The study of the spectrum as suggested that an electron in atom exist in several discrete energy states called quantum states.

**i)**Principle Quantum Number

**(n)**

**ii)**Orbital Quantum Number

**(l)**

**iii)**Magnetic Quantum Number

**(m)**

**iv)**Spin quantum Number

**(s)**

*. In addition to these, there is a fourth quantum number called spin quantum number*

**Principle quantum number(n), Orbital quantum number(l), magnetic quantum number(s)***, which represents the spin of the electron. These four quantum numbers completely specify an electron in an atom. Thus quantum numbers may be defined as :*

**(s)**

“the set of four numbers which give a complete information about the electron in an atom i.e. it’s energy, shape, orientation & also it’s spin”.

**i) Principle Quantum Number(n):**

**‘n’**. It determines the main the main energy level or shell in which an electron in an atom is present & also the energy associated with it. It also determines average distance of electron from nucleus in particular shell.

**K, L, M, N,… etc.**or as

**1,2,3,4,…..etc.**

**2n^2.**

**K**shell

**(n=1)**can have maximum of

**two**electrons.

**L**shell

**(n=2)**have

**eight**electrons.

**M (n=3)**accommodate eighteen electrons.

**n**‘ we can determine energy of Hydrogen electron & other one electron species i.e.

**He+**&

**Li2+**ion. The mathematical expression for the same is :

**ii) Azimuthal or Orbital Quantum Number :**

**(n)**do not have the same energy. Based on the energy of electrons, the shells are divided into

**sub-levels or sub-shells**and these have been described with the help of ‘

**It was given by**

*l*‘.**Sommerfeld.**

*depends upon the value of shell(n).*

**‘l’**

*“For a particular value of n, l can have all integer values ranging from 0 to (n-1).Each value of l represents one particular subshells”.*

**l = 0(s) ,1(p), 2(d) ,3(f) ,…….(n-1)**

**iii) Magnetic quantum number(m):**

*Zeeman effect.*In order to explain this effect,

*proposed an electron because of it’s angular motion around the nucleus produces an electric field which in turn leads to magnetic field of the earth.*

**Linde****m**‘ . The values of m are linked to ‘

**l**‘ therefore it is sometimes denoted by ‘

**ml**‘.

**–**to

*l**with*

**+l**

**0.***values*

**m= 2l +1**

**.**

*e.g.*

**for l =1**,m = 2+1=3 values.*which are = -1 ,0 ,+1*

**for l=2,**m = 4+1=5 values.*which are = -2 ,-1, 0 ,+1 ,+2.*

**iv) Spin Quantum Number(s):**

**.**

*spin quantum number***s**‘. It was given by

*.*

**Goudsmit****Inner Quantum Number:**

**i) Orbital**

**ii) Spin**

*Total angular momentum of electrons:*

Thus the four quantum numbers specify completely the quantum state of an electron in atom & hence determines its energy & angular momentum.

**If you like this post share it with others too..**