Step 1: Understand the given elements.
The elements given are Li, Na, Be, Mg, B, and Al. These belong to the second and third periods of the periodic table. As we move from left to right across a period, the atomic radius decreases due to an increase in effective nuclear charge.
Step 2: Identify the element with the least atomic radius.
Among the given elements:
Li → Na → Be → Mg → B → Al
Comparing their positions in the periodic table:
- Li, Be, and B are in the 2nd period.
- Na, Mg, and Al are in the 3rd period.
Since atomic radius decreases across a period and increases down a group, **Boron (B)** has the smallest atomic radius among the given elements.
Step 3: Determine the type of oxide formed by the element.
Boron forms **boron trioxide**, \( B_2O_3 \).
The general formula of the oxide formed by elements of group 13 is \( \text{A}_2\text{O}_3 \).
Step 4: Nature of the oxide.
\( B_2O_3 \) is an acidic oxide, as boron is a metalloid. However, the question asks for the type of oxide based on the formula, not its acidic or basic nature.
Step 5: Final Answer.
The type of oxide formed by the element (boron) with the least atomic radius is:
\[
\boxed{\text{A}_2\text{O}_3}
\]