In the context of electron configuration and the filling of orbitals, the "2n" rule for d orbitals refers to the maximum number of electrons that can occupy a given set of d orbitals.
The d orbitals have a total of five suborbitals, labeled as dxy, dxz, dyz, dx^2-y^2, and dz^2. These suborbitals are degenerate, meaning they have the same energy. According to Hund's rule, when filling degenerate orbitals, electrons prefer to occupy different orbitals with the same spin before pairing up.
Applying the 2n rule, where "n" represents the principal quantum number, the d orbitals can hold a maximum of 10 electrons. This is because when "n" is equal to 2 (as in the case of d orbitals), the value of 2n is equal to 4. Since there are five d orbitals, each with a capacity for two electrons (due to the Pauli exclusion principle), the total number of electrons that can be accommodated in the d orbitals is 5 x 2 = 10.
It's worth noting that the 2n rule is a simplified guideline and is based on the behavior of electrons in the atom. The actual filling of orbitals follows the principles of quantum mechanics and takes into account factors such as electron-electron repulsion and energy considerations. Nonetheless, the 2n rule provides a useful approximation for understanding the electron capacity of the d orbitals.