Question

In a multi-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields?

• A. $\begin{array}{ccc}n& l& m_l\\ 2& 0& 0\end{array}$
• B. $\begin{array}{ccc}n& l& m_l\\ 2& 1& 1\end{array}$
• C. $\begin{array}{ccc}n& l& m_l\\ 3& 2& 1\end{array}$
• D. $\begin{array}{ccc}n& l& m_l\\ 3& 2& 0\end{array}$

Answer 1

Answer: (C), (D)

$\begin{array}{ccc}n& l& m_l\\ 3& 2& 0\end{array}$

(a) is 2s
(b) is 2p
(c) is 3d
(d) is 3d
Thus, (c) and (d) will have equal energy.
Energy is directly proportional to $n+l$ values. $m$ has no role to play in deciding energies.