Video Transcript
Which of the following explains why the radius of the positive ion, the cation, is
smaller than its atomic radius? (A) The atom has more neutrons; therefore, the attraction force of the effective
nuclear charge on the electrons increases. (B) The cation has more neutrons; therefore, the attraction force of the effective
nuclear charge on the electrons increases. (C) The atom has more mass; therefore, the attraction force of the effective nuclear
charge on the electrons increases. (D) The cation has fewer electrons; therefore, the attraction force of the effective
nuclear charge on the electrons increases. (E) The atom has more electrons; therefore, the attraction force of the effective
nuclear charge on the electrons increases.
Let’s start this problem off by comparing a neutral atom, sodium in this case, to the
cation, a sodium one plus ion. The sodium cation has one less electron than a sodium atom, but it has the same
number of protons and neutrons. So we can eliminate answer choices (A) and (B) right away, because the cation doesn’t
have more or less neutrons than the atom. We can also eliminate answer choice (C). It’s true that the sodium atom has slightly more mass because of the extra
electron. But the mass of the electron is so small that there’s not much of a difference.
So that leaves us with either answer choice (D) or (E). It’s true that the cation has fewer electrons and the atom has more electrons. So it seems we have to determine whether the cation or the neutral atom has a greater
attractive force on the electrons due to the effective nuclear charge.
To think about this, let’s look at the electron configurations of the sodium atom and
the sodium cation. As we said earlier, both the atom and the cation have 11 protons in the nucleus. All of the electrons in both the atom and the cation are attracted to the positively
charged nucleus. But if we consider the outer electron in the sodium atom, that electron isn’t
experiencing the full attractive force of the 11 protons in the nucleus, because the
outer electron is shielded by the inner electrons. As a result, the attractive force on that outer electron, called the effective
nuclear charge, is less than the attractive force due to the charge of the 11
protons in the nucleus.
If we compare that to an outer electron in the sodium cation, now the outer electron
is only shielded by two inner electrons. This means that the attractive force on the outer electrons, the effective nuclear
charge, is again less than the attractive force due to the charge of the 11 protons
in the nucleus. Since there are fewer electrons shielding the outer electrons in the cation, the
effective nuclear charge on the outer electrons in the cation is greater than the
effective nuclear charge on the outer electrons in the atom.
The overall result of this is that the outer electrons in the cation experience more
of an attractive pull towards the nucleus than the electrons in the atom do. And since the outer electrons are being pulled closer to the nucleus in the cation,
the radius of the cation is smaller than the radius of the atom.
Our discussion matches answer choice (D), which is the correct answer. The radius of a cation is smaller than its atomic radius because the cation has fewer
electrons. Therefore, the attractive force of the effective nuclear charge on the electrons
increases.
