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The nuclear charge of an atom is simply the number of protons in its nucleus. However, the effective nuclear charge is a measure of how much of the nuclear charge is actually felt by any given particle; basically, what fraction of the "full" charge is actually being applied.
The reason the full charge is not felt is because electrons can only fit into certain spaces surrounding the nucleus, progressively farther and farther away as inner regions are filled with the maximum number of electrons. Because electrons are negative and protons are positive, they attract, while electrons will repel each other. This creates a complex series of dynamics, where all electrons are repelled by each other while simultaneously being attracted to the same point. Electrons that are closer to that point have, in a sense, "priority" over claiming a share of the positive charge.
Therefore, effective nuclear charge is a measure of how much of the positive charge remains after those electrons which are closer to the nucleus have claimed their share of it. While in reality this would require some complex math in order to determine the exact charge at various points in space, it can be summarized as
Zeff = Z - S
where Zeff is effective nuclear charge, Z is the full charge, and S is the number of nonvalence electrons (those which are closer to the nucleus). Electrons farther from the nucleus don't factor into this equation.
Gallium is element 31, so Z = 31.
Its electron orbitals are;
1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p1
So, a 3p electron would be ignoring the 4s, 3d and 4p shell electrons, for an "ignorance" of 13 electrons. It would also ignore the other 3p electrons, bringing the total to 18.
31- 18 = 13
31 - 13 = 18
So the effective nuclear charge felt at the 3p shell is 18.
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