Which of the following option is the correct order of the basic strength of metallic hydroxides

Options

A. `Al(OH)_(3)ltLu(OH)_(3)ltCe(OH)_(3)ltCa(OH)_(2)`
B. `Ca(OH)_(2)ltAu(OH)_(3)ltLu(OH)_(3)ltCe(OH)_(3)`
C. `Lu(OH)_(3)ltCe(OH)_(3)ltAl(OH)_(3)ltCa(OH)_(2)`
D. `Lu(OH)_(3)ltCe(OH)_(3)ltCa(OH)_(2)ltAl(OH)_(3)`

Explanation

To determine the correct order of the basic strength of metallic hydroxides, we need to consider the following factors:

1. **Understanding Basic Strength**: Basic strength of metallic hydroxides is primarily determined by the ability of the metal ion to release hydroxide ions (OH⁻) into the solution. The more readily a metal hydroxide can dissociate to release OH⁻, the stronger it is as a base.

2. **Metal Ion Size and Bond Length**: As the size of the metal ion increases, the bond length between the metal and hydroxide ion also increases. A longer bond length generally means that the bond is weaker, making it easier for the hydroxide ion to dissociate.

3. **Trends in the Periodic Table**: The basic strength of hydroxides generally increases down a group in the periodic table. This is because as we move down a group, the size of the metal ions increases, leading to longer and weaker bonds with hydroxide ions.

4. **Comparing Hydroxides**: For example, if we compare hydroxides of alkali metals (like NaOH, KOH, etc.) and alkaline earth metals (like Mg(OH)₂, Ca(OH)₂), we can see that alkali metal hydroxides are generally stronger bases than alkaline earth metal hydroxides due to the larger size and lower charge density of alkali metals.

5. **Conclusion**: Based on the above points, we can conclude that the order of basic strength of metallic hydroxides will depend on the size of the metal ions and their position in the periodic table.

### Step-by-Step Solution:
1. **Identify the Hydroxides**: List the metallic hydroxides you are comparing (e.g., NaOH, KOH, Ca(OH)₂, Mg(OH)₂).
2. **Consider Metal Ion Size**: Note that as we move down a group, the size of the metal ion increases.
3. **Analyze Bond Length**: Recognize that larger metal ions will have longer bond lengths with hydroxide ions, leading to weaker bonds.
4. **Determine Basic Strength Order**: Based on the above analysis, arrange the hydroxides in order of increasing metal ion size and thus increasing basic strength.
5. **Final Order**: Write down the final order of basic strength for the hydroxides.