Given atomic radius relations in group 13

The pairs given are:

$B < Al,\, Al < Ga,\, Ga < In,\, In < Tl$

We need to identify the incorrect pair in terms of atomic radius, and then in that pair find the element $X$ whose ionic radius as $M^{3+}$ is higher than the other.

Actual trend of atomic radii in group 13

Down the group, atomic radius generally increases, but there are important exceptions due to d-block contraction and poor shielding by d and f electrons.

For group 13:

$B < Al$ This is correct.

$Al < Ga$ This is incorrect. In fact, due to d-block contraction, gallium has nearly the same size as aluminium and is slightly smaller than aluminium. So actually:

$Ga < Al$

$Ga < In$ This is correct.

$In < Tl$ This is generally correct for atomic radius.

Hence, the incorrect pair is $(Al < Ga)$, i.e. the elements are Al and Ga.

Compare ionic radii of $Al^{3+}$ and $Ga^{3+}$

We now need the element in this incorrect pair whose ionic radius $M^{3+}$ is greater.

Due to poor shielding by the $3d$ electrons in Ga, the size of $Ga^{3+}$ becomes slightly larger than $Al^{3+}$.

Therefore:

$r(Ga^{3+}) > r(Al^{3+})$

So, $X = Ga$

Atomic number of Ga

Gallium has atomic number:

$Z = 31$

Final answer

The correct option is:

$\boxed{31}$

So, Option C is correct.