What is the theory associated with the radius of an atom as it (a) gains an electron (b) loses an electron?

take Lithium as one example when Lithium become #Li^+1# it loses an electron. As# Lithium_3^7# The atom has two electron in the first shell like Helium and one electron in the second shell. The electrons in the first shell shield the electron in the second shell from the pull of the positive protons (+3) in the nucleus. When the third electron in the second shell is gone, the radius become much smaller because there is a direct pull on the two remaining electrons which are in a shell much closer to the protons in the nucleus.

Take Oxygen as another example when Oxygen become #O^-2# it gains two electrons. As Oxygen #O_8^16# has eight electrons 2 in the first shell and 6 in the second shell gaining two more electrons decreases the pull of the protons in the nucleus (+8). the decrease in the pull of the electrons causing the electrons to move further from the nucleus causing an increase in the radius of the atom ( now an ion)

The effect is caused by electron shielding.

It considers that the electrons are attracted to the nucleus and are also repelled by each other.

An outer electron is "shielded" from the attraction of the nucleus by the inner electrons and a bit by the other outer electrons.

The greater the shielding, the less the attraction experienced by the outermost electrons.

(a) Gaining an electron

Consider a fluorine gaining an electron to form a fluoride ion.

A fluorine atom has nine electrons and nine protons.

An outer electron is partially screened by the other eight electrons.

It "sees" only an effective charge of +5.2, and this determines its atomic radius.

If we add a tenth electron, it is now partially screened by the other nine electrons.

It sees an effective charge of +4.85.

The attraction for the nucleus is less, so the electrons spend more of their time further from the nucleus.

The atomic radius increases.

(b) Removing an electron

Consider a sodium atom gaining an electron to form a sodium ion.

A sodium atom has 11 electrons and 11 protons.

The outer electron "sees" only an effective charge of +2.2, and this determines its atomic radius.

If we remove this electron, we remove some of the screening effect.

Each outer electron now sees an effective charge of +6.85.

The attraction for the nucleus is greater, so the electrons spend more of their time closer to the nucleus.

The atomic radius decreases.