Analyze Statement I

In group 13, the common oxidation state is $+3$. However, as we move down the group, the $+1$ oxidation state becomes more stable due to the inert pair effect.

• Boron: $+1$ is not stable
• Aluminium: $+1$ is very unstable
• Gallium: $+1$ is more stable
• Indium: $+1$ is still more stable
• Thallium: $+1$ is the most stable

Therefore, the stability of the $+1$ oxidation state increases down the group.

So, Statement I is correct.

Analyze Statement II

Statement II says: The atomic size of gallium is greater than that of aluminium.

Normally, atomic size increases down a group. So one may expect gallium to be larger than aluminium. But in group 13, there is an exception due to poor shielding by the intervening $3d$ electrons.

Because of the poor shielding effect of $3d$ electrons in gallium, the effective nuclear charge on outer electrons increases, causing gallium to have an atomic size almost equal to or slightly less than aluminium.

Hence, the statement that gallium has greater atomic size than aluminium is incorrect.

So, Statement II is incorrect.

Evaluate the options

• A: Statement I incorrect, Statement II correct $ightarrow$ false
• B: Statement I correct, Statement II incorrect $ightarrow$ true
• C: Both correct $ightarrow$ false
• D: Both incorrect $ightarrow$ false

Final Answer

The correct option is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer: B

My derived answer: B

Hence, they agree.