The Physics that deals with subatomic particles is known as Quantum Mechanics. The basic solutions obtained are:

• The orbital of the electron in an atom is defined by a set of parameters known as Quantum Numbers (QN);    n, l, m and s.
• The values allowed are:
  • n can only take the values of 1, 2, 3, 4, etc. (that is positive integers)
  • l can only take the values of 0, 1, 2, 3, 4, etc, but it must be less than n.
  • m can only take the values of 0, ±1, ±2, ±3, etc, but must not be greater than l, though it can be equal to it.
  • s can only take the values of ±½.

Let us try to apply the results. We will start with n=1. Then there is only one value possible for l and m. That is:    l=0, m=0, and s=±½. The orbitals obtained would be    (n=1, l=0, m=0, s=½) and (n=1, l=0, m=0, s= -½). These are then the orbitals for the electrons in the helium atom, which has 2 electrons.

When n=1 and l=0 the orbital is known as 1s. So the electron configuration of the helium atom is given by:    He: 1s²    The superscript "2" is to denote that there are two electrons in the 1s orbitals, one with s=½ and the other with s= -½.

Tutorial 1

Construct the electron configurations for neon and argon.    Answer

This defines the region in space where you can find the electron. This is the greatest revelation of the Quantum Theory as compared to Bohr's atom. The electron is no longer considered a particle circling the nucleus like the earth around the sun. When l=0 the area where you can find the electron is a spherical region around the nucleus. When l=2, the area is in the shape of a cone around a certain axis. (Orbitals)

Magnetic Quantum Number, m

This defines the orientation of the orbital in space (under the influence of a magnetic field).

In our discussion we have not considered the value of m. If l=0, then the value of m can only be 0. But if l=1, then the value of m can be 1, 0, or -1. So we actually have three sets of orbitals. Referring to their orientation in space we named them p_x, p_y, p_z.

W. Pauli

Spin Quantum Number, s This defines the direction of rotation of the electron particle about its axis. They can only spin in opposing direction, i.e. s=±½. This is a contribution from Wolfgang Pauli, and is now known as the "Pauli Exclusion Principle", which states that no two electrons may have identical set of four quantum numbers.

SHELL

The energy of the orbital is defined by the Principal Quantum Number. In the initial study mathematicians gave the name K when they were trying to solve the energy for n=1. (just like we would use "x" in any equation we try to solve.) From here on we are stuck with the name K-shell for the energy of the electrons in the orbital when n=1. The mathematicians continued to name the successive shells L, M, etc. The last level was Q.

ABNORMALITY

If course the Quantum Mechanics for an actual atom is difficult to work with so the mathematicians used a hypothetical hydrogen atom (or hydrogen-like atom). For example a hydrogen atom with the electron in n=2.

However in real atoms for n=2, m=1 (i.e. 2p) there must be electrons in n=2, m=0 (i.e. 2s orbitals). 2s orbitals are closer to the nucleus than the 2p orbitals. This will affect their energy. As expected the 2s in the L shell actually has a "slightly" lower energy level than the 2p orbitals.

THE d ORBITALS

When n=3, l can also take the values of 2 as well. This will be discussed when we come to the transition elements. So be patient. All you need to know (to make this topic complete) is that the set of quantum numbers will be (n=3, n=2, m={2, 1, 0, -1, -2}). The orbital is known as d, and the shell M.

Again the 3s, 3p, and 3d orbitals, even though they are known to be in the M shell, do not have the same energy.

Tutorial 2

Construct the electron configurations for Krypton.
Present the energy of the 3s, 3p, and 3d, in increasing order.    Answer