A metal crystallizes in a face-centered cubic lattice.The radius of the atom is 196 pm and the density of the element is 1.55 g/cm³.What is the volume of the unit cell?

Question

Quizplus · Accepted Answer

First, we need to find the length of the edge of the unit cell. 
In a face-centered cubic lattice, there are 4 atoms per unit cell. 
Since the radius of the atom is given as 196 pm, the diameter of each atom is 392 pm. 
The length of the edge of the unit cell can be found as:

a = 2 * radius(diagonal of the face) + dia(atom) 
  = 2 * (sqrt(2)*196 pm) + 392 pm 
  = 4.08 Å

We convert this to pm:

4.08 Å * (100 pm/1 Å) = 408 pm

The volume of the unit cell can be found as:

V = a^3 / 4

Substituting a = 408 pm, we get:

V = (408 pm)^3 / 4 
  = 1.7 × 10^18 pm^3

Therefore, the answer is (C) 1.7 × 10^18 pm^3.

A Metal Crystallizes in a Face-Centered Cubic Lattice