PENETRATION AND SHIELDING

Electrons are negatively charged and are pulled pretty close to each other by their attraction to the positive charge of a nucleus. The electrons are attracted to the nucleus at the same time as electrons repel each other. The balance between attractive and repulsive forces results in shielding. The orbital (n) and subshell (ml) define how close an electron can approach the nucleus. The ability of an electron to get close to the nucleus is penetration.

Coulomb's Law (an analogy with classical physics) can be used to describe the attraction and repulsion between atomic particles:

The force that an electron feels is dependent on the distance from the nearest charge (i.e., an electron, usually with bigger atoms and on the outer shells) and the amount of charge. More distance between the charges will result in less force, and more charge will have more force of attraction or repulsion.

In the simplest case, every electron in an atom would feel the same amount of "pull" from the nucleus. For example, in Li, all three electrons might "feel" the +3 charge from the nucleus. However, this is not the case when observing atomic behavior. When considering the core electrons (or the electrons closest to the nucleus), the nuclear charge "felt" by the electron (Effective Nuclear Charge (Zeff)) is close to the actual nuclear charge. As you proceed from the core electrons to the outer valence electrons, Zeff falls significantly. This is because of shielding, or simply the electrons closest to the nucleus decrease the amount of nuclear charge affecting the outer electrons. Shielding is caused by the combination of partial neutralization of nuclear charge by core electrons, and by electron-electron repulsion.

The amount of charge felt by an electron depends on its distance from the nucleus. The closer an electron comes to the nucleus, or the more it penetrates, the stronger its attraction to the nucleus. Core electrons penetrate more and feel more of the nucleus than the other electrons.

Where,

• Z is the charge of the nucleus (i.e., number of protons)

• e is the charge of an electron or proton

• r is the radius, or distance between the proton and the electron

Penetration and shielding result in an Effective force (Feff) that holds the outer electrons to the atom, akin to Equation 2, but with Zeff substituted for Z: