Effective Nuclear Charge

Effective Nuclear Charge measures the net positive charge of nucleus acting on an electron in a multi electron system. It is different from the actual nuclear charge acting between two charged species. This is because there is electron present between nucleus and the electrons in the valence shell which cause repulsion among them countering the attraction of nucleus and electron.

In atomic physics and chemistry, the effective nuclear charge is important in deeper understanding of atomic structure and periodic trends. This article will explore what an effective nuclear charge means, calculate the effective nuclear charge, Slater’s rules, the values of effective nuclear charge, and its trends.

What is Effective Nuclear Charge?

Effective Nuclear Charge is the net positive charge experienced by an electron in a multi-electron atom. The term Effective indicates that the shielding effect of electron prevent electrons from getting completely affected by the nuclear charge. Another name for Effective Nuclear charge is Core Charge. Effective Nuclear Charge is denoted by Z_eff or Z*

Shielding Effect

To understand Effective Nuclear Charge, first, we need to understand why every electron in an atom does not feel the same nuclear charge. It is because, in a multi-electron atom, electrons occupy various orbitals or shells inside the atom, where each shell is situated at different levels from the nucleus. The electrons that are present in the innermost shells repel the electrons that are present in the outer shells. This phenomenon of shielding or screening the outermost electrons from fully experiencing the attraction force of protons in the nucleus by the inner electrons is known as the Shielding effect. This shielding arises between electrons in different shells due to electrostatic repulsion between negatively charged electrons.

Effective Nuclear Charge Formula

To calculate effective charge two parameters we need to consider following two factors:

• The total number of protons present in the nucleus (original nuclear charge), which is given by the atomic number (Z) of that element.
• The shielding constant, which accounts for the repulsion between electrons.

Therefore, the mathematical expression for Effective Nuclear Charge is :

Z_eff = Z – S

where,

• Zeff is Effective Nuclear Charge
• Z is Number of Proton(Atomic Number)
• S is Number of electrons between Nucleus and the electron for which we have to calculate Z_eff

Slater’s Rules

Slater’s Rule is a set of rules used to calculate the effective nuclear charge, where we assign screening constants to each electron in an atom based on its principal quantum number (n) and azimuthal quantum number (l), i.e., the type of orbital (s, p, d, f). Electrons are arranged into groups based on their principal quantum number (n), representing the electron’s energy level. Within each energy level, electrons are further organized into subgroups based on their azimuthal quantum number (l), which describes the shape of the orbital. Here, we consider electrons in s and p orbitals together as they have similar energies. The considerations of Slater’s Rule are mentioned below:

• Electrons that are present in the same group contribute a shielding constant of 0.35. Here, an exception exists for the electron in the [1s] group, where the contribution is 0.30.
• Each electron with a principal quantum number (n-1) contributes a value of 0.85 to the shielding constant.
• Each electron with a principal quantum number less than or equal to (n-2) contributes a value of 1.00 to the shielding constant.
• Each electron with a principal quantum number less than (n) and electrons with a principal quantum number n and an azimuthal quantum number less than (l) contributes a value of 1.00 to the shielding constant because those electrons are closer to the nucleus.

Let’s look at an example of an Iron atom with a nuclear charge of 26 and an electronic configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s².

Electron Configuration	Screening Constant (S)	Effective Nuclear Charge (Zeff)
4s	0.35 × 1 + 0.85 × 14 + 1.00 × 10 = 22.25	26.00 – 22.25 = 3.75
3d	0.35 × 5 + 1.00 × 18 = 19.75	26.00 – 19.75 = 6.25
3s, 3p	0.35 × 7 + 0.85 × 8 + 1.00 × 2 = 11.25	26.00 – 11.25 = 14.75
2s, 2p	0.35 × 7 + 0.85 × 2 = 4.15	26.00 – 4.15 = 21.85
1s	0.30 × 1 = 0.30	26.00 – 0.30 = 25.70

How to Calculate Effective Nuclear Charge

To calculate the effective nuclear charge we need to follow the steps mentioned below:

Step 1: Find the number of proton in the atom i.e. value of Z

Step 2: Write the Electronic Configuration of the Atom

Step 3: Assign Shielding Value to Each Electron

Step 4: Sum all the shielding values

Step 5: Use Effective Nuclear Charge Formula

Effective Nuclear Charge Periodic Trends

It is essential to understand the trends in effective nuclear charge for predicting atomic properties like atomic radii, ionization potential, electron gain enthalpy, etc.

