Question

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

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

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

Answer 1

According to the information I have, gallium crystallizes in the orthorhombic system so that a is not = to b is not = to c. If you mean the primitive unit cell to be a SIMPLE cubic cell, then a = 2*radius but I don't believe that is correct.

For Au, it crystallizes in the face centered cubic system, FCC.
density = mass of unit cell/volume of unit cell.
mass of unit cell:
For a fcc crystal, there are 4 atoms per unit cell.
4 Ga atoms x atomic mass Ga atom/6.022 x 10^23 atoms = mass of 1 Ga atom.
volume of unit cell:
a^3 where a is the length of the edge which is listed in the problem. I suggest you change pm to cm before making the calculation so that volume comes out in cubic centimeters (cc). That way the density will be in g/cc.
Post your work if you get stuck.