Chemistry EXTRA STABILITY OF HALF-FILLED AND COMPLETELY FILLED ORBITALS

Exceptional Configurations (Extra stability of half-filled and fully-filled sub shell) :

The electronic configuration of most of the atoms follow the Aufbau's rule. However, in certain elements such a `Cr`, `Cu` etc. electron fills in `3d` in preference to `4s` provided the subshell become either half-filled or fully filled.

`text()_24Cr -> [Ar] 3d^5, 4s^1` and not `[Ar] 3d^4, 4s^2`; `text()_29Cu -> [Ar] 3d^(10) 4s^1` and not `[Ar]3d^9, 4s^2`

It has been found that there is extra stability associated with these electronic configurations. This stabilization is due to the following two factors

(i) `text(Symmetrical distribution of electron)` : It is well known that symmetry leads to stability. The completely filled or half-filled subshells have symmetrical distribution of electrons in them and are therefore more stable. This effect is more dominant in `d` and `f`-orbitals.

This means three or six electrons in `p`-subshell, `5` or `10` electrons in `d`-subshell, and `7` or `14` electrons in `f`-subshell forms a stable arrangement.

(ii) `text(Exchange Energy)` : This stabilizing effect arises whenever two or more electrons with the same spin are present in the degenerate orbitals of a subshell. These electrons tend to exchange their positions and the energy released due to this exchange is called exchange energy. The number of exchanges that can take place is maximum when the sub-shell is either half-filled or full filled. As a result the exchange energy is maximum and so is the stability. See fig.1.

Total exchanges= `10`

� If `n` is the number of electron with parallel spins then can you calculate total number of possible exchanges.

For e.g. - See fig.2.

The stabilsation due to exchange energy will compensate for the energy required for excitation from `4s` to `3d`.

However in case of carbon `(text()_6C): 1 s^2, 2s^2 2p`. See fig.3.

The stabilsation due to exchange energy will not be able to compensate for the energy required for excitation from `2s` to `2p`.

Electronic Configuration of Ions :

Note that while filling electrons in various orbitals they are filled according to the three laws - Aufbau, Pauli and Hund's. For removing electrons to form cations, electrons are removed from outermost shell as they are bound to the nucleus by lesser forces of attraction because of shielding effect.

For example for iron,

`text()_26Fe -> 1s^2, 2s^2 2p^6, 3s^2 3p^6, 3d^6, 4s^2` & the configuration of ions would be

`Fe^(2+) -> 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^6` & `Fe^(3+) -> 1s^(2), 2s^2, 2p^6, 3s^2, 3p^6, 3d^5`

Similarly for copper `text()_29Cu -> 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^(10), 4s^1` & for its ions

`Cu^(+) -> 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^(10)` & `Cu^(2+) -> 1s^2, 2s^2, 2p^2 , 3s^2, 3p^6, 3d^9`

The anions are formed by adding electrons to the vacant orbital of lowest energy [follow (`n +l`) rule]

For example `text()_9F -> 1s^2, 2s^2, 2p^5` & that of its ion `F^(-) -> 1s^2, 2s^2, 2p^6`

Similarly for Chlorine `text()_17Cl -> 1s^2, 2s^2, 2p^6, 3s^2, 3p^5` & that of its ion `Cl^(-) -> 1s^2, 2s^2 2p^6, 3s^2 3p^6`

Some Exceptional Electronic Configuration :

`text()_24Cr : 1s^2, 2s^2 2p^6, 3s^2 3p^6 3d^5, 4s^1` `text()_47Ag : 1s^2, 2s^2 2p^6, 3s^2 3p^6 3d^10, 4s^2 4p^6 5s^1`

`text()_(29)Cu : 1s^2, 2s^2 2p^6, 3s^2 3p^6 3d^(10), 4s^1` `text()_42Mo : 1s^2, 2s^2 2p^6, 3s^2 3p^6 3d^(10), 4s^2 4p^6 4d^5, 4s^1`

Applications of Electronic Configuration :

(i) Calculation of Magnetic Moment `(mu) : =>mu = sqrt(n (n+2))` Bohr Magneton

Where `n -> no`. of unpaired electrons & `1` BM (Bohr Magneton) ` = (e h)/(4 pi m_n)`

When `mu = 0` (Diamagnetic, repelled by magnetic field)

If `mu ne 0` (Paramagnetic, attracted by magnetic field).

(ii) Colour : It has been observed that the species having unpaired `e^-` generally impart colour.