• Effective Nuclear Charge increases across Period: As you move across a period (left to right), the number of protons and electrons increases. Still, here, the increase in nuclear charge is more than the rise in shielding because the electrons are added to the same energy level, i.e., with the same principal quantum number (n). Therefore, the effective nuclear charge experienced by outer electrons increases across a period.
• Effective Nuclear Charge decreases down the Group: As you move across a group (top to bottom), the number of energy levels (shells) increases, which leads to more electron shielding from inner electrons. As a result, the outer electrons do not experience the full effect of the nucleus. Even though there is an increase in the number of protons as you move down the group (due to the increase in atomic number), the rise in shielding by additional inner electrons outweighs the increase in nuclear charge. Therefore, the effective nuclear charge experienced by outer electrons decreases as you move down a group.

Factors Affecting Effective Nuclear Charge

Following factors affect the effective nuclear charge of an electron in an atom:

• Atomic Radius: As you move across a period (left to right), the increasing effective nuclear charge pulls the outer electrons closer to the nucleus, decreasing atomic radius. But while moving down a group, the atomic radius increases due to the increasing energy levels and electron shielding, which outweighs the increase in nuclear charge.
• Ionization Energy: As you move across a period (left to right), the ionization energy generally increases due to the increasing effective nuclear charge, making it more challenging to remove outer electrons. However, while moving down a group, ionization energy decreases typically due to the decreasing effective nuclear charge and increasing electron shielding, making removing outer electrons easier. Electron affinity also follows similar trends.

Conclusion

Effective nuclear charge is an essential concept in atomic physics and chemistry. It helps in understanding atomic structures and periodic trends by reflecting the nuclear charge experienced by electrons. By considering electron shielding and Slater’s rules, scientists can predict various atomic properties, such as atomic radii, ionization energy, and electron affinity. In different periods, the rise in nuclear charge leads to stronger electron attachment. Conversely, in groups, the shielding effect of electrons reduces this influence. This understanding allows scientists to comprehend and manipulate atomic behaviour across various scientific fields.

Related Reads
Periodic trends in Chemical Properties	Group 14 Elements
Electron Affinity	Electronegativity
Chalcogens	Group 17 Elements

Effective Nuclear Charge FAQs

Define Effective Nuclear Charge.

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. The shielding effect of the inner electron cloud, reduces the attraction between the nucleus and the outermost electrons. This shielding effect is stronger for electrons in higher energy levels, resulting in a lower effective nuclear charge for these electrons.

What is Effective Nuclear Charge Formula?

Effective Nuclear Charge Formula is given as Z_eff = Z – S where Z is atomic number and S is the number of electrons between the nucleus and electron under consideration

What are the trends in effective nuclear charge across the periodic table?

As we move across a period (left to right) in the periodic table, the effective nuclear charge generally increases. This is because the nuclear charge increases as protons are added while the shielding effect of the inner electrons remains relatively constant. Down a group, there is a slight decrease in effective nuclear charge as the number of energy levels (shells) increases, which leads to more electron shielding from inner electrons.

Explain the role of Effective Nuclear Charge in chemical bonding.

Effective nuclear charge influences the type of chemical bond formed between atoms, which determines how strongly an atom can attract and share electrons. Elements with higher effective nuclear charges tend to form stronger bonds because they have a greater ability to attract and hold onto electrons.

How does Z_eff change across a period?

Across the period as the atomic size decreases, the effective nuclear charge increases

What is Slate’s Rule?

Slater’s Rule is method of calculating effective nuclear charge by assigning shielding constant to the electrons.

What is Effective Nuclear Charge of Carbon?

Effective Nuclear Charge for Carbon is given as Z = 6 and S = 6 – 4 = 2, Z_eff = Z – S = 6 – 4 = 2