point that is located at the corner of a unit cell is shared by how many unit cells ?

Options

A. a) 2
B. b) 4
C. c) 6
D. d) 8

Answer

To solve the question of how many unit cells share a point located at the corner of a unit cell, we can follow these steps:

### Step 1: Understand the Structure of a Unit Cell
A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. It can be visualized as a cube in many cases.

**Hint:** Visualize a cube and consider its corners and how they relate to neighboring cubes.

### Step 2: Identify the Position of the Corner Atom
In a cubic unit cell, there are atoms located at each of the eight corners of the cube. Each corner atom is part of the unit cell but is also shared with adjacent unit cells.

**Hint:** Think about how many unit cells meet at a point in 3D space.

### Step 3: Determine How Many Unit Cells Share the Corner Atom
Each corner atom is shared among eight different unit cells. This is because a corner atom is located at the intersection of eight unit cells—one in each direction (up, down, left, right, front, back).

**Hint:** Consider how many unit cells would surround a single corner atom in three-dimensional space.

### Step 4: Conclusion
Thus, the point located at the corner of a unit cell is shared by **eight unit cells**.

**Final Answer:** A point that is located at the corner of a unit cell is shared by **8 unit cells**.