Question

A cubic crystal has a unit cell edge length of 0.4 nm. What is the volume of the unit cell?

• A. 0.064 nm\(^3\)
• B. 0.016 nm\(^3\)
• C. 0.064 cm\(^3\)
• D. 0.004 nm\(^3\)

Hint:

Unit Cell Volume. For a cubic unit cell with edge length 'a', the volume is \(V = a^3\). Ensure consistent units.

Answer 1

The Correct Option is A

The crystal structure is cubic, meaning the unit cell is a cube.
The edge length of the unit cell is given as \(a = 0.
4\) nm.
The volume (\(V\)) of a cube is calculated as the edge length cubed: $$ V = a^3 $$ Substitute the given edge length: $$ V = (0.
4 \, \text{nm})^3 $$ $$ V = 0.
4 \times 0.
4 \times 0.
4 \, \text{nm}^3 $$ $$ V = 0.
16 \times 0.
4 \, \text{nm}^3 $$ $$ V = 0.
064 \, \text{nm}^3 $$ The volume of the unit cell is 0.
064 nm\(^3\).
Option 3 is incorrect due to the unit (cm\(^3\)).