Answer
The order of the atoms in increasing radii: Be, Si, Al.
Work Step by Step
In the periodic table, there are two trends in bonding atomic radii:
1) From left to right across a period, the bonding atomic radii of the atoms tend to become smaller and smaller (due to the increasing effective nuclear charge).
2) From top to bottom across a group, the bonding atomic radii of the atoms tend to increase (due to the expansion of the principal quantum number n, giving the electrons more chance to be further from the nucleus)
Al and Si are in the same period. From left to right, the elements appear in the following order: Al, Si.
That means the radius of Al is greater than the radius of Si.
Be is in the lower period from Si. This shows that the radius of Be is smaller than the radius of Si.
Overall, the order of atoms in increasing radius: Be, Si, Al.