Effective nuclear charge (Zeff) periodic trend across the period and down the group.
What is effective nuclear charge and how does it vary?
The presence of shielding electrons reduces the electrostatic attraction between the positively charged protons in the nucleus and the outer electrons. Moreover, the repulsive forces between electrons in a many-electron atom further offset the attractive force exerted by the nucleus. Net effect of these two forces means less positive charge filtered out and that positive charge felt by an electron is called as Z effective.
It is the positive charge from the nucleus felt by an electron.
It depends on
- Shielding effect or screening by inner core electrons and
- The nuclear charge.
How does effective nuclear charge (Zeff) change across the period in the periodic table?
Zeff = Z – σ
Zeff » Z – number of inner or core electrons
0 < σ < Z (σ= shielding constant)
|
Period no 3 |
No of shells |
Z | Inner core ( σ) |
Z eff |
Radius of atom(pm) |
|
Na |
3 |
11 |
10 |
11-10=1 |
190 |
|
Mg |
3 |
12 |
10 |
12-10=2 |
160 |
|
Al |
3 |
13 |
10 |
13-10=3 |
143 |
|
Si |
3 |
14 |
10 |
14-10=4 |
132 |
The effective nuclear charge (Zeff) increases across a period because:
- The number of protons in the nucleus increases, strengthening the nuclear attraction.
- The number of electron shells remains the same, so electrons are not farther from the nucleus.
- The number of shielding (inner) electrons stays constant, so they do not significantly offset the increased nuclear charge.
In 3rd period elements
All elements have only three shells and number of inner shell electrons in all elements are 10. However nuclear charge increases by 1 so Zeff increases. This results in more attraction between the nucleus and outermost shell of the atom. Due to increase in attractions, valence shell electrons are more pulled inside closer to the nucleus and decreases the size of the element.
Zeff increases across the period.
How does effective nuclear charge (Zeff) change down the group in the periodic table?
The effective nuclear charge (Zeff) decreases down a group because:
- There are more electron shells, increasing the distance between the nucleus and the valence electrons.
- There are more inner (shielding) electrons, which reduce the net attraction felt by the outermost electrons.
In 1st group elements
How does Zeff change across the periodic table?
Effective nuclear charge (Zeff ) and shielding effect explained:
As we move down the group, number of shells are increasing and number of electrons screening the valence electron are also increasing. However nuclear charge is also increasing but number of shell and more screening effect outweighs increase in nuclear charge. This results in decrease in effective nuclear charge down the group.
As Zeff decrease, the force of attraction between outermost shell and nucleus decreases. Less attraction with nucleus and more repulsion among the electrons results in expansion of the valence shell .Hence atomic size increases with increase in atomic size.
| Group No 1 | No of shells | Z | Inner core (σ) | Radius of atom(pm) |
| Li | 2 | 3 | 2 | 167 |
| Na | 4 | 11 | 10 | 190 |
| K | 5 | 19 | 18 | 243 |
| Rb | 6 | 37 | 36 | 265 |