force becomes negligible) are both larger. Therefore it takes more energy and is harder to remove.
Another way to remove electrons though is through photo ionization and this allows you to remove more strongly bound electrons first. Any electron can be removed providing the energy required is less than the photon energy. You could thus conclude that depending on your photon source, it should never be harder to remove a more weakly bound electron. However this is not necessarily so. The probability of ejecting particular electrons depends on how strongly the photons interact with particular electron orbital. A very high energy photon source (eg. Xrays) has a very short wavelength and will actually interact preferentially with the inner electrons whose orbital size is smaller.
Answered by: Stuart Taylor, Chemistry Graduate Student, Oxford University, UK
Electrons occupy different energy levels, given by the principal quantum number "n", and their orbits have different shapes, defined by the secondary quantum number l, and orientations, defined by the magnetic quantum number m.
The principal quantum number tells us how far from the nucleus a certain electron is, i.e. what level it occupies, the greater is n, the farther it is from the nucleus.
The extent to which an electron feels the positive charge of the protons of the nucleus around which it "rotates" is directly related to the atom's electronegativity, i.e. to the energy needed to let an electron escape from the nucleus it belongs to.
The greater the electronegativity, the higher the energy needed to take the electron out of the nucleus' electric field. Likewise, the closer an electron is to its nucleus, the harder it will be to remove it from the atom because the electronegativity of the atom is greater.
Now, if an electron is on the third level it is first of all farther from the nucleus than on the second level and, moreover, it will be shielded from the positive charge of the protons at the first and second levels and thus it will be easier to remove it from the atom than it would be to remove an electron from the second level.
Funnily enough gold is that colour because of a trick played by its lowest spherical level electrons which are 20% closer to the nucleus than they are expected to be, and thus all electrons at the higher levels are, in turn, closer so that light hitting gold is reflected with the particular golden colour.
Answered by: Roberto Ruggiu, M.S., Free-lance scientific consultant
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'