The atomic radius of a gallium atom is 135 pm, and the ionic radius of the ion G

Question

The atomic radius of a gallium atom is 135 pm, and the ionic radius of the ion Ga3+ is 62 pm. Explain the relative radii by estimating Zeff for each of these species. The atomic radius of a gallium atom is 135 pm, and the ionic radius of the ion Ga3+ is 62 pm. Explain the relative radii by estimating Zeff for each of these species. The atomic radius of a gallium atom is 135 pm, and the ionic radius of the ion Ga3+ is 62 pm. Explain the relative radii by estimating Zeff for each of these species.

Explanation / Answer

Galium
Ga
Z = 31 (protons)
Electron configuration:
[Ar] 3d10 4s2 4p1
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p1

Zeff = Z - S
Z, number or protons
S, shielding constant

Rules to calculate shielding constant:

Electrons in the same group of the evaluated electron contribute 0.35 (except in 1s, where it contribute 0.30)
For groups s or p located (n-1) from the evaluated electron, contribute an amount of 0.85 for each electron.
For groups s or p located (n-2) from the evaluated electron, contribute an amount of 1.00 for each electron.
If the electron is found in a group d or f, every other electron except those in the same orbital, contributes an amount 1.00.

Calculate S for the most external electron (4p1):
(1s2) (2s2 2p6) (3s2 3p6 3d10) (4s2)
S = (2x1) + (8x1) + (18x0.85) + (2x0.35)
S = 26

Zeff = 31 - 26
Zeff = 5

______________________________


Galium
Ga3+
Z = 31 (protons)
Electron configuration:
[Ar] 3d10 (preferable configuration to complete d shell)
1s2 2s2 2p6 3s2 3p6 3d10

Calculate S for the most external electron (3d10):
(1s2) (2s2 2p6) (3s2 3p6) (3d10)
S = (2x1) + (8x1) + (8x1) + (9x0.35)
S = 21.15

Zeff = 31 - 21.15
Zeff = 9.85

______________________________


The gallium cation has the largest effective nuclear charge (Zeff). If the nuclear charge increases, the electron cloud is closer to the core of the atom, resulting in a smaller atomic radius, therefore Ga3+ has the smallest atomic radius.

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