Increasing Order of Atomic Radii of Group Thirteen Elements

To determine the correct increasing order of atomic radii among the given Group 13 elements ($\text{Al}$, $\text{Ga}$, $\text{In}$, and $\text{Tl}$), we analyze the periodic trends and structural considerations down the group:

1. General Trend: Generally, atomic radii increase down a group in the periodic table due to the addition of new electron shells at each successive principal energy level.

2. Anomaly between $\text{Al}$ and $\text{Ga}$:

   • Electronic configuration of Aluminium ($\text{Al}$, $Z = 13$): $[\text{Ne}]\,3s^2\,3p^1$
   • Electronic configuration of Gallium ($\text{Ga}$, $Z = 31$): $[\text{Ar}]\,3d^{10}\,4s^2\,4p^1$

   Gallium contains $10$ inner $d$-electrons ($3d^{10}$). Because $d$-orbitals are diffuse, they offer poor shielding against nuclear attraction for the outermost electrons ($4s$ and $4p$). Consequently, the effective nuclear charge ($Z_{\text{eff}}$) felt by the valence electrons in $\text{Ga}$ increases significantly, pulling the electron cloud closer to the nucleus. This phenomenon (known as $d$-block contraction) results in $\text{Ga}$ having a smaller atomic radius than $\text{Al}$.

3. Trend from $\text{Ga}$ to $\text{In}$ and $\text{Tl}$: Beyond gallium, the effect of adding new principal shells predominates, restoring the usual increase in atomic radii:

   • $\text{Radius of Ga} = 135\text{ pm}$
   • $\text{Radius of Al} = 143\text{ pm}$
   • $\text{Radius of In} = 167\text{ pm}$
   • $\text{Radius of Tl} = 170\text{ pm}$

Combining these experimental values gives the overall increasing order of atomic radii: $\text{Ga} < \text{Al} < \text{In} < \text{Tl}$

Thus, the correct option is (B).