Maximum number of electrons in a subshell can be

The correct option is 4l + 2.

To understand why this is the correct expression, let us break down the quantum mechanical rules that govern the arrangement of electrons in an atom step-by-step:

1. Azimuthal Quantum Number (l):
Each subshell in an atom is defined by its azimuthal (or orbital angular momentum) quantum number, denoted by $l$. The value of $l$ determines the shape of the subshell (for example, $l=0$ for an s-subshell, $l=1$ for a p-subshell, $l=2$ for a d-subshell, and so on).

2. Number of Orbitals in a Subshell:
For a given subshell with azimuthal quantum number $l$, the magnetic quantum number $m_l$ can take any integer value ranging from $-l$ to $+l$, including zero.
Therefore, the total number of orbitals in a subshell is given by the formula:
Number of orbitals = $2l+1$

3. Maximum Number of Electrons per Orbital (Pauli Exclusion Principle):
According to the Pauli Exclusion Principle, a single orbital can hold a maximum of 2 electrons, which must have opposite spins (spin quantum numbers $m_s=+1/2$ and $m_s=-1/2$).

4. Deriving the Formula for Maximum Electrons in a Subshell:
Since each orbital can accommodate at most 2 electrons, the maximum number of electrons that can reside in a subshell is twice the number of orbitals in that subshell:
Maximum electrons = $2\times (2l+1)$
Expanding this expression gives:
Maximum electrons = $4l+2$