Explanation:

Surface Energy:
Surface energy is the excess energy per unit area that a solid material possesses due to the presence of its surface. It is a measure of the energy required to create or break the bonds at the surface.

BCC Metal:
BCC (Body-Centered Cubic) is a crystal structure commonly found in metals. In a BCC structure, the atoms are arranged in a cubic lattice with one atom at the center of the cube and eight atoms at the corners.

Surface Orientation:
Different crystallographic planes have different surface energies due to the arrangement of atoms in the lattice. The surface energy of a specific plane is determined by the arrangement and strength of the bonds between atoms on that plane.

(100) Plane:
The (100) plane of a BCC metal consists of atoms arranged in a square lattice. In this plane, the atoms are densely packed, resulting in a high surface energy. The bonds between atoms on this plane are relatively strong.

(110) Plane:
The (110) plane of a BCC metal consists of atoms arranged in a rectangular lattice. In this plane, the atoms are less densely packed compared to the (100) plane, resulting in a lower surface energy. The bonds between atoms on this plane are relatively weaker.

Surface Energy Ratio:
The ratio of the surface energy per unit area of the (100) plane to that of the (110) plane for a BCC metal is between 1.3 and 1.5. This means that the surface energy of the (100) plane is approximately 1.3 to 1.5 times higher than that of the (110) plane.

Reasoning:
The higher surface energy of the (100) plane can be attributed to the denser packing of atoms and stronger bonds between them. The (100) plane exposes more atoms to the surface, resulting in a higher energy requirement to create or break the bonds.

On the other hand, the (110) plane has a lower surface energy due to the less dense packing of atoms and weaker bonds between them. The rectangular lattice arrangement exposes fewer atoms to the surface, reducing the energy requirement for bond creation or breaking.

Overall, the surface energy ratio between the (100) and (110) planes for a BCC metal falls between 1.3 and 1.5, indicating the relative difference in energy required to create or break bonds on these planes.