Question

following the aufbau principle, which orbital is filled after 3p?

Explanation:

Step1: Recall the Aufbau principle

The Aufbau principle states that electrons fill orbitals starting from the lowest - energy orbitals. The order of orbital filling is based on the \(n + l\) rule (where \(n\) is the principal quantum number and \(l\) is the azimuthal quantum number). For a \(3p\) orbital, \(n = 3\) and \(l=1\), so \(n + l=3 + 1=4\).

Step2: Calculate \(n + l\) for each option

• For \(4p\): \(n = 4\), \(l = 1\), \(n + l=4+1 = 5\)
• For \(3d\): \(n = 3\), \(l = 2\), \(n + l=3 + 2=5\)
• For \(3f\): \(l\) value for \(n = 3\) can be at most \(l=2\) (since \(l=0,1,\cdots,n - 1\)), so \(3f\) does not exist.
• For \(4s\): \(n = 4\), \(l = 0\), \(n + l=4+0 = 4\)

When two orbitals have the same \(n + l\) value (e.g., \(3d\) and \(4p\) in some cases, but not relevant here), the orbital with the lower \(n\) value is filled first. Since \(4s\) has the same \(n + l\) value as \(3p\) (when considering the correct order of filling before higher - \(n + l\) orbitals) and is the next in the Aufbau order after \(3p\)

Answer:

\(4s\)