EFFECTIVE NUCLEAR CHARGE OF POTASSIUM: WHAT IT IS AND EXAMPLES - CHEMISTRY - 2025

The effective nuclear charge of potassium is +1. The effective nuclear charge is the total positive charge perceived by an electron belonging to an atom with more than one electron. The term "effective" describes the shielding effect that electrons exert near the nucleus, from their negative charge, to protect electrons from higher orbitals.

This property is directly related to other characteristics of elements, such as their atomic dimensions or their disposition to form ions. In this way, the notion of effective nuclear charge provides a better understanding of the consequences of the protection present on the periodic properties of the elements.

In addition, in atoms that have more than one electron -that is, in polyelectronic atoms- the existence of the shielding of the electrons produces a decrease in the electrostatic attractive forces existing between the protons (positively charged particles) of the nucleus of the atom. and electrons at outer levels.

In contrast, the force with which electrons repel each other in polyelectronic atoms counteracts the effects of attractive forces exerted by the nucleus on these oppositely charged particles.

What is the effective nuclear charge?

When it comes to an atom that has only one electron (hydrogen type), this single electron perceives the net positive charge of the nucleus. On the contrary, when an atom has more than one electron, it experiences the attraction of all the external electrons towards the nucleus and, simultaneously, the repulsion between these electrons.

In general, it is said that the greater the effective nuclear charge of an element, the greater the attractive forces between the electrons and the nucleus.

Similarly, the larger this effect, the lower the energy belonging to the orbital where these outer electrons are located.

For most main group elements (also called representative elements) this property increases from left to right, but decreases from top to bottom in the periodic table.

To calculate the value of the effective nuclear charge of an electron (Z _eff or Z *) the following equation proposed by Slater is used:

Z * = Z - S

Z * refers to the effective nuclear charge.

Z is the number of protons present in the nucleus of the atom (or the atomic number).

S is the average number of electrons that are between the nucleus and the electron being studied (number of electrons that are not valence).

Effective nuclear charge of potassium

This implies that, having 19 protons in its nucleus, its nuclear charge is +19. As we speak of a neutral atom, this means that it has the same number of protons and electrons (19).

In this order of ideas, the effective nuclear charge of potassium is calculated by an arithmetic operation, by subtracting the number of internal electrons from its nuclear charge as expressed below:

(+19 - 2 - 8 - 8 = +1)

In other words, the valence electron is protected by 2 electrons from the first level (the one closest to the nucleus), 8 electrons from the second level, and 8 more electrons from the third and penultimate level; that is, these 18 electrons exert a shielding effect that protects the last electron from the forces exerted by the nucleus on it.

As can be seen, the value of the effective nuclear charge of an element can be established by its oxidation number. It should be noted that for a specific electron (at any energy level), the calculation of the effective nuclear charge is different.

Examples of effective nuclear charge of potassium explained

Here are two examples to calculate the effective nuclear charge perceived by a given valence electron on a potassium atom.

- Firstly, its electron configuration is expressed in the following order: (1 s) (2 s, 2 p) (3 s, 3 p) (3 d) (4 s, 4 p) (4 d) (4 f) (5 s, 5 p), and so on.

- No electron to the right of the group (ns, np) contributes to the calculation.

- Each electron in the group (ns, np) contributes 0.35. Each electron of the (n-1) level contributes 0.85.

- Each electron of level (n-2) or lower contributes 1.00.

- When the protected electron is in a group (nd) or (nf), each electron of a group to the left of the group (nd) or (nf) contributes 1.00.

Thus, the calculation begins:

First example

In the case that the only electron in the outermost shell of the atom is in the 4 s orbital, its effective nuclear charge can be determined as follows:

(1 s ²) (2 s ² 2 p ⁵) (3 s ² 3 p ⁶) (3 d ⁶) (4 s ¹)

The average number of electrons not belonging to the outermost level is then calculated:

S = (8 x (0.85)) + (10 x 1.00)) = 16.80

Taking the value of S, we proceed to calculate Z *:

Z * = 19.00 - 16.80 = 2.20

Second example

In this second case, the only valence electron is in the 4 s orbital. Its effective nuclear charge can be determined in the same way:

(1 s ²) (2 s ² 2 p ⁶) (3 s ² 3 p ⁶) (3 d ¹)

Again, the average number of non-valence electrons is calculated:

S = (18 x (1.00)) = 18.00

Finally, with the value of S, we can calculate Z *:

Z * = 19.00 - 18.00 = 1.00

conclusion

Making a comparison of the previous results, it can be observed that the electron present in the 4 s orbital is attracted to the nucleus of the atom by forces greater than those that attract the electron that is located in the 3 d orbital. Therefore, the electron in the 4 s orbital has lower energy than that in the 3 d orbital.

Thus, it is concluded that an electron can be located in the 4 s orbital in its ground state, while in the 3 d orbital it is in an excited state.

References

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