The maximum number of orbitals which can be identified with $$n = 4$$ and $$m_l = 0$$ is ______

Find the maximum number of orbitals with $$n = 4$$ and $$m_l = 0$$.

For $$n = 4$$, the subshells correspond to $$l = 0, 1, 2, 3$$, that is, the 4s, 4p, 4d, and 4f subshells.

Next, check which subshells have $$m_l = 0$$. Every subshell has exactly one orbital with $$m_l = 0$$:

- $$l = 0$$: $$m_l = 0$$ → 1 orbital (4s)

- $$l = 1$$: $$m_l \in \{-1, 0, 1\}$$ → $$m_l = 0$$ exists → 1 orbital (4p)

- $$l = 2$$: $$m_l \in \{-2, -1, 0, 1, 2\}$$ → $$m_l = 0$$ exists → 1 orbital (4d)

- $$l = 3$$: $$m_l \in \{-3, ..., 3\}$$ → $$m_l = 0$$ exists → 1 orbital (4f)

In total, there are 4 orbitals.

The correct answer is 4.