Place the following orbitals in order of increasing energy in a multielectron atom: a. n=2, ℓ=1

step 1 For this question, we're given values for n. N is the principal quantum number. And we're given

Place the following orbitals in order of increasing energy...

Key Concepts

Principal Quantum Number

The principal quantum number, represented as n, indicates the main energy level of an electron in an atom. It is a measure of the electron’s distance from the nucleus and overall energy. In multielectron atoms, orbitals with higher n values are generally of higher energy due to the increased average distance from the nucleus and reduced effective nuclear attraction.

Azimuthal Quantum Number

The azimuthal, or angular momentum, quantum number (l) determines the shape of the orbital and influences its energy. Orbitals with lower l values tend to penetrate closer to the nucleus and experience a stronger effective nuclear charge, which can lower their energy compared to orbitals with higher l values in the same principal quantum level.

n+l Rule (Madelung Rule)

The n+l rule, also known as the Madelung rule, is used to predict the order of orbital filling in multielectron atoms. It states that orbitals are filled in order of increasing values of the sum (n+l), and in cases where two orbitals have the same n+l sum, the one with the lower n value fills first. This rule explains the systematic energy ordering of orbitals beyond the hydrogen atom.

Effective Nuclear Charge and Electron Shielding

Effective nuclear charge is the net positive charge experienced by an electron in a multielectron atom, after accounting for the shielding effects of other electrons. Electrons in orbitals that penetrate closer to the nucleus experience a higher effective nuclear charge, which generally results in lower energy. This concept is crucial for understanding why orbitals with different n and l values do not simply follow the hydrogen-like energy ordering.

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