Extent of hydrolysis depends on the (charge ÷ radius) ratio. So greater the charge and lesser the size , greater will be the hydrolysis.

Since all of them have same charge of +3, we will decide by size .

Since size increases down the group, Al has smallest size.

So Al3+ has greatest efficiency of hydrolysis.

Maximum efficiency of cationic hydrolysis will be shown by:

The maximum efficiency of cationic hydrolysis refers to the ability of a cation to undergo hydrolysis, which results in the formation of hydrated metal ions. This process occurs when a cation reacts with water molecules, resulting in the formation of a hydroxide ion and a positively charged hydrated metal ion.

Among the given options, the cation that will show the maximum efficiency of cationic hydrolysis is Tl3+ (Thallium III) [D].

Explanation:

1. Hydrolysis of Cations:
Cationic hydrolysis involves the reaction of a cation with water molecules. The water molecules act as Lewis bases, donating a pair of electrons to the cation, which acts as a Lewis acid.

2. Factors influencing cationic hydrolysis efficiency:
The efficiency of cationic hydrolysis depends on several factors, including:
- Charge of the cation: Higher charge on the cation promotes stronger interactions with water molecules, leading to a higher efficiency of hydrolysis.
- Size of the cation: Smaller cations have a higher charge density, making them more efficient in attracting water molecules and undergoing hydrolysis.
- Polarizability of the cation: Cations with higher polarizability have more available electron density, resulting in stronger interactions with water molecules and increased hydrolysis efficiency.

3. Comparison of cations:
Considering the given options, we can compare the cations based on their charge, size, and polarizability to determine the maximum efficiency of cationic hydrolysis.

- Al3+ (Aluminum III): Al3+ has a +3 charge and a relatively small size. However, it has low polarizability, limiting its ability to interact effectively with water molecules. Therefore, Al3+ is less efficient in cationic hydrolysis compared to other options.

- Ga3+ (Gallium III): Ga3+ also has a +3 charge and a similar size to Al3+. It has slightly higher polarizability than Al3+, but still lower than the remaining options. Therefore, Ga3+ is less efficient in cationic hydrolysis compared to Tl3+.

- Tl1+ (Thallium I): Tl1+ has a +1 charge and a larger size compared to Al3+ and Ga3+. While the size of Tl1+ promotes better interaction with water molecules, its lower charge limits its efficiency in cationic hydrolysis.

- Tl3+ (Thallium III): Tl3+ has a +3 charge and a larger size compared to Al3+, Ga3+, and Tl1+. The combination of higher charge and larger size results in stronger interactions with water molecules, making Tl3+ more efficient in cationic hydrolysis compared to the other options.

Conclusion:
Among the given options, Tl3+ (Thallium III) will show the maximum efficiency of cationic hydrolysis. Its higher charge and larger size promote stronger interactions with water molecules, leading to the formation of hydrated metal ions.