Question

Now let's calculate the mass of a 3-D unit cell. Assume that each sphere has a mass m and the sphere lies at the center of the faces of the cube. What will be the mass in the following case?

• A. $2m$
• B. $4m$
• C. $m$
• D. $\frac{1}{2}m$

Answer 1

The correct option is A

$2m$

We can go about this from first principles. Let's start by calculating how many atoms this cube (unit cell) actually holds. Since there are 4 at the face centers, each sphere will contribute 1/2 of its volume to this unit cell.

So, 4 $\times$ $\frac{1}{2}$ = 2

There are effectively 2 atoms in this cube. That means the mass will be 2m.