Why 4s Orbitals Have Lower Energy Than 3d Orbitals: Understanding Electron Shielding and Penetration

When studying atomic orbitals, the energy levels of electrons can sometimes be counterintuitive, especially when comparing orbitals with different quantum numbers. This article will explore why 4s orbitals, commonly associated with higher energy levels, can actually have lower energy than 3d orbitals due to electron shielding and penetration effects.

Principal Quantum Number (n)

The principal quantum number, denoted by n, indicates the main energy level of an electron. Generally, for multielectron atoms, the energy levels do not strictly follow the nl rule, where n is the principal quantum number and l is the angular momentum quantum number. In this case, the 4s orbital has n 4, while the 3d orbital has n 3. Despite the higher n value, the 4s orbital can still have lower energy.

A Angular Momentum Quantum Number (l)

The angular momentum quantum number, denoted by l, determines the shape of the orbital and its energy. The 4s orbital has l 0 (which corresponds to an s orbital), while the 3d orbital has l 2 (which corresponds to a d orbital). The shape of the orbitals plays a crucial role in their energy levels and interaction with the nucleus.

Energy Levels in Multielectron Atoms

In a hydrogen-like atom, the energy levels are determined solely by the principal quantum number n. However, in multielectron atoms, electron-electron interactions and shielding effects play significant roles. Electrons in s orbitals can penetrate closer to the nucleus more effectively than those in d orbitals due to their higher ability to overcome electronic repulsion and nuclear shielding.

Penetration and Shielding

The 4s orbital can penetrate the region close to the nucleus more effectively than the 3d orbital. This means that electrons in the 4s orbital experience less shielding from the nucleus by inner electrons, resulting in a lower energy state. Electron shielding refers to the phenomenon where inner electrons block some of the nuclear charge from outer electrons, thus affecting their energy levels.

Order of Filling

According to the Aufbau principle, orbitals are filled in order of increasing energy. When filling orbitals in multielectron atoms, the 4s orbital is filled before the 3d orbital, even though the 4s orbital has a higher principal quantum number. This is because the 4s orbital's lower energy state in the presence of other electrons allows it to be filled first.

The closer an electron is to the nucleus, the less energy it has to escape from the atom. As a result, the 4s electrons are "safer" and thus have lower energy. This is because in a single-electron atom, an electron would fall through all the energy levels until it reaches the first level. In the presence of other electrons, however, the 4s orbital, being closer to the nucleus and experiencing less shielding, has a lower energy state.

Considering the electron-electron repulsion, the s orbitals (which are spherical and can reach the nucleus from all directions) typically fill before the p orbitals (which are directional and thus have a slight disadvantage in reaching the full charge of the nucleus). Similarly, the d orbitals (which are even more directional) fill after the s orbitals in the same energy level. The d orbitals of the third level fill only after the s orbitals of the fourth level, and the fourth p orbitals fill after the third d orbitals.

When it comes to higher d orbitals, the nd orbitals only fill after the n1s orbitals have been filled. This pattern continues for even higher orbitals, such as the nf orbitals, which only fill after the n2s orbitals have been filled. This phenomenon can be attributed primarily to the electron repulsion effect, where outer electrons have a harder time overcoming the repulsion of inner electrons to get closer to the nucleus.

These principles help us understand why the 4s orbitals can have lower energy than the 3d orbitals. Electron shielding and penetration effects play crucial roles in determining the energy levels of electrons in multielectron atoms.