## Quantum Numbers

Since a sub-shell can only contain two electrons so, an atom generally has a large number of shells and sub-shells.

The different sub=shells are differentiated from each other on the basis of their size, shape, orientation and these parameters are expressed in terms of different quantum numbers.

Quantum numbers are basically set of numbers associated with an electron with the help of which one can get complete information about that electron. There are four quantum numbers. These four quantum numbers define the location, energy, type, and shape of orbital and spin of the electron.

#### (1) Principal Quantum Number (n):

This quantum number defines that electron is in which shell and also it tells us about the approximate distance of electron from the nucleus.

Also, for a value of n, the maximum number of electron that can be presented in that shell is 2n^{2}.

Shell |
Principal Quantum Number (n) |
Maximum number of electrons |

K | 1 | 2 |

L | 2 | 8 |

M | 3 | 18 |

N | 4 | 32 |

#### (2) Azimuthal Quantum Number (l):

This quantum number is also called Angular Quantum number and it represents the number of sub-shell present in the shell.

The sub-shells are represented by s, p, d, f…

This quantum number also represents the shape of the sub-shells or orbital.

The orbital angular momentum of an electron can be calculated by using the formula

For a given shell having principal quantum number n, there are ‘n’ possible sub shells having values ranging from 0 to ‘n-1’.

__(3) THE MAGNETIC QUANTUM NUMBER (m):__

Because of the angular movement of an electron around the nucleus, the electric field is generated. The magnetic field is produced by this electric field.

Under the influence of the external magnetic field, the electrons of a sub shell can orient them in certain preferred regions of space around the nucleus called orbitals.

The magnetic quantum number determines the number of preferred orientations of the electron present in a sub-shell. The magnetic quantum number determines the number of preferred orientations of the electron present in a sub-shell.

The values of magnetic quantum number depends upon the Azimuthal quantum number l.

The magnetic quantum number ‘m’ can have all integer values between -l to +l including zero.

Thus m can be – 1 , 0 , + 1 for l = 1. Total values of m associated with a particular value of l is given by (2l + 1).

__(4) THE SPIN QUANTUM NUMBER (S):__

An electron not only revolves but also spin about its own axis in an atom. There are two possibilities for spinning of electron i.e. clockwise or anti-clockwise. Therefore for any particular value of the magnetic quantum number, the spin quantum number can have two values.

The two values of spin quantum number +1/2 and -1/2 are represented by two arrows pointing in opposite directions, i.e. ↑ and ↓.

When an electron goes to a vacant orbital, it can have a clockwise or anti clockwise spin

i.e., + 1/2 or – 1/2

This quantum number helps to explain the magnetic properties of the substances.

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