Quantum Numbers

Quantum Numbers: They define:

The volume of space (orbital) where there is maximum probability of finding the electrons.
The energy of each orbital
The shape of each orbital
The direction of each orbital

Principal quantum number (n): Used by Bohr in explaining the spectrum of the hydrogen atom.It describes:

The size of the principle energy level
The energy of the principle energy level
The order of the principle energy level or electron shells (7 shells in the heaviest atom)

Values of n are 1, 2, 3, 4, and so on - Cannot be zero
Every principle energy level divided into no. of energy sublevels
The number of electrons required to fill a given energy level = 2n2
Examples:

The 1st shell saturated by (2x12) = 2 electronsThe 2nd shell saturated by (2x22) = 8 electrons
The 3rd shell saturated by (2x32) = 18 electrons
The 4th shell saturated by (2x42) = 32 electrons
The 5th, 6th, 7th shells doesn't obey this law because the atom becomes unstable if no. of > 32 electrons

Subsidiary quantum number (l) (azimuthally): Shown by Summerfield when he used a spectroscope, he found that the single spectral line is indeed a number of fine spectral lines representing electron transition between very near energy levels (sublevels)It describes:

The shape of each energy sublevels within each principle energy level
The energy of each energy sublevels within each principle energy level
The number of energy sublevels within each principle energy level
The (s) orbital are spherical (l = 0)
The (p) orbital are polar (l = 1)
The (d) orbital are clover-leaf shaped (l = 2)
The (f) orbital are complicated (l = 3)

Can be any integer between 0 and n – 1 (less than n)

For n = 1, (l) can be 0 (1s)
For n = 2, (l) can be 0, 1, and 2 (2s, 2p)
For n = 3, (l) can be 0, 1, and 2 (3s, 3p, 3d)

Magnetic quantum number (m): It describes:

The orientation of each orbitals within each energy sublevel
The number of orbitals within each energy sublevel

Can be any integer between - l and + l

For s: (l) = 0 (m) = 0                                    No. of orbitals for (s) = 1
For p: (l) = 1 (m) = -1, 0, 1                          No. of orbitals for (p) = 3 (Px, Py, Pz)
For d: (l) = 2 (m) = -2, -1, 0, 1, 2                No. of orbitals for (d) = 5
For f: (l) = 3 (m) = -3. -2, -1, 0, 1, 2,3        No. of orbitals for (f) = 7

Spin quantum number (ms):
It Detect:

The direction in which the electron spin around its axis during its rotation (clockwise or anti- clockwise) in order to form 2 opposite magnetic fields to decrease the repulsion force between the 2 electrons.
It has only two possible value (+ 1/2 OR - 1/2 )