# Quantum Numbers and types

Quantum numbers

**quantum numbers** are useful to locate the address of electron in the atom. There are four types of quantum numbers, they are

1) Principal quantum numbers

2) Azimuthal quantum numbers

3) Magnetic quantum numbers

4) Spin quantum numbers**Principal quantum numbers**

These are proposed by **Niels Bhor** and are represented by ‘**n**’. This number represents the number of principal orbits to which the electron belongs. Principal quantum numbers have integral values like n=1,2,3,4 or K, L, M , N. these signifies the size of an atom by measuring radius. By knowing these quantum numbers many things like energy of electron, number of sub shells in an orbit, number of orbital’s in an orbit and number of electrons in a orbit can be calculated **Azimuthal quantum number**

**Sommerfeld** introduced azimuthal quantum numbers and are basically denoted by ** ’l’**. The value of

**depends on**

*’l’***and can be calculated by subtracting 1 form the value of**

*’n’***.**

*’n’***can have all the integral values starting from zero to n-1.**

*’l’*When l=0 then the corresponding electron belongs to

**s**sub shell

Similarly

When l=1 p-sub shell

When l=2 d-sub shell

When l=3 f-sub shell

So for the above we can conclude that one can predict the position of electron by knowing the value of azimuthal quantum number. Azimuthal quantum number helps in finding out the shape of orbital. This quantum number is also called as angular momentum quantum number of subsidiary quantum number. This quantum number helps in calculating number of electrons in an electron (4l+2), number of orbitals in a sub shell (2l+1)

**Magnetic Quantum number**

This set of quantum numbers is proposed by

**Lande**and are denoted by

**. The range of**

*’m’***lies between**

*’m’***to**

*’-l’***. This quantum number signified the spatial orientations of an electron in orbital. If an electron is in**

*’+l’***sub shell then**

*’s’*

*’l=0’***, so there is one orientation in magnetic field of all the electrons corresponding to**

*’m=0’***sub shell. Similarly there are three orientations for a**

*’s’***sub shell they are Px, Py, Pz and for**

*’p’***sub shell there are five degenerate orbitals and seven for**

*’d’***sub shell. This quantum numbers are proposed for the explanation of Zeeman and Stark effect.**

*’f’***Spin Quantum Numbers**

**Uhlenbeck and Goudsmith**are the persons who proposed these quantum numbers. These quantum numbers are denoted by

**. electron spins around its axis in addition to revolving round the nucleus. In general a electron has two types of spins.**

*’s’***Clock wise and Anti-clock wise spins**. The possible values of spin quantum numbers are + ½ and – ½ and these values are denoted by arrows which indicate upward or downward directions.