In which one of the following pairs the radius of the second species is greater than that of first ?

Options

A. `Na,Mg`
B. `O2−,N3−`
C. `Li+,Be2+`
D. `Ba2+,Sr2+`

Explanation

To determine in which pair the radius of the second species is greater than that of the first, we will analyze each option provided.

### Step-by-step Solution:

1. **Analyze the first pair: Sodium (Na) and Magnesium (Mg)**
- Sodium (Na) is an alkali metal (Group 1), and Magnesium (Mg) is an alkaline earth metal (Group 2).
- As we move from left to right across a period, atomic size decreases due to an increase in nuclear charge (more protons) pulling the electrons closer to the nucleus.
- Therefore, the radius of Na is greater than that of Mg.
- **Conclusion:** Na > Mg (incorrect).

2. **Analyze the second pair: Oxide ion (O²⁻) and Nitride ion (N³⁻)**
- Both O²⁻ and N³⁻ are isoelectronic species (both have 10 electrons).
- O²⁻ has 8 protons, while N³⁻ has 7 protons.
- The effective nuclear charge is greater in O²⁻ due to more protons, which pulls the electrons closer, resulting in a smaller radius.
- Therefore, the radius of N³⁻ is greater than that of O²⁻.
- **Conclusion:** N³⁻ > O²⁻ (correct).

3. **Analyze the third pair: Lithium ion (Li⁺) and Beryllium ion (Be²⁺)**
- Both Li⁺ and Be²⁺ are isoelectronic species (both have 2 electrons).
- Li⁺ has 3 protons, while Be²⁺ has 4 protons.
- The greater nuclear charge in Be²⁺ pulls the electrons closer, resulting in a smaller radius.
- Therefore, the radius of Li⁺ is greater than that of Be²⁺.
- **Conclusion:** Li⁺ > Be²⁺ (incorrect).

4. **Analyze the fourth pair: Barium ion (Ba²⁺) and Strontium ion (Sr²⁺)**
- Both Ba²⁺ and Sr²⁺ belong to Group 2 (alkaline earth metals).
- As we move down a group, atomic size increases due to the addition of electron shells.
- Therefore, Ba²⁺ will have a larger radius than Sr²⁺.
- **Conclusion:** Ba²⁺ > Sr²⁺ (incorrect).

### Final Conclusion:
The only pair where the radius of the second species is greater than that of the first is **O²⁻ and N³⁻**. Thus, the correct answer is the second option.

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