For an atom or ion having single electron, compare the energies of the following orbitals: = a spher — Atomic Structure Chemistry Question
Question
For an atom or ion having single electron, compare the energies of the following orbitals: $S_1$ = a spherically symmetrical orbital having two spherical nodes. $S_2$ = an orbital which is double dumb-bell and has no radial node. $S_3$ = an orbital with orbital angular momentum zero and three radial nodes. $S_4$ = an orbital having one planar and one radial node.
💡 Solution & Explanation
For single-electron species, energy depends only on $n$. $S_1$: s-orbital ($l=0$) with 2 radial nodes $\implies n-1=2 \implies n=3$. $S_2$: d-orbital ($l=2$) with 0 radial nodes $\implies n-3=0 \implies n=3$. $S_3$: s-orbital ($l=0$) with 3 radial nodes $\implies n-1=3 \implies n=4$. $S_4$: p-orbital ($l=1$) with 1 radial node $\implies n-2=1 \implies n=3$. Thus, $n_1=3, n_2=3, n_4=3$ and $n_3=4$. Hence $E_1 = E_2 = E_4 < E_3$. Therefore, correct answer is B.