Let's analyze each statement:
i.
**Atomic radius of Ga is less than that of Al.
**
Generally, atomic radius increases down a group.
However, due to the poor shielding effect of the \( 3d \) electrons in Gallium (Ga), the effective nuclear charge experienced by the valence electrons in Ga is higher than expected.
This leads to a contraction in the atomic size of Ga, making its atomic radius slightly smaller than that of Aluminum (Al).
The order is Al>Ga.
Therefore, this statement is correct.
ii.
**The order of ionization enthalpy of group 13 elements is B>Al>Ga>In>Tl.
**
The first ionization enthalpy generally decreases down a group due to increasing atomic size and shielding effect.
However, there are exceptions due to electronic configurations and effective nuclear charge.
The actual order for Group 13 is approximately B>Tl>Ga>Al>In.
The ionization enthalpy of Ga is higher than that of Al due to the poor shielding effect of the \( 3d \) electrons in Ga, leading to a higher effective nuclear charge.
The order given in the statement is incorrect.
iii.
**Boron trioxide is amphoteric in nature.
**
Boron trioxide (\( B_2O_3 \)) is primarily acidic in nature.
It reacts with basic oxides to form borates and with water to form boric acid (\( H_3BO_3 \)).
While it can react with very strong acids under specific conditions, its acidic character is dominant.
Aluminum oxide (\( Al_2O_3 \)) and Gallium oxide (\( Ga_2O_3 \)) are amphoteric.
Therefore, this statement is incorrect.
The statements that are not correct are ii and iii.