Posted by ea on .
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
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.