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What are Quantum numbers ?

Quantum numbers – Definition

A set of numbers used to describe an electron completely in an atom are called quantum numbers. Quantum numbers are used to explain the position and energy of electron in an atom. There are four types of quantum numbers.

  1. Principal quantum number
  2. Azimuthal quantum number
  3. Magnetic quantum number
  4. Spin quantum number

Principal quantum number :

The principal quantum number was introduced by Neils Bohr. It reveals the size of the atom. With the increase in the value of ‘n’ the distance between the nucleus and the orbit also increases.

It is denoted by the letter ‘n’. It can have any simple integer value 1,2,3, …. but not zero. These are also termed as K, L, M, N etc.

The radius and energy of an orbit can be determined basing on “n” value.

The radius of nth orbit is 

r_{n} = \frac{n^{2}h^{2}}{4\pi^{2} me^{2}}

The energy of nth orbit is E_{n} = \frac{-2\pi^{2} me^{4}}{n^{2}h^{2}}

Azimuthal quantum number :

It was proposed by Sommerfield. It is also known as angular momentum quantum number or subsidiary quantum number.

It indicates the shapes of orbitals. It is denoted by ‘l’. The values of ‘l’ depend on the values of ‘n’. ‘l’ has values from’0’ to (n – 1) i.e., l = 0, 1, 2, …..(n – 1). The maximum number of electrons present in the subshells s, p, d, f, are 2, 6, 10, 14 respectively.

Magnetic quantum number :

It was proposed by Lande. It shows the orientation of the orbitals in space. ‘p’ – orbital has three orientations. The orbital oriented along the x-axis is called p_{x} orbital, along the y-axis is called p_{y} – orbital and along z- axis is called p_{z} orbital. In a similar way d – orbital has five orientations. They are d_{xy}d_{yz}d_{zx}d_{x^{2}-y^{2}} and d_{z^{2}}. It is denoted by ‘m’. Its value depends on azimuthal quantum number. ‘m’ can have all the integral values from –l to +l including zero. The total number of ‘m’ values are (2l + 1).

Spin quantum number :

It was proposed by Uhlenbeck and Goudsmit. It is denoted by “s”. It shows the spin of the electron, whether it is spinning clockwise direction or anticlockwise direction. If the spinning is clockwise, s value is +\frac{1}{2} and if it is anticlockwise the value of s is -\frac{1}{2}.

The direction is also represented by arrows \uparrow for clockwise and \downarrow for anticlockwise direction.

Electrons spinning in the same direction are said to have parallel spins \upuparrows or \downdownarrows. When spins are opposed they are said to be paired up or antiparallel spin \upharpoonleft\downharpoonright.