(Chemistry Ch-2) 9. Filling of Orbitals in Atom & Electronic Configuration of Atoms

Aufbau Principle

• In the ground state of atoms, the orbitals are filled in the increasing order of their energy.
• The given table shows the arrangement of orbitals with increasing energy on the basis of (n + l) rule.

Orbitals	Value of n	Value of l	Value of (n + 1)
1s	1	0	1 + 0 = 1
2s	2	0	2 + 0 = 2
2p	2	1	2 + 1 = 3	2p (n = 2) has lower energy than 3s
3s	3	0	3 + 0 = 3	3s (n = 3)
3p	3	1	3 + 1 = 4	3p (n = 3) has lower energy than 4s
4s	4	0	4 + 0 = 4	4s (n = 4)
3d	3	2	3 + 2 = 5	3d (n = 3) has lower energy than 4p
4p	4	1	4 + 1 = 5	4p (n = 4)

• Increasing order of the energy of the orbitals and hence, the order of the filling of orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, …

Pauli Exclusion Principle

• No two electrons in an atom can have the same set of all the four quantum numbers.
• Two electrons can have the same value of three quantum numbers n, l, and m_e, but must have the opposite spin quantum number (s).
• The maximum number of electrons in the shell with the principal quantum number n is equal to 2n².

Hund’s Rule of Maximum Multiplicity

• Pairing of electrons in the orbitals belonging to the same sub-shell (p, d, or f) does not take place until each orbital belonging to that sub-shell has got one electron each (i.e., singly occupied).
• Orbitals of equal energy (i.e., same sub-shell) are called degenerate orbitals.

Electronic Configuration of Atoms

• Can be represented in two ways:

• s^a p^b d^c …
• Orbital diagram

• a, b, c, …, etc. represent the number of electrons present in the sub-shell. In an orbital diagram, an electron is represented by an up arrow (↑) indicating a positive spin, or a down arrow (↓) indicating a negative spin.
• For example,

Stability of completely filled and half-filled sub-shells

• p³, p⁶, d⁵, d¹⁰, f⁷, f¹⁴, etc. configurations, which are either half-filled or fully filled, are more stable.

• Symmetrical Distribution of Electrons
  • Symmetry leads to stability.
  • The completely filled or half-filled sub-shells have symmetrical distribution of electrons in them. Hence, they are stable.
• Exchange Energy
  • Whenever two or more electrons with the same spin are present in the degenerate orbitals of a sub-shell, the stabilising effect arises.
  • Such electrons tend to exchange their positions and the energy released due to the exchange is called exchange energy.
  • If the exchange energy is maximum, then the stability is also maximum.
  • The number of exchanges that can take place is maximum when the sub-shell is either half-filled or completely filled.
  • Possible exchange for d⁵ configuration:

Total number of exchanges = 4 + 3 + 2 + 1 = 10.