Question

which electron configuration of the 4f energy sublevel is the most stable?
4f14
4f13
4f7
4f

Explanation:

Electron configurations follow the principle that half - filled (\(n = \frac{\text{max electrons}}{2}\)) or completely - filled (\(n=\text{max electrons}\)) sub - levels are more stable. For the \(4f\) sub - level, the maximum number of electrons is \(14\) (since for \(l = 3\) ( \(f\) sub - level), the number of orbitals \(= 2l + 1=7\) and each orbital can hold \(2\) electrons, \(7\times2 = 14\)). A completely - filled \(4f^{14}\) configuration has all the orbitals in the \(4f\) sub - level filled with electrons, which minimizes electron - electron repulsion and maximizes stability. The \(4f^{7}\) configuration is half - filled but less stable than the completely - filled one. The \(4f^{13}\) and \(4f^{1}\) configurations are neither half - filled nor completely - filled.

Answer:

\(4f^{14}\)