Explain the stability of completely filled and half-filled subshells by giving reasons.

(N/A) The stability of completely filled and half-filled subshells is attributed to the following factors:
$1$. Symmetrical distribution of electrons: The completely filled or half-filled subshells have a symmetrical distribution of electrons,which leads to greater stability. In these configurations,the shielding of electrons from one another is relatively small,and the electrons are more strongly attracted by the nucleus.
$2$. Exchange energy: The stabilizing effect arises whenever two or more electrons with the same spin are present in degenerate orbitals. They can exchange their positions,and the energy released due to this exchange is called exchange energy. The number of possible exchanges is maximum for half-filled and completely filled configurations,leading to maximum stability.
For example,in a $d^{5}$ electron configuration,all five electrons have the same spin. This allows for the maximum number of exchanges,resulting in the maximum release of energy,which makes the $d^{5}$ configuration highly stable.
In summary,the extra stability of half-filled and completely filled subshells (like $3d^{5}$ and $3d^{10}$) is due to:
$i$. Relatively small shielding.
$ii$. Smaller coulombic repulsion energy.
$iii$. Larger exchange energy.