Space Quantization.

Quantum numbers(n,l,m)

Hydrogen atom is spherical symmetric. The Schrodinger equation in spherical polar coordinates can be separated by three independent equations,each giving rise to a quantum number n,l and mₗ, the physical significance of these number is explained as follows.

Quantum number 'n' (Principal quantum number).

The quantum number 'n' is called the principal quantum number (or radial) quantum number. It can have only positive integral values 1,2,3,......n.

The principal quantum number defines the total energy of the electron in the orbit.

Eₙ ∝ 1/n²

Quantum number 'l' (orbital quantum number).

The quantum number 'l' is the orbital quantum number. It defines the orbital angular momentum of the electron given by

Orbital angular momentum.

It can have only positive integral values 0,1,2,.....(n-1).

For example, for n=3, the possible values of l are 0,1,2, only.

Quantum number mₗ (magnetic quantum number)

The magnetic quantum number decides the Z-component of the orbital angular momentum given by

Z component of orbital angular momentum.

Where mₗ can have integral values

-l,-(l-1),...0.....(l-1),l.

Space quantization;

Space quantization.

Comments

LS coupling and jj coupling.

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