In a multi-electron atom, the inherent energy of a specific atomic orbital is strictly determined by

Question

In a multi-electron atom, the inherent energy of a specific atomic orbital is strictly determined by which of the following quantum number(s) in the complete absence of external fields?

Professor PC Thomas Classes · Answer

(a) : Unlike single-electron species (like Hydrogen) where orbital energy relies exclusively on the principal quantum number '$n$', in multi-electron atoms, shielding effects and electron-electron repulsions cause subshell splitting. Consequently, the energy of an orbital in a multi-electron atom depends on both '$n$' and '$l$' (often governed by the $n+l$ rule). The magnetic quantum number ($m_l$) only splits energies in the presence of an external magnetic field.