Question

list these electron subshells in order of increasing energy.
4s, 2p, 3s, 3p
note for advanced students: you may assume these subshells are all in an atom with many electrons, not a hydrogen atom.

Explanation:

For multi - electron atoms, the energy of electron subshells is determined by the \(n + l\) rule (where \(n\) is the principal quantum number and \(l\) is the azimuthal quantum number).

• For \(2p\): \(n = 2\), \(l=1\), so \(n + l=2 + 1=3\)
• For \(3s\): \(n = 3\), \(l = 0\), so \(n + l=3+0 = 3\). When \(n + l\) values are equal, the subshell with the lower \(n\) value has lower energy. So \(2p\) has lower energy than \(3s\) (since \(2<3\) when \(n + l\) is same)
• For \(3p\): \(n = 3\), \(l = 1\), so \(n + l=3 + 1=4\)
• For \(4s\): \(n = 4\), \(l = 0\), so \(n + l=4+0 = 4\). When \(n + l\) values are equal (for \(3p\) and \(4s\)), the subshell with the lower \(n\) value has lower energy. So \(3p\) has lower energy than \(4s\) (since \(3<4\) when \(n + l\) is same)

Answer:

\(2p<3s<3p<4s\)