What Is Zeff In Chemistry? Comparison With Periodic Trends

What is Zeff in Chemistry?

Atoms of elements are made of subatomic particles with charges that could be positive, negative, or neutral. The interaction between these particles and some other factors is the basis of many periodic trends.

One of the least talked about periodic trends is Zeff, the effective nuclear charge of an electron. Zeff is most commonly seen in atomic physics as the amount of energy each electron in a multi-electron atom feels from the proton in the nucleus.

Effective nuclear charge, Zeff, is also seen in chemistry as a periodic trend. This is what this article looks into.

What is Zeff in chemistry?

In every multi-electron atom, the nucleus of that atom has a pull on the electrons in each electron shell. This positive charge is called the Zeff of that atom. Zeff means the effective nuclear charge.

Zeff considers the number of electron shells. It is also known as the core charge of that electron.

Electrons in lower energy levels shield electrons in higher energy levels from the pull of the nucleus. This is where the term effective best describes the difference between Zeff and nuclear charge.

The energy each of the outer electrons feels after the screening effect of the inner electrons is the effective nuclear charge.

In simpler words, Zeff measures the electrostatic interactions between the electrons and protons in an atom.

How to find Zeff of elements in chemistry

The formula for the effective nuclear charge, Zeff, is,

Zeff = Z – S

  • Z is the nuclear charge (number of protons in the atom or the atomic number)
  • S is the shielding constant. The shielding constant can be determined using Slater’s rule

Here’s how to find the shielding constant:

  • Start by writing out the electronic configuration of the atom
  • Assign electron values according to the shell levels and shape of the orbitals as follows:
    • No value will be assigned to the electron of concernElectrons in the same shell (ns np) as the electron of concern will have a shielding effect of 0.35Electrons in shells with one energy lower (n-1) will have a shielding effect of 0.85Electrons in shells with two energy levels lower (n-2) will have a shielding effect of 1
    • If the electron of interest is a d or f electrons, all electrons will have a shielding effect of 1
  • You can find the shielding constant for sodium with the above steps
    • The electronic configuration for sodium is 1s22s22p63s1Since the electron in 3s1 is the electron of concern, it will not have an electron valueThe electron in 1s2 has a shielding effect of 1 and the electrons in 2s2 and 2p6 have a shielding effect of 0.85
    • Therefore, (2 x 1) + (2 x 0.85) + (6 x 0.85) + 0 = 8.8
  • To find the Zeff, the nuclear charge (Z) of sodium is 11. Substituting all values into the formula: Zeff = 11 – 8.8 = 2.2

What factors determine the Zeff of an element?

The Zeff of an element depends on the nuclear charge (Z) of the element, the charge of an electron, and the distance between the nucleus and the electron.

Electrons closer to the nucleus experience greater charge than electrons far from the nucleus.

Is Zeff the same as nuclear charge?

Zeff and nuclear charge sound similar but they are very different. The nuclear charge of an atom (Z) is the overall positive charge on the nucleus of that atom due to the number of protons. For instance, an atom with 7 protons has a nuclear charge of +7e.

On the other hand, Zeff is the total charge on the nucleus and the inner electrons. It is a difference between nuclear charge and the shielding constant of the atom.

Is Zeff the same as the ionic charge?

Zeff is the core charge on an electron while the ionic charge is the charge on an element due to electron loss or gain. Zeff describes the positive charge the nucleus has on each valence electron while ionic charge considers the charge one or more electrons (lost or gained) has on the overall atom.

Is Zeff the same as electron affinity?

Electron affinity is the amount of energy released when a neutral atom gains an electron and forms an anion. Electron affinity increases with increasing Zeff but they are different trends.

Moreso, they are both determined by similar factors such as nuclear charge, atomic size, electronic configuration, and screening. Since Zeff is primarily centered on the nucleus and electron attraction, this attraction determines how well a neutral atom will gain electrons.

Is Zeff the same as ionization energy?

No, they are not. Although Zeff and ionization energy both increase across the period and decrease down the group, they are two different periodic trends.

Ionization energy is the amount of energy required to remove an electron from a neutral atom so it forms an ion. Zeff, on the other hand, is the amount of pull the nucleus has on each valence electron.

As you move from left to right across the periodic table, Zeff increases with decreasing atomic size, and ionization energy also becomes higher.

What is the difference between Zeff and the shielding effect?

Electron shielding or the shielding effect is the repulsive effect electrons have on each other as they try to shield themselves from the charge of the protons in the nucleus.

As the protons try to pull the valence electrons, the inner electrons repel this attraction. This is the electron shielding phenomenon. This phenomenon influences the atomic size and explains why it is easier to remove valence shells from the atom.

Zeff, on the other hand, describes the net positive charge the nucleus exerts on the valence electrons (taking into consideration all electron-electron repulsion). It is the difference between the nuclear charge (or atomic number) of the atom and the shielding constant (Zeff = Z – S).

In simple words, the effective nuclear charge is the exact amount of positive charge on an electron in an atom with multiple electrons while the shielding effect is the reduced force of attraction between the electrons and the nucleus that reduces the Zeff of the atom.


Does Zeff increase with atomic size?

No, it does not. Zeff increases with decreasing atomic size. Across the period, more electrons are added to orbitals and are more tightly drawn to the nucleus.

Consequently, the atom shrinks and the charge between the protons in the nucleus and the valence electrons increases.

Why does Zeff increase across a period?

As you move from left to right across the periodic table, more electrons are added but the number of shells remains the same.

Moreover, the atomic radius decreases across the period. This means that there is no change in shielding effect and the valence electrons are more drawn to the nucleus. Since the electrons are held more tightly to the nucleus, the effective nuclear charge increases.

Why does Zeff decrease down a group?

Zeff decreases down the group because as you move down a group of the periodic table, more electrons are added, and the number of shells increase.

As the number of shells increase, the shielding effect also increases. The shielding electrons shield the valence electrons from the nuclear charge and the attraction (the effective nuclear charge) decreases.


Zeff, the effective nuclear charge, is different from the nuclear charge of an element. Although other factors influence the effective nuclear charge of an atom, it largely depends on the atomic number and atomic size of the element.

Therefore, the trend increases with increasing atomic number and decreasing atomic size. As atomic charge increases across the period and the shielding effect remains constant, Zeff will also increase.

You can also learn about the ionization energy trend on the periodic table.

Thanks for reading.