Question

A metal crystallizes in simple cubic lattice. The volume of one unit cell is \( 6.4 \times 10^{-7} \, \text{pm}^3 \). What is the radius of the metal atom in pm?

• A. 100
• B. 200
• C. 300
• D. 400

Hint:

In simple cubic lattices, the edge length of the unit cell is twice the radius of the atoms. Use this to relate volume and atomic radius.

Answer 1

The Correct Option is B

For a simple cubic lattice, the relationship between the unit cell volume \( V_{\text{unit}} \) and the atomic radius \( r \) is: \[ V_{\text{unit}} = (2r)^3 \] Given that the volume is \( 6.4 \times 10^{-7} \, \text{pm}^3 \), solving for \( r \) gives us a radius of 200 pm.