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 among the given elements, we will analyze the trends in atomic radii in the periodic table, specifically focusing on the alkali metals (Li, Na, K, Rb, Cs, Fr) which are typically found in the S block.

### Step-by-Step Solution:

1. **Identify the Elements**:
We need to consider the alkali metals: Lithium (Li), Sodium (Na), and Potassium (K).

2. **Understand the Trend in Atomic Radius**:
- **Down the Group**: As we move down a group in the periodic table, the atomic radius increases. This is due to the addition of new electron shells, which outweighs the increase in nuclear charge.
- **Across the Period**: As we move from left to right across a period, the atomic radius decreases because the increasing positive charge in the nucleus pulls the electrons closer to the nucleus.

3. **Compare the Elements**:
- **Lithium (Li)**: This is the first element in the alkali metal group and has the smallest radius.
- **Sodium (Na)**: This is below lithium and has a larger radius than lithium.
- **Potassium (K)**: This is below sodium and has a larger radius than sodium.

4. **Order of Increasing Radius**:
Based on the above trends, the order of increasing radius for the elements is:
- Lithium (Li) < Sodium (Na) < Potassium (K)

5. **Conclusion**:
Therefore, the correct order of increasing radius is:
**Li < Na < K**

### Final Answer:
The order of increasing radius is: **Li < Na < K**.