Quantum number

 A set of number or quantities that can explain the possible state of the system within atom. In hydrogen like atom to state the position, orientation and spin of the electron there have four quantum number. 

Principle quantum numner

Azimuthal quantum number 

Magnetic quantum number 

Spin quantum number.

To describe the states of subatomic particles there need new quantum number. For examples, flavor of quark can describes by another new quantum number.

1. Principle Quantum number describes in which energy state electron placed. If it placed in 4th energy state then principle quantum number would be 4.

Indicates atomic size and Randi,  the distance of electron from nucleus

Indicates the energy of an electron 

It should be positive value equal to 1 or greater than 1

Increased value of quantum number of an atom indicates the absorption of energy

Azitmuthal quantum number indicates the shape of the orbital. It is the total number of angular node of orbital. 

The azimuthal quantum number indicates electrons position either in S,  p,  d or f orbital

It's value depends on principle quantum number. It should be 0 to n - 1

If n is 3, the possible azimuthal quantum number would be 0, 1, 2.

Hence,  the subshell would be S,  p,  d

In third energy state 3d orbital is possible.

But in second energy state 2d orbital is not possible. Because in second energy state azimuthal quantum number is 0, 1. Hence, 2d is not possible.

Magnetic quantum number indicates possible orientation of orbitals and the total number of orbital in a subshell. 

It's value is related to azimuthal quantum number as well as principle quantum number. It is equal to 2l+1.

If azimuthal quantum number is 2, the magnetic quantum number would be -2, -1, 0, +1, +2

In 3rd energy state 3d is possible. In 3d orbital azimuthal quantum number would be 2. Hence,  magnetic quantum number is -2, -1, 0, +1, +2. Here, number 5 orbital exist. Each orbital can contain maximum 2 electron. Hence, total number of electron in 3d orbital is 10.

Spin quantum number of any electron would be +½ and -½.