Question 31

In an atom how many orbital(s) will have the quantum numbers; $$n = 3$$, $$l = 2$$ and $$m_l = +2$$?

Solution

For a $$d$$-subshell ($$l = 2$$), there are $$2l + 1 = 5$$ possible orbitals. These are represented by the magnetic quantum numbers:

$$m_l = -2, -1, 0, +1, +2$$

Each unique value of $$m_l$$ corresponds to exactly one specific orbital. Since the question specifies a unique value for $$m_l$$ ($$+2$$), it refers to only one orbital within the $$3d$$ subshell.

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In an atom how many orbital(s) will have the quantum numbers; $$n = 3$$, $$l = 2$$ and $$m_l = +2$$?

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