Why radius of cation is smaller than its parent atom? Why atomic size of sodium (Na) is greater than sodium Cation ?

Anand Classes explains the radius of a cation is always smaller than that of its parent atom. This is because a cation is formed when one or more electrons are lost from a gaseous atom, often resulting in the complete removal of the outermost electron shell. For example, when a sodium atom (Na) loses its single 3s electron to form a Na⁺ ion, the entire 3s shell disappears, leading to a significant reduction in size—from 186 pm in Na to just 95 pm in Na⁺. This size decrease occurs because the nuclear charge remains the same while the number of electrons decreases, causing the remaining electrons to be pulled closer to the nucleus due to the increased effective nuclear charge.

Why is the radius of a cation smaller than that of its parent atom?

The radius of a cation is always smaller than that of the corresponding neutral atom.

A cation is formed when one or more electrons are lost from a gaseous atom. This process usually involves the complete removal of the outermost shell of electrons, resulting in a significant reduction in the overall size of the particle.

Loss of Outer Shell

When the outermost electrons are removed, the corresponding electron shell disappears completely.

• Example – Sodium (Na):
  Sodium atom has only one electron in its outermost 3s subshell: $$\text{Na}: 1s^2\, 2s^2\, 2p^6\, 3s^1$$ During cation formation: $$\text{Na} \; \longrightarrow \; \text{Na}^+ + e^-$$ The 3s subshell disappears entirely, leaving the configuration: $$1s^2\, 2s^2\, 2p^6$$ This disappearance of the outer shell causes a sharp decrease in radius.
  • Size comparison:
    • Na atom: 186 pm
    • Na⁺ ion: 95 pm

Multiple Electron Loss

When more than one electron is removed, an even greater reduction in size occurs because more electron shells may be affected.

• Example – Magnesium (Mg): $$\text{Mg}: 1s^2\, 2s^2\, 2p^6\, 3s^2$$ In cation formation: $$\text{Mg} \; \longrightarrow \; \text{Mg}^{2+} + 2e^-$$ Resulting configuration: $$1s^2\, 2s^2\, 2p^6$$
• This disappearance of the outer shell causes a sharp decrease in radius.
  • Size comparison:
    • Mg atom: 160 pm
    • Mg²⁺ ion: 72 pm

Role of Nuclear Charge

When electrons are removed:

• The nuclear charge (number of protons) remains unchanged.
• The number of electrons decreases.

This means that the same positive charge now acts on fewer electrons.

Example: Sodium atom has nuclear charge +11 and 11 electrons; Na⁺ has the same nuclear charge (+11) but only 10 electrons. The same positive charge (+11) now attracts fewer electrons (10), increasing the effective nuclear charge per electron. The same positive charge now attracts fewer electrons, increasing the effective nuclear charge per electron. This stronger attraction pulls electrons closer to the nucleus, causing a decrease in atomic size.

As a result:

• Effective nuclear charge per electron increases.
• The electrons are pulled closer to the nucleus.
• The electron cloud shrinks, leading to a smaller ionic radius.

Example: Sodium Ion Formation (Reason for Size Reduction)

• Nuclear charge (Z): +11 (remains the same for Na and Na⁺)
• Number of electrons:
  • Na atom → 11 electrons
  • Na⁺ ion → 10 electrons
• Since +11 charge now pulls only 10 electrons, the attraction per electron is stronger → smaller size.

Sodium atom has nuclear charge +11 and 11 electrons; Na⁺ has the same nuclear charge (+11) but only 10 electrons. The same positive charge (+11) now attracts fewer electrons (10), increasing the effective nuclear charge per electron. The same positive charge now attracts fewer electrons, increasing the effective nuclear charge per electron. This stronger attraction pulls electrons closer to the nucleus, causing a decrease in atomic size.

FAQs on Cation Radius

Q1. Why is the radius of a cation smaller than its parent atom?

A cation is formed by the loss of one or more electrons, often from the outermost shell. This removal reduces the electron cloud size, and the same nuclear charge now attracts fewer electrons more strongly, pulling them closer to the nucleus and decreasing the radius.

Q2. Does the nuclear charge change when a cation is formed?

No. The number of protons (nuclear charge) remains the same, but the number of electrons decreases. This increases the effective nuclear charge per electron, leading to a smaller radius.

Q3. Why is Na⁺ much smaller than Na?

Sodium (Na) has an outermost 3s electron, which is completely lost during cation formation, removing an entire electron shell. Na has a radius of 186 pm, while Na⁺ has only 95 pm.

Q4. Why are Mg²⁺ ions even smaller than Mg atoms?

In magnesium, two outermost 3s electrons are removed to form Mg²⁺, eliminating the 3rd shell entirely. The radius decreases from 160 pm in Mg to 72 pm in Mg²⁺.

Q5. Is the size reduction the same for all cations?

No. The size decrease depends on the number of electrons removed, the charge on the ion, and the original atomic size. Higher positive charge results in a greater decrease in ionic radius.

Q6. Which has a smaller radius — Li⁺ or Na⁺?

Li⁺ has a smaller radius (60 pm) compared to Na⁺ (95 pm) because lithium has fewer electron shells, making the ion more compact.

Comparative Sizes of Atoms and Their Cations

✅ Key Points to Remember:

1. Cations are always smaller than their parent atoms.
2. Loss of electrons causes loss of entire outer shell.
3. Effective nuclear charge increases after electron loss, pulling electrons closer.
4. Greater the positive charge, smaller the cation.

💡 Do You Know? – Interesting Facts about Cation Radius

• Complete Shell Loss: When a cation forms, it may lose an entire outer electron shell, drastically reducing its size.
• Stronger Pull: The same number of protons now attracts fewer electrons, increasing the effective nuclear charge and pulling electrons closer.
• High Charge, Smaller Size: The higher the positive charge on a cation, the smaller its radius — e.g., Al³⁺ (50 pm) is much smaller than Na⁺ (95 pm).
• Drastic Reduction: Some cations can be almost 50% smaller than their parent atoms, such as Mg²⁺ (72 pm) compared to Mg (160 pm).
• Trend in Periodic Table: Across a period, cations generally become smaller due to increasing nuclear charge; down a group, ionic radius increases due to added shells.
• Size Difference Example: Na atom (186 pm) → Na⁺ ion (95 pm) shows nearly half the size reduction after losing one electron.

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