Each orbital, where an electron moves, differs in its energy and shape. The energy levels of orbitals can be represented using discrete set of integrals and half-integrals known as quantum numbers. There are four quantum numbers used to define a wave function.
Principal Quantum number
The first quantum number that describes an electron is the Principal quantum number. Its symbol is n. It specifies the size or order (energy level) of the number. As the value of n increases, the average distance from electron to nucleus also increases, as well, the energy of the electron also increases. The main energy level can be understood as a shell.
Angular Momentum Quantum number
This quantum number has l as its symbol. This l indicates the shape of the orbital. It ranges from 0 to n-1.
l = 0, 1, 2 …n-1
For the first shell, n = 1.
i.e., for n-1, l = 0 is the only possible value of l as n = 1.
So, then l = 0, it is called as S orbital. The shape of S is spherical. The following figure represents the shape of S.
Description: Spherical
If n = 2, then l = 0, 1 as these are the two possible values for n = 2.
We know that it is S orbital for l = 0, but if l = 1, it is P orbital.
The P orbital where the electrons are more likely to find is in dumbbellshape. It is shown in the following figure.
Description: Dumbbell
Magnetic Quantum number
This quantum number is denoted by ml which represents the orientation of an orbital around the nucleus. The values of ml depend on l.
ml=∫(−lto+l)ml=∫(−lto+l)
For l = 0, ml = 0 this represents S orbital.
For l = 1, ml = -1, 0, +1 these are the three possible values and this represents P orbital.
Hence we have three P orbitals as shown in the following figure.
Description: Orbitals
Spin Quantum number
This is represented by ms and the electron here, spins on the axis. The movement of the spinning of electron could be either clockwise or anti-clockwise as shown here under.
Description: Spin Quantum Numbe
The possible values for this spin quantum number will be like,
ms=+12upms=+12up
For a movement called spin up, the result is positive half.
ms=−12downms=−12down
For a movement called spin down, the result is negative half.
These are the four quantum numbers.
According to Pauli Exclusion Principle, no two electrons in an atom can have the same set of four identical quantum numbers. It means, if any two electrons have same values of n, s, ml (as we just discussed above) then the l value would definitely be different in them. Hence, no two electrons will have same energy.
Electronic shells
If n = 1 is a shell, then l = 0 is a sub-shell.
Likewise, n = 2 is a shell, and l = 0, 1 is a sub-shell.
Shells of electrons corresponding to n = 1, 2, 3….. are represented by K, L, M, N respectively. The sub-shells or the orbitals corresponding to l = 0, 1, 2, 3 etc. are denoted by s, p, d, f etc. respectively.
Description: Electronic Shells
Let us have a look at the electronic configurations of carbon, silicon and germanium (Group IV – A).
Description: Groups
It is observed that the outermost p sub-shell in each case contains only two electrons. But the possible number of electrons is six. Hence, there are four valence electrons in each outer most shell. So, each electron in an atom has specific energy. The atomic arrangement inside the molecules in any type of substance is almost like this. But the spacing between the atoms differ from material to material.
In gaseous substances, the arrangement of molecules is not close. In liquids, the molecular arrangement is moderate. But, in solids, the molecules are so closely arranged, that the electrons in the atoms of molecules tend to move into the orbitals of neighboring atoms. Hence the electron orbitals overlap when the atoms come together.
Due to the intermixing of atoms in solids, instead of single energy levels, there will be bands of energy levels formed. These set of energy levels, which are closely packed are called as Energy bands.
Valance Band
The electrons move in the atoms in certain energy levels but the energy of the electrons in the innermost shell is higher than the outermost shell electrons. The electrons that are present in the outermost shell are…
The gap between valence band and conduction band is called as forbidden energy gap. As the name implies, this band is the forbidden one without energy. Hence no electron stays in this band. The valence electrons, while going to the conduction band, pass through this.
The forbidden energy gap if greater, means that the valence band electrons are tightly bound to the nucleus. Now, in order to push the electrons out of the valence band, some external energy is required, which would be equal to the forbidden energy gap.
The following figure shows the valance band, conduction band, and the forbidden gap.
Description: Forbidden Gap
Depending upon the size of the forbidden gap, the Insulators, the Semiconductors and the Conductors are formed.