Question

Incorrect order of atomic radius is

• A. \( \mathrm{B<Al} \)
• B. \( \mathrm{In<Tl} \)
• C. \( \mathrm{Al<Ga} \)
• D. \( \mathrm{Ga<In} \)

Hint:

While atomic radius usually increases down a group, exceptions like \( \mathrm{Ga} \) and \( \mathrm{Tl} \) occur because of poor shielding by \( d \)- and \( f \)-electrons. Always remember d-block contraction and lanthanoid contraction for such comparisons.

Answer 1

The Correct Option is C

Step 1: Understand the trend of atomic radius in a group.
Atomic radius generally increases as we move down a group in the periodic table because new electron shells are added. So, for Group 13 elements, the expected trend is that size should increase from \( \mathrm{B} \) to \( \mathrm{Al} \) to \( \mathrm{Ga} \) to \( \mathrm{In} \) to \( \mathrm{Tl} \), but there are important exceptions due to poor shielding effects of inner electrons.
Step 2: Analyze the actual order for Group 13 elements.
The elements involved here are \( \mathrm{B, Al, Ga, In, Tl} \), all belonging to Group 13. Normally, radius should increase down the group. However, \( \mathrm{Ga} \) has a slightly smaller atomic radius than expected because of the poor shielding by \( 3d \) electrons. This is called d-block contraction. Similarly, \( \mathrm{Tl} \) does not become much larger than \( \mathrm{In} \) because of lanthanoid contraction.
Thus, the relevant correct comparisons are:
\[ \mathrm{B<Al} \] \[ \mathrm{Ga<Al \; \text{or nearly equal, but generally} \; Ga<Al} \] \[ \mathrm{Ga<In} \] \[ \mathrm{In<Tl} \] Step 3: Check each option carefully.
\begin{itemize} \item (A) \( \mathrm{B<Al} \): Correct. Atomic radius increases from boron to aluminium. \item (B) \( \mathrm{In<Tl} \): Correct. Thallium is slightly larger than indium. \item (C) \( \mathrm{Al<Ga} \): Incorrect. Due to poor shielding by \( 3d \) electrons, gallium has a radius slightly smaller than aluminium. So this order is wrong. \item (D) \( \mathrm{Ga<In} \): Correct. Atomic radius increases from gallium to indium. \end{itemize} Step 4: Conclusion.
Therefore, the incorrect order of atomic radius is \( \mathrm{Al<Ga} \), because in reality gallium is slightly smaller than aluminium due to d-block contraction.
Final Answer: \( \mathrm{Al<Ga} \).