Quantum Numbers

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Key learnings:
  • Quantum Numbers Definition: Quantum numbers are defined as values that describe the location, energy level, and spin of electrons in an atom.
  • Principal Quantum Number: This number, denoted as ‘n’, represents the main energy level or shell an electron occupies.
  • Orbital Quantum Number: Also known as the azimuthal quantum number, this number, denoted as ‘l’, indicates the subshell and shape of the orbital.
  • Magnetic Quantum Number: This number, denoted as ‘m or ml’, describes the orientation of orbitals within a subshell and ranges from -l to +l.
  • Spin Magnetic Quantum Number: This number, denoted as ‘ms’, represents the spin direction of an electron and can be either +1/2 or -1/2.

Quantum numbers are like the addresses of electrons in an atom. They indicate the location, energy level, and spin of each electron, helping to define the electron configuration. There are four types of quantum numbers:

  1. Principal quantum number (n)
  2. Orbital or Azimuthal quantum number (l)
  3. Magnetic quantum number (m or ml)
  4. Spin magnetic quantum number (ms)

Principal Quantum Number (n)

The principal quantum number represents the main energy level, shell, or orbit an electron occupies. It is denoted by ‘n’ and has integral values like 1, 2, 3, 4, etc. This number is used in the Bohr and Sommerfeld atomic models.
The electrons having principal quantum number, are associated with same energy levels (shells). These energy levels are denoted by the letters K, L, M, N, ……. etc. For different energy level (shells) the value of “Principal quantum Number ‘n’ and maximum number of electrons associate with different energy levels are given in table below-

Sl. No.Energy level or Orbit (shell)Principal quantum number ‘n’Maximum Number of electrons (2n2)
1K12×12=2
2L22×22=8
3M32×32=18
4N42×42=32

As the principal quantum number increases, the distance of the shell from the nucleus also increases. Therefore, shells have different energy levels, which decrease as the quantum number increases.

Orbital or Azimuth Quantum Number (l)

Orbital or azimuth quantum number represents the subshell of orbital to which the electron is associated. The each main shell (energy level) is subdivided into sub energy levels/subshells.

These subshell are also called orbitals. These subshell /orbitals are designated by s, p, d, f, ……. etc. with corresponding orbital quantum number l = 1, 2, 3, 4……etc. The number subshells is any main shell is equal to principal quantum number ‘n’. The capacity of any main shell can be determined by adding the electron capacity of subshells. The capacity of subshells are given in table below-

Sl. No.SubshellQuantum number (l)Electron capacity of subshell 2(2l + 1)
1s12(2 × 0 + 1)=2
2p22(2 × 1 + 1)=6
3d32(2 × 2 + 1)=10
4f42(2 × 3 + 1)=14

The orbital or azimuthal quantum number represents the angular momentum and shape of the orbital associated with an electron. For example, when l = 0, the angular momentum is zero, and the orbital is a straight line. For l = 1, the orbital shape is an ellipse with some angular momentum. For l = 2, the shape becomes a more rounded ellipse with greater angular momentum.
For different values of orbital or azimuth quantum number, the shape of orbitals is shown in table below-
In electron configuration, the principal quantum number is stated just before the letter and the number of electrons with same orbital quantum number is represented as superscript of letter. For example: If an atom is having 6 electrons with principal quantum number 2 in subshell of ‘p’. Then in electron configuration it will be denoted as’2p6‘.

Magnetic Quantum Number (m or ml)

The magnetic quantum number (ml) represents the orbitals of a given subshell. For a given value of l, the value of magnetic quantum number (ml) ranges form – l to + l. For example, for p-subshell, the value of ml will be, ml = – 1, 0, + 1. The orbitals are represented as px, py and pz. Where, the subscript represents the direction of axis of rotation. For given value of l, there are 2l + 1 possible values of ml. The shell with principal quantum number of ‘n’, has n2 orbitals in that shell (energy level). For subshells the number of possible orbitals and magnetic quantum numbers are given in table below-

SubshellOrbital or Azimuthal quantum number (l)Number of Orbital
3l + 1
Magnetic quantum number (m or ml)
s010
p13(px, py, pz)-1, 0, + 1
d25 (dx2-y2, dz2, dxy, dxz, dyz)– 2, -1, 0, + 1, + 2
f37(fz3, fxz2,fxyz, fx(x2-3y2), fyz2, fz(x2-y2), fy(3x2-y2))-3, – 2, – 1, 0, + 1, + 2, + 3

Spin Magnetic Quantum Number (ms)

As the earth revolve around the sun and rotates about it axis, in similar way the electrons in atom revolves around nucleus and rotates about its axis which is called ‘Spin’ of electron. The direction of rotation (spin) of electrons about it axis is represented by “Spin magnetic quantum number”. This quantum number does not affects the energy level of electrons. The “Spin magnetic quantum number”can only have one value either + 1/2 or – 1/2. In general, the electron with ms = + 1/2 is called an alpha electron, and electron with ms = – 1/2, is called beta electron. No two paired electrons can have same spin value.

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