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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

  • chemistry -

    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.

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