Question

A metal crystallizes in simple cubic lattice. The radius of the metal atom is $x\, pm$. What is the volume of the unit cell in $pm^3$?

• A. \(x^3\)
• B. \(4x^3\)
• C. \(8x^3\)
• D. \(16x^3\)

Hint:

In simple cubic structure, unit cell edge length is twice the atomic radius, so volume is cube of edge length.

Answer 1

The Correct Option is C

In simple cubic lattice: \[ \text{Edge length} = a = 2r \] Given radius \(r = x\, pm\), so \[ a = 2x \] Volume of unit cell: \[ V = a^3 = (2x)^3 = 8x^3\, pm^3 \]