A sub-shell with n = 6 , l = 2 can accommodate a maximum of

The correct option is 10 electrons.

To understand why this is correct, we can break down the relationship between quantum numbers and the maximum capacity of a sub-shell:

1. Principal Quantum Number (n): Here, $n=6$. This represents the main energy level or shell in which the sub-shell is located.
2. Azimuthal (Orbital Angular Momentum) Quantum Number (l): Here, $l=2$. This quantum number specifies the shape of the sub-shell. Specifically, $l=2$ corresponds to a d-subshell (where $l=0$ is s, $l=1$ is p, $l=2$ is d, and $l=3$ is f).

3. Number of Orbitals in a Sub-shell: The number of orbitals within a given sub-shell is determined by the formula:
$$\text{Number of Orbitals}=2l+1$$

Substituting the value of $l=2$ into the formula:
$$2\left(2\right)+1=5\text{orbitals}$$

4. Maximum Number of Electrons: According to the Pauli Exclusion Principle, each orbital can hold a maximum of 2 electrons with opposite spins. Therefore, the formula for the maximum number of electrons that a sub-shell can accommodate is:
$$\text{Maximum Electrons}=2(2l+1)$$

Substituting $l=2$:
$$2Õ5=10\text{electrons}$$

Thus, any sub-shell with $l=2$ (which is a d-subshell, in this case the 6d sub-shell) can hold a maximum of 10 electrons.