Info:

Question

The atoms of crystalline solid pack together into a three-dimensional array of many small repeating units called unit cells. The simplest of the unit cells are those that have cubic symmetry, with atoms positioned at the corners of a cube. Atoms can also be found in the sides (faces) of the cube, or centered within the body of the cube. It is important to realize that a unit cell is surrounded by other unit cells in every direction. Therefore, face and corner atoms are shared with neighboring unit cells. The fraction varies with the type of atom as shown in the following table.

Type of atom / Fraction in unit cell
corner 1/8
face 1/2
body 1

The size of a unit cell in any given solid can be calculated by using its density. This and the reverse calculation are common test questions in general chemistry courses.

**I am having problems with the following 2 questions:

1. Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362pm. What is the radius of a gallium atom?

Express your answer numerically in picometers.

"radius = _____pm"

&

2. The face-centered gold crystal has an edge length of 407pm. Based on the unit cell, calculate the density of gold.

Express your answer numerically in grams per cubic centimeter.

density = ______g/cm^3

Answer 1

For a primitive unit cell, a = 2r where a is the length of the edge of the cell and r is the radius.

For the fcc gold atom, density = mass/volume.
volume calculation:
Volume = (edge)³. Don't forget to change the pm to cm if you want density in g/cc.

mass calculation:
There are 4 atoms per unit cell along the face of one cube.
mass = (4atoms)(atomic mass Au)/6.02 x 10^23 atoms mol^-1

Then density = mass/volume