In which of the following pairs the radii of second species is greater than of first ?

Options

A. K, Ca
B. H, He
C. `Mg^(+), Mg^(2+) `
D. `O^(2-), O^(-)`

Answer

To determine in which of the following pairs the radii of the second species is greater than that of the first, we will analyze each pair based on the principles of atomic size and effective nuclear charge.

### Step-by-Step Solution:

1. **Understand Atomic Size Trends**:
- Atomic size increases down a group due to the addition of electron shells.
- Atomic size decreases across a period from left to right due to increased effective nuclear charge (Z-effective), which pulls electrons closer to the nucleus.

2. **Evaluate Each Pair**:
- **Pair 1: Potassium (K) and Calcium (Ca)**:
- K is in Group 1 and Ca is in Group 2 of the same period.
- As we move from K to Ca across the period, the atomic size decreases.
- **Conclusion**: K > Ca (not our answer).

- **Pair 2: Hydrogen (H) and Helium (He)**:
- H has 1 electron (1s¹) and He has 2 electrons (1s²).
- Helium is a noble gas with a compact structure and higher effective nuclear charge, leading to a smaller size.
- However, Van der Waals radius of H is larger than that of He due to repulsion in He.
- **Conclusion**: H > He (this is our answer).

- **Pair 3: Mg⁺ and Mg²⁺**:
- Mg has 12 protons and 12 electrons in its neutral state.
- Mg⁺ has 11 electrons and 12 protons; Mg²⁺ has 10 electrons and 12 protons.
- The effective nuclear charge increases as electrons are removed, causing the size to decrease.
- **Conclusion**: Mg⁺ > Mg²⁺ (not our answer).

- **Pair 4: O⁻ and O²⁻**:
- O has 8 protons and 8 electrons in its neutral state.
- O⁻ has 9 electrons and 8 protons; O²⁻ has 10 electrons and 8 protons.
- Adding electrons increases electron-electron repulsion, leading to a larger size for O²⁻.
- **Conclusion**: O²⁻ > O⁻ (this is our answer).

3. **Final Answer**:
- The pairs where the radius of the second species is greater than that of the first are:
- **H > He** (Van der Waals radii)
- **O²⁻ > O⁻**

### Summary:
The correct pairs where the radius of the second species is greater than that of the first are:
- Hydrogen (H) has a larger Van der Waals radius than Helium (He).
- O²⁻ has a larger radius than O⁻ due to increased electron repulsion.