Quantum Numbers

Quantum Numbers

What are Quantum Numbers?

Quantum numbers are basically those numbers which help us in describing the orbital occupied by an electron.

It tells us the following four things:

  • The distance of the electron from the nucleus.
  • The shape of the orbital
  • The position of the orbital
  • The spin of an electron

There are four quantum numbers that help us to describe the location and behavior of an electron. They are:

  • Principal Quantum Number
  • Angular Quantum Number
  • Magnetic Quantum Number
  • Spin Projection Quantum Number

Principal Quantum Number

The first is the principal quantum number (n) which describes the main energy level and size of an orbital i.e. the distance of the orbital from the nucleus. It is also referred to as a shell and the number of orbital in a shell and is given by n2.

Angular Quantum Number

The second is named as the azimuthal quantum number and also known as orbital angular momentum is denoted by l. It describes the shape and the type of orbital. There are 4 types of orbitals i.e. s, p, d, and f. The value of l ranges from 0 to n-1.

Magnetic Quantum Number

The third is the magnetic quantum number which is denoted by m. This describes the spatial orientation of the orbital. The s-orbital has only 1 possible position, p-orbital has 3 possible positions, d-orbital has 5 possible positions and f-orbital has 7 possible positions. The number of possible positions in an orbital is given as 2l + 1.

Spin Projection Quantum Number

The fourth is the spin quantum number (ms). It deals with the spin of an electron in a subshell about an axis. The spin quantum number describes the intrinsic electronic spin in which +12 denotes the counterclockwise spin of an electron and −12 represents the clockwise spin.  The maximum number of electrons in an orbital is two and these two electrons should have opposite spins.

The shape of the s-orbital is spherical, p-orbital is dumb-bell shaped. The shapes of d and f orbital are very complex and cannot be determined easily. It has been observed that d-orbital are pear-shaped.

Quantum Numbers

The shape of Single electron orbitals

To explore more about quantum numbers and the orbital theory, stay tuned with Byju’s

Practise This Question

What is the maximum capacity of a shell of quantum number n?