Which of the following (anions/atom/cations) has the smallest radius?
1 Cl
2 Ar
3 K
4 Ca2+
The correct answer and explanation is :
The correct answer is Ca²⁺ (option 4).
Here’s an explanation:
The size of an ion or atom is primarily determined by its effective nuclear charge, the number of electrons, and the electron configuration. Let’s break down the four options and their factors affecting their radius:
- Cl⁻ (Chloride ion):
- Chlorine normally has 17 electrons and 17 protons. When it gains an electron to form Cl⁻, it has 18 electrons and still only 17 protons. This increases the electron-electron repulsion because the additional electron is added to the same electron shell. Despite this, the larger number of electrons results in a relatively large ionic radius compared to neutral atoms of smaller elements.
- Radius of Cl⁻: About 181 pm.
- Ar (Argon atom):
- Argon, a noble gas, has 18 protons and 18 electrons. The electron configuration is stable, and it doesn’t gain or lose electrons under normal conditions. Its atomic radius is larger than Ca²⁺ because its electrons are not pulled in as tightly due to a lower effective nuclear charge compared to Ca²⁺.
- Radius of Ar: About 71 pm.
- K (Potassium atom):
- Potassium has 19 protons and 19 electrons. The atomic radius of potassium is larger than Argon because potassium is in a lower period (Period 4), meaning its outermost electrons are farther away from the nucleus.
- Radius of K: About 220 pm.
- Ca²⁺ (Calcium ion):
- Calcium (Ca) has 20 protons and 20 electrons. However, when it loses two electrons to form the Ca²⁺ ion, it has only 18 electrons. This gives it a significantly smaller ionic radius than its neutral atomic form because the same number of protons (20) now pulls on fewer electrons (18), creating a stronger attraction between the nucleus and the electrons.
- Radius of Ca²⁺: About 100 pm.
Why Ca²⁺ is the smallest:
- Effective nuclear charge (Z_eff): In the case of Ca²⁺, the loss of two electrons results in a higher effective nuclear charge (because the 20 protons are now holding onto 18 electrons instead of 20). This causes the electrons to be drawn more tightly toward the nucleus, resulting in a smaller radius compared to neutral atoms and other ions with the same electron configuration.
Thus, Ca²⁺ has the smallest radius because of the greater nuclear pull on fewer electrons, which contracts the electron cloud more than in neutral or less charged ions.