Question

The set of quantum numbers, n = 3, l = 2, $m_l$ = 0

• A. describes an electron in a 2s orbital
• B. is not allowed
• C. describes an electron in a 3p orbital
• D. describes one of the five orbitals of same energy

Answer 1

Answer: (D)

describes one of the five orbitals of same energy

Answer 2

The principal quantum number is $n=3$. The azimuthal quantum number is $l=2$. This is allowed as $l \le n-1$ ($2 \le 3-1$). $l=2$ corresponds to a d-subshell. For $l=2$, the magnetic quantum number $m_l$ can take values from $-l$ to $+l$. The given $m_l=0$ is a valid value since $-2 \le 0 \le 2$. The set ($n=3, l=2$) defines the 3d subshell. For $l=2$, the number of orbitals is $2l+1 = 2(2)+1=5$. These 5 orbitals (with $m_l = -2, -1, 0, +1, +2$) are degenerate, meaning they have the same energy. The given quantum numbers specify one of these five 3d orbitals.