Zeff, also known as the effective nuclear charge, represents the net positive charge experienced by an electron in an atom. This charge is not the full positive charge of the nucleus due to the shielding effect of other electrons.
Understanding Effective Nuclear Charge
The reference defines Zeff as the net positive charge pulling electrons towards the nucleus. This pull is determined by two main forces:
- Positive Nuclear Charge: The protons in the nucleus exert a positive attraction on the negatively charged electrons.
- Shielding/Screening Effect: Inner electrons repel outer electrons, reducing the net positive charge experienced by the outer electrons.
The interplay between these two forces determines the effective nuclear charge. Electrons closer to the nucleus experience a greater Zeff because they are less shielded than the outer electrons.
Calculating Effective Nuclear Charge (Simplified)
While the exact calculation of Zeff is complex, it's often approximated using the following formula:
Zeff ≈ Z – S
Where:
- Z is the total number of protons in the nucleus (the atomic number)
- S is the number of core electrons shielding a given electron.
For example, for a valence electron, S is often the number of non-valence electrons.
However, this is a very simplified way and can lead to incorrect results sometimes, while for practical purposes this could be enough.
Importance of Zeff
The effective nuclear charge has a profound impact on various atomic properties:
- Atomic Size: A higher Zeff pulls the electrons closer to the nucleus, leading to a smaller atomic radius.
- Ionization Energy: Electrons experiencing a higher Zeff are more tightly bound to the nucleus, requiring more energy to remove.
- Electronegativity: Atoms with a higher Zeff tend to attract electrons more strongly, thus having higher electronegativity.
- Chemical Reactivity: Zeff plays a critical role in how atoms interact and form chemical bonds.
Example
Let's consider lithium (Li) with an atomic number of 3. It has 2 core electrons and one valence electron.
- Z = 3 (3 protons)
- S = 2 (2 core electrons for valence)
Therefore, the approximate Zeff for the valence electron in Li is:
- Zeff ≈ 3 - 2 = +1
This shows that even with a total positive charge of +3, the outer electron only experience an effect equivalent to a +1 charge due to the shielding from core electrons.Summary
In summary, Zeff is a measure of the net positive charge that an electron in an atom actually "feels" taking into account the attraction of the nucleus and the repulsion by other electrons. A high Zeff means the electron is more tightly bound, affecting the physical and chemical properties of elements.
