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Problems · Problem 3.5

Q.Which of the following species will have the largest and the smallest size? Mg, Mg2+, Al, Al3+Mg,\ Mg^{2+},\ Al,\ Al^{3+}.

Chhattisgarh CgbseTextbookSubjective· 2mImportance★★★★★est
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The key idea is that cationic size decreases sharply with increasing positive charge, while neutral atoms are larger. Among MgMg, Mg2+Mg^{2+}, AlAl, and Al3+Al^{3+}, the largest species is the neutral MgMg atom and the smallest is the Al3+Al^{3+} ion.


Why this approach works

The size of an atom or ion depends on two competing factors: the number of electron shells (principal quantum number nn) and the effective nuclear charge (ZeffZ_{\text{eff}}) pulling those electrons inward.

For neutral atoms in the same period, size decreases left to right because ZeffZ_{\text{eff}} increases. But when an atom loses electrons to form a cation, two things happen:

  • The electron count drops, often removing an entire shell.
  • The remaining electrons feel a stronger pull from the same nucleus (fewer electrons to shield each other).

So cations are always smaller than their parent atoms. And among cations with the same number of electrons (isoelectronic species), the one with the higher nuclear charge is smaller.

Here, we have two neutral atoms (MgMg, AlAl) and two cations (Mg2+Mg^{2+}, Al3+Al^{3+}). Let’s compare them systematically.


Step-by-step reasoning

1. Locate the elements in the periodic table.

MgMg (atomic number 12) and AlAl (atomic number 13) are in the third period. MgMg is in group 2, AlAl in group 13.

2. Compare the neutral atoms: MgMg vs AlAl.

Across a period, atomic radius decreases as nuclear charge increases. AlAl has one more proton than MgMg, so its electrons are pulled in slightly tighter.

Thus: MgMg (neutral) > AlAl (neutral) in size.

3. Compare the cations: Mg2+Mg^{2+} vs Al3+Al^{3+}.

Mg2+Mg^{2+} has the electron configuration of neon (1s22s22p61s^2 2s^2 2p^6), with 10 electrons and 12 protons.

Al3+Al^{3+} also has the neon configuration, with 10 electrons but 13 protons.

These two ions are isoelectronic — same number of electrons, same shells. The ion with the larger nuclear charge (Al3+Al^{3+}) pulls the same electron cloud more strongly, so it is smaller.

Thus: Mg2+Mg^{2+} > Al3+Al^{3+} in size.

4. Compare neutral atoms with their own cations.

When MgMg loses two electrons to become Mg2+Mg^{2+}, it loses its entire third shell (n=3n=3). The ion has only two shells (n=1,2n=1,2), so it is dramatically smaller than the neutral atom.

Similarly, Al3+Al^{3+} is much smaller than neutral AlAl.

So the ordering from largest to smallest is:

MgMg (neutral) > AlAl (neutral) > Mg2+Mg^{2+} > Al3+Al^{3+}.

Watch out

A common mistake is to think AlAl is larger than MgMg because aluminium has more protons. Actually, more protons decrease size across a period. Another pitfall: assuming Mg2+Mg^{2+} is larger than Al3+Al^{3+} because magnesium is below aluminium in the periodic table — but here they are isoelectronic, so nuclear charge decides.

5. Confirm the extremes.

  • Largest: MgMg (neutral, two shells more than its cation).
  • Smallest: Al3+Al^{3+} (highest charge, same electron count as Mg2+Mg^{2+} but more protons).

✓Final answer

The largest species is MgMg and the smallest is Al3+Al^{3+}.

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