# What are Quantum numbers?

## What are Quantum numbers?

Electrons revolve around the nucleus at different energy levels. There are four quantum numbers (n, l, m, and s) that describe the size, shape, orientation, and spin directions of energy levels of electrons in an atom. These numbers are called quantum numbers.

These are-

a) Principal Quantum Number(n)

b) Subsidiary Quantum Number(l)

c) Magnetic Quantum Number(m) and

d) Spin Quantum Number(s).

With the help of four quantum numbers, an electron can be described easily. Knowing the address, a person can be easily identified. Similarly, knowing the values of four quantum numbers, an electron can easily be identified. The four quantum numbers are disscussed below:

**a) Principal Quantum Number**

According to Bohr, the electrons revolve around the nucleus at certain energy levels. The numbers which designate the stationary energy levels are called principal quantum numbers. The principal quantum number is expressed by the letter, n. n has a whole number value, 1, 2, 3, ......... etc.

**b) Subsidiary Quantum Number**

Each electron revolving around principal energy levels is divided into some sublevels. These sublevels indicate the shape of the electron's movement. This type of quantum number is used to locate the position of electrons in a sublevel of a particular principal energy level. This quantum number is denoted by the letter 'l'. 'l' has values from 0 to n-1. The subsidiary quantum number indicates the shape of the orbital.

For example, if n = 1, l = 0

if n = 2, l = 0, 1

if n = 3, l = 0, 1, 2

**c) Magnetic Quantum Number**

The earth has a magnetic field. The effects of positively charged proton and negatively charged electrons in atoms tend to create a magnetic field. These two magnetic fields always tend to affect the movement of electrons. As a result, the electron's motion is oriented by the magnetic field. Thus, the magnetic quantum number is used to indicate the orientation of orbitals. This is expressed by 'm'.

The value of m depends on the subsidiary quantum number, l. 'm' values can range from +l to -l with zero included. Mathematically, m = ±l.

**d) Spin Quantum Number**

The spin quantum number represents the direction of the electron spin and is denoted by s. The direction of spin is investigated in the presence of external magnetic field and it is found that all electrons spin either in one direction (say, clockwise direction) or in the direction directly opposite (anti-clockwise).

The spin quantum numbers can have values ±½ or ½ which are the mathematical notations for the spin direction of electrons.

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