Nodes

Radial nodes: 

Radial nodes are nodes inside the orbital lobes

Angular nodes: 

Angular nodes are not internal countours of electron probability, but rather are planes that go through the orbital

• Total number of nodes = n – 1
• Total number of Angular nodes = l
• Total number of Radial nodes = (n – l – 1)
• n is principle Quantum number, l is azimuthal Quantum number.

Filling of orbitals in Atom:-

                

The filling of electrons into the orbitals of different atoms takes place according to the aufbau principle which is based on the Pauli’s exclusion principle, the Hund’s rule of maximum multiplicity and the relative energies of the orbitals.

The order of the energies of orbitals in increasing order is

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s……..

It can be remembered by using the method shown beside.

1.       Aufbau principle:-

• According to this the filling up of orbitals by electrons depending upon their energies i.e., the electrons first occupy the lowest energy orbital then enter into higher energy orbitals only after the lower energy orbitals are filled.

2.      Pauli’s Exclusion Principle:-

• It states that No two electrons in an atom can have the same set of four quantum numbers. 
• It can be stated as “only 2 electrons may exist in the same orbitals and there electrons must have opposite spins”.

3.       Hund’s rule:-

• It states that pairing of electrons in the orbitals belonging to the same sub shell (p, d and f) does not takes place until they are half filled. i.e., pairing of electrons takes place only after the orbitals are half filled.
• The completely filled and half-filled sub shells are most stable than the incompletely filled sub shells. Depending on this we write the electronic configurations of elements. 

Extra stability

The extra stability of half-filled and completely filled subshell is due to:

(i)      relatively small shielding,

(ii)    smaller coulombic repulsion energy, and

(iii)   Larger exchange energy - the energy released due to the exchange of position of electrons whenever two or more electrons with the same spin are present in the degenerate orbitals of a subshell.

Ex: The valence electronic configuration of Cr is 3d⁵ 4s¹ instead of 3d⁴ 4s² and the Valence electronic configuration of Cu and 3d¹⁰ 4s¹ respectively and not and 3d⁹ 4s²