Final answer:
A unit cube has a side length of one unit, a volume of 1 cubic unit, and a surface area of 6 square units which gives it a surface area to volume ratio of 6:1. This concept is also applied in materials science to discuss the atomic structure of simple cubic lattices, where each atom at the corner contributes 1/8 of an atom to the unit cell.
Step-by-step explanation:
What is true about a unit cube? A unit cube is a cube with a side length of one unit, which can be defined in meters, centimeters, or other measures of length. The volume of a unit cube is 1 cubic unit since volume is calculated as s³ (side length raised to the third power). The surface area of a unit cube is 6 square units, given that it has 6 faces and SA = 6s² (surface area is 6 times the side length squared). This means that the surface area to volume ratio (SA:V) for a unit cube is 6:1, indicating that for each unit of volume, there are 6 units of surface area.
The concept of a unit cube is often used in physics and materials science to discuss properties such as the arrangement of atoms in a crystal lattice. For example, a simple cubic lattice consists of atoms positioned at the corners of a cubic structure, and each atom is shared by eight adjacent unit cells, contributing 1/8 of an atom to the unit cell. A typical unit cell contains a total of 1 atom when accounting for the fact that each of the 8 corner atoms is shared by 8 unit cells (1/8 atom from each of the 8 corners).