Atomic radius is a measure of the size of atoms and can be defined as the distance between the nuclei of two atoms of the same element when they are bonded together. The bonding atomic radius of an atom X can be calculated by taking the difference between two distances, d1 and d2. The distance d1 is the sum of the covalent radii of atoms A and X, which is also equal to the covalent radius of the atom A. The distance d2 is the sum of the bonding atomic radii of atoms A and X, which can be written as d2 = rX + d1 /2, where rX is the bonding atomic radius of atom X.

When two atoms of the same element are covalently bonded, the bonding atomic radius of each atom is half the distance between the two nuclei, because they equally attract each other. This can be written as rX = d2 – d1 /2. In other words, the bonding atomic radius of atom X can be found by subtracting the difference between d1 and d2 from the covalent radius of the atom A.

For example, consider a molecule depicted above, where A and X are two different elements, and d1 and d2 are the bond lengths. In this case, the bonding atomic radius of atom X can be determined by subtracting the difference between d1 and d2 from the covalent radius of atom A, which will be equal to rX = d2 – d1 /2.

In conclusion, the bonding atomic radius of an atom X can be defined in terms of d1 and d2 by subtracting the difference between d1 and d2 from the covalent radius of atom A. This can be written as rX = d2 – d1 /2, where rX is the bonding atomic radius of atom X.