Which is the correct order of ionic sizes ?
(Atomic no . : Ce = 58 , Sn = 50 , Yb = 70 and Lu)

Options

A. `Ce^(3+)gt Sn^(2+)gt Yb^(3+)gt Lu^(3+)`
B. `Sn^(2+)gt Yb^(3+) gt Ce^(3+) gt Lu ^(3+)`
C. `Sn^(2+)gt Ce^(3+) gt Yb^(3+) gt Lu ^(3+)`
D. `Lu^(2+)gt Yb^(3+) gt Sn^(3+) gt Ce ^(3+)`

Answer

To determine the correct order of ionic sizes for the elements Cerium (Ce), Tin (Sn), Ytterbium (Yb), and Lutetium (Lu), we will analyze the ionic sizes based on their atomic numbers and the charge of their ions.

### Step-by-Step Solution:

1. **Identify the Elements and Their Charges**:
- Cerium (Ce) - Atomic number 58, typically forms +3 ion (Ce³⁺).
- Tin (Sn) - Atomic number 50, typically forms +2 ion (Sn²⁺).
- Ytterbium (Yb) - Atomic number 70, typically forms +3 ion (Yb³⁺).
- Lutetium (Lu) - Atomic number 71, typically forms +3 ion (Lu³⁺).

2. **Understand the Trends in Ionic Size**:
- Ionic size generally decreases across a period due to increasing nuclear charge, which pulls the electrons closer to the nucleus.
- The size of cations decreases with increasing positive charge because more protons attract fewer electrons, leading to a stronger pull on the remaining electrons.

3. **Compare the Ionic Sizes**:
- **Tin (Sn²⁺)**: Has 50 protons and 48 electrons. The relatively lower positive charge means it has a larger ionic size compared to the others.
- **Cerium (Ce³⁺)**: Has 58 protons and 55 electrons. The higher positive charge compared to Sn²⁺ results in a smaller ionic size.
- **Ytterbium (Yb³⁺)**: Has 70 protons and 67 electrons. Similar to Ce³⁺, it has a high positive charge, resulting in a smaller ionic size than Ce³⁺.
- **Lutetium (Lu³⁺)**: Has 71 protons and 68 electrons. It has the highest positive charge and the highest number of protons, leading to the smallest ionic size.

4. **Establish the Order of Ionic Sizes**:
- From the analysis, we can conclude the order of ionic sizes from largest to smallest is:
- Sn²⁺ > Ce³⁺ > Yb³⁺ > Lu³⁺

### Final Order:
**Sn²⁺ > Ce³⁺ > Yb³⁺ > Lu³⁺**