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Effective nuclear charge is the phenomena of inner electrons shielding the effects of the attraction from the nucleus on outer electrons. Because the outer electrons are more loosely bound, the radius of the atom increases.
example: with oxygen (+8), the outer electrons are being blocked from the full charge by the inner electrons. the inner electrons shield the outer electrons from the electrostatic attraction of a positive nucleus. the outer electrons feel a reduced electrostatic attraction and this results in an effective nuclear charge.
The effective nuclear charge is the less intense attraction that the electron feels when it is shielded by other electrons. Because the full charge of the nucleus does not reach the electron, it is not pulled to the center of the atom as strongly, so this results in a bigger atomic radius.
atomic radius increases down a group and decreases down a period. Because the # of shells stays the same across a period, the effective nuclear charge is increasing because the atomic # (therefore charge of nucleus) is increasing. Because this is happening, the atomic radius decreases due to attraction happening and the effective nuclear charge is increasing.
For atomic radius: let's say we are going from right to left across a period. The effective nuclear charge would increase, as the number of protons increase but the number of inner electrons stay the same. Thus, the nucleus will have a higher hold on the outer electrons, decreasing the atom's radius.
In short, it just means that the further away from the electron from the nucleus, the lesser the attraction they would feel from the nucleus due to the opposite charge. As you go across a period, you are increasing the number of protons (hence so is the number of electron but since the mass of an electron is so insignificant compared to the mass of a proton), meaning there are more "pulling/attraction" which leads to the decreasing in size of an atom
If I understand correctly, it's basically all about how the electrons are pulled/attracted to the nucleus. The further they're out (the larger the atomic radius), the less attraction they'd feel since it's 1) they're further away, and 2) the other electrons are repulsing them as well.
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