Question

according to the aufbau principle, which orbital is filled after 4s?

Explanation:

Step1: Recall Aufbau principle

The Aufbau principle states that electrons fill orbitals starting from the lowest - energy orbital. The energy of orbitals is determined by the \(n + l\) rule (where \(n\) is the principal quantum number and \(l\) is the azimuthal quantum number).
For \(4s\): \(n = 4\), \(l=0\), so \(n + l=4\)
For \(4p\): \(n = 4\), \(l = 1\), so \(n + l=5\)
For \(4d\): \(n = 4\), \(l = 2\), so \(n + l=6\)
For \(4f\): \(n = 4\), \(l = 3\), so \(n + l=7\)
For \(5s\): \(n = 5\), \(l=0\), so \(n + l=5\)

Step2: Compare energy levels

After \(4s\) (\(n + l = 4\)), the next - lowest \(n + l\) value is \(5\). Among the orbitals with \(n + l=5\), the one with lower \(n\) is filled first. So, after \(4s\), the \(5s\) orbital (\(n = 5\), \(l = 0\)) is not filled next. The \(4p\) (\(n=4\), \(l = 1\)) has \(n + l = 5\) and \(n = 4\) (lower than \(n = 5\) for \(5s\))

Answer:

\(4p\)