Elements involved

The group 13 elements given are: $\text{Al, Ga, In, Tl}$

General trend of atomic radius down a group

Normally, atomic radius increases down a group because a new electron shell is added at each step.

So the expected trend would be: $\text{Al} < \text{Ga} < \text{In} < \text{Tl}$

Important exception: Al and Ga

Gallium does not have a larger radius than aluminium as expected.

This is because Ga has filled $3d$ electrons: $\text{Ga}: [Ar] \, 3d^{10}4s^24p^1$

The $3d$ electrons shield poorly, so the effective nuclear charge on the outer electrons of Ga is higher than expected. This causes Ga to contract slightly.

Therefore, $r(\text{Ga}) < r(\text{Al})$

Comparing all four elements

After this anomaly, the radii increase normally down the group: $\text{Ga} < \text{Al} < \text{In} < \text{Tl}$

Checking options

• A: $\text{Al} < \text{Ga} < \text{In} < \text{Tl}$ ❌ incorrect, because $\text{Ga} < \text{Al}$
• B: $\text{Ga} < \text{Al} < \text{In} < \text{Tl}$ ✅ correct
• C: $\text{Al} < \text{In} < \text{Ga} < \text{Tl}$ ❌ incorrect
• D: $\text{Al} < \text{Ga} < \text{Tl} < \text{In}$ ❌ incorrect

Final answer

The increasing order of atomic radii is: $\boxed{\text{Ga} < \text{Al} < \text{In} < \text{Tl}}$

So the correct option is B.