The number of orbitals with $$n = 5$$, $$m_l = +2$$ is ________. (Round off to the Nearest Integer).

We need to find the number of orbitals with principal quantum number $$n = 5$$ and magnetic quantum number $$m_l = +2$$.

For a given value of $$n$$, the azimuthal quantum number $$l$$ can take values from $$0$$ to $$n - 1$$. For $$n = 5$$, we have $$l = 0, 1, 2, 3, 4$$.

The magnetic quantum number $$m_l$$ ranges from $$-l$$ to $$+l$$. For $$m_l = +2$$ to be valid, we need $$l \geq 2$$. So the allowed values of $$l$$ are $$l = 2$$ (d-orbital), $$l = 3$$ (f-orbital), and $$l = 4$$ (g-orbital).

Each combination of $$(n, l, m_l)$$ corresponds to one unique orbital. Therefore, there are 3 orbitals with $$n = 5$$ and $$m_l = +2$$: the $$5d$$, $$5f$$, and $$5g$$ orbitals (each with $$m_l = +2$$).

The answer is $$3$$.