Quantum numbers

Quantum numbers: These are numbers which are used to specify the location and energy of an electron and size, shape and orientation of the orbital to which a particular electron belongs.

Principal or total quantum number (n): This quantum number is identical with that used in Bohr Sommer field theory. It can have only non zero positive integral values.

i.e. n= 1, 2, 3, 4 ……….ꝏ

It quantizes the principal orbits. It controls the size of electron orbit and also controls the electron energy. The energy levels or shells of electrons are denoted by means of capital letters as indicated.

Azimuthal quantum number (ℓ). It determines the shape of electron orbits as well as the orbital angular momentum of the electron. It can have values of 0, l , 2, 3…. (n -1). Each value refers to an energy sub-shell. The second principal sub-shell or L shell will have two sub-shells. With two values of azimuthal quantum number (ℓ) they are designated as follows:

s sub-shell when ℓ = 0 , p sub-shell when ℓ =1

Magnetic orbital quantum number (m_ℓ): It is due to the quantization of the direction of orbital angular momentum and determines the exact orientation of the electron orbit in space. It can have values from ℓ to – ℓ at unity intervals i.e., ℓ, ℓ-l, ℓ-2,….1. 0-1- ….. (ℓ -l),i.e. all integral values between 0 to ± ℓ.

Magnetic spin quantum number (m_s): This number is due to the orientation of the spin angular momentum and determines the spin orientation of the electrons about their own axis. It can have only two values +½ and -½ .