Which of the following is arranged in order of incresing radius?

Options

A. `K^(+) (aq) lt Na^(+)(aq) lt Li^(+)(aq)`
B. `Na^(+)(aq) lt K^(+)(aq) lt Li^(+)(aq)`
C. `K^(+)(aq) lt Li^(+)( aq) lt Na^(+)(aq)`
D. `Li^(+)(aq) lt Na^(+) (aq) lt K^(+)(aq)`

Answer

To determine the order of increasing radius for the given hydrated ions, we need to consider the size of the ions and their hydration energies.

### Step-by-Step Solution:

1. **Understanding Hydrated Ions**: Hydrated ions are ions that are surrounded by water molecules. The size of a hydrated ion is influenced by the size of the actual ion and the hydration energy.

2. **Ion Size and Hydration Energy**: The size of the hydrated ion is inversely proportional to the size of the actual ion. This means that smaller ions will have higher hydration energy, leading to a larger hydrated radius.

3. **Comparing Ions**: In the case of lithium (Li⁺), sodium (Na⁺), and potassium (K⁺):
- Li⁺ is the smallest ion among the three.
- Na⁺ is larger than Li⁺.
- K⁺ is the largest ion among the three.

4. **Hydration Energy Trend**: As we move down the group from Li⁺ to Na⁺ to K⁺, the size of the ions increases, and thus the hydration energy decreases. Therefore, the order of hydrated ion sizes will be:
- Li⁺ (smallest ion, highest hydration energy, largest hydrated radius)
- Na⁺ (medium size, medium hydration energy)
- K⁺ (largest ion, lowest hydration energy, smallest hydrated radius)

5. **Arranging in Order of Increasing Radius**: Since we are looking for the order of increasing radius, we can summarize:
- K⁺ < Na⁺ < Li⁺

Thus, the correct order of increasing radius for the hydrated ions is:
**K⁺ < Na⁺ < Li⁺**