Ionic radii of

Options

A. `Ti^(4+)ltMn^(7+)`
B. `""^(35)Cl^(-)lt""^(37)Cl^(-)`
C. `K^( +)gtCl^(-)`
D. `P^(3+)gtP^(5+)`

Answer

To solve the question regarding the comparison of ionic radii of different ions, we will analyze each pair of ions step by step.

### Step 1: Compare Titanium (Ti⁴⁺) and Manganese (Mn⁷⁺)
- **Titanium (Ti)** has an atomic number of 22, meaning it has 22 protons and 22 electrons.
- For **Ti⁴⁺**, 4 electrons are removed, resulting in 18 electrons and 22 protons.
- **Manganese (Mn)** has an atomic number of 25, meaning it has 25 protons and 25 electrons.
- For **Mn⁷⁺**, 7 electrons are removed, resulting in 18 electrons and 25 protons.
- Both ions have the same number of electrons (18), but Mn⁷⁺ has more protons (25) than Ti⁴⁺ (22). The greater positive charge from the protons in Mn⁷⁺ pulls the electrons closer, resulting in a smaller ionic radius.

**Conclusion:** Mn⁷⁺ < Ti⁴⁺ (Mn⁷⁺ has a smaller ionic radius than Ti⁴⁺).

### Step 2: Compare 35Cl⁻ and 37Cl⁻
- Both ions are isotopes of chlorine, with atomic number 17, meaning they both have 17 protons.
- Both 35Cl⁻ and 37Cl⁻ have gained an electron, resulting in 18 electrons each.
- Since they have the same number of protons and electrons, their ionic radii will be the same.

**Conclusion:** 35Cl⁻ = 37Cl⁻ (Both have the same ionic radius).

### Step 3: Compare Potassium (K⁺) and Chloride (Cl⁻)
- **Potassium (K)** has an atomic number of 19, meaning it has 19 protons and 19 electrons.
- For **K⁺**, 1 electron is removed, resulting in 18 electrons and 19 protons.
- **Chlorine (Cl)** has an atomic number of 17, meaning it has 17 protons and 17 electrons.
- For **Cl⁻**, it gains an electron, resulting in 18 electrons and 17 protons.
- K⁺ has more protons (19) than Cl⁻ (17) while both have the same number of electrons (18). The greater positive charge in K⁺ will pull the electrons closer, resulting in a smaller ionic radius.

**Conclusion:** K⁺ < Cl⁻ (K⁺ has a smaller ionic radius than Cl⁻).

### Step 4: Compare Phosphorus (P³⁺) and Phosphorus (P⁵⁺)
- **Phosphorus (P)** has an atomic number of 15, meaning it has 15 protons and 15 electrons.
- For **P³⁺**, 3 electrons are removed, resulting in 12 electrons and 15 protons.
- For **P⁵⁺**, 5 electrons are removed, resulting in 10 electrons and 15 protons.
- Both ions have the same number of protons (15), but P⁵⁺ has fewer electrons (10) than P³⁺ (12). Fewer electrons mean less electron-electron repulsion and a smaller ionic radius.

**Conclusion:** P⁵⁺ < P³⁺ (P⁵⁺ has a smaller ionic radius than P³⁺).

### Final Summary
1. Mn⁷⁺ < Ti⁴⁺ (Incorrect option)
2. 35Cl⁻ = 37Cl⁻ (Incorrect option)
3. K⁺ < Cl⁻ (Incorrect option)
4. P⁵⁺ < P³⁺ (Correct option)

Thus, the correct answer is option number 4.

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