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Physics > Atomic and Molecular Structure > What is Effective Nuclear Charge and How to Calculate it?
Atomic and Molecular Structure

What is Effective Nuclear Charge and How to Calculate it?

Introduction to Effective Nuclear charge

Effective nuclear charge refers to the charge that the outermost (valance) electron have. Also, the electron or multi-electron takes into account the number of shielding electrons that surrounds the nucleus.

In this topic, we are going to discuss the effective nuclear charge and how to calculate it. Moreover, in the process, we will also learn various things about the nuclear charge.

effective nuclear charge

Effective Nuclear Charge Formula

Besides, the formula for calculating the effective nuclear charge of a single electron is as follows:

Zeff = Z – S


Zeff = the effective nuclear charge
Z = denotes the number of protons existing in the nucleus
S = average amount of density between the nucleus and the electron.

Also, we solve this to find the effective charge of the electron.

Moreover, you can use this formula to find the effective nuclear charge for an electron in lithium, especially the “2s” electrons.

 Find Z: Atomic Number

Firstly, determine the value of Z which is the number of protons in the nucleus of the atom. Furthermore, it determines the positive charge of the nucleus. In addition, the number of protons in the nucleus of an atom is the atomic number of the atom that we can find on the periodic table of the elements.

Besides, in the above-mentioned example of Lithium, the value for Z is 3.

Find S: Slater’s Rules

Use Slater’s rule to find the value of S. Moreover, it provides numerical values for the effective nuclear charge concept. Furthermore, we can achieve this by writing out the electron configuration of the element in the following groupings and order:

(1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f), (5s, 5p), (5d), (5f), etc.

Besides, the electron configuration corresponds to the shell level of the electrons in the atom (how far is the electron from the nucleus) and the letter corresponds to the given shape of an electron’s orbit.

In simple terms, “s” is the sphere-shaped orbit, “p” looks like a figure eight with two lobes, “d” looks like a figure eight with a doughnut around the centre, and the character “f” looks a lot like 2 number 8s that divides every other.

For example, the electron configuration of Lithium (3 electrons) will look like this: (1s)2, (2s)1. It means that there are two electrons in the first shell and one in second shell spherical orbital shapes

Find S: Assign electron value

In this assign the value of electron according to their shell level and orbital shape. Moreover, an electron in an “s” or “p” orbit in the same shell as the electron for which you’re solving contribute 0.35, also one energy level orbital lower than this contributes 0.85, and an orbital shell which is two-level lower contribute 1.

 Find S: Add values together

For calculating the value of S adds the number you assign to each electron in Slater’s Rules.

For Example S = .85 +.85 = 1.7 (the sum of values of two-electron)

Subtract S from Z

Finally subtract the value of S from Z to find the value of effective nuclear charge, Zeff.

For example, Us the Lithium atom, then Z =3 (atomic number) and S = 1.7. Now put the variables in the formula to know the value of Zeff (effective nuclear charge).

Zeff = Z- S
Zeff = 3 – 1.7 = 1.3

So, the value of effective nuclear charge of 2s electron in Lithium atom is 1.3.

Solved Question for You

Question. What is the effective nuclear charge of chlorine?

A. 5
B. 6
C. 7
D. 9

Answer. The correct answer is option C.

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