Calculating Atomic Mass and Radius from a Unit Cell (12.3.4) Flashcards
• Atomic mass and atomic radius can be calculated based on unit cell data.
• Atomic mass and atomic radius can be calculated based on unit cell data.
In the face-centered cubic (fcc) lattice shown, each
corner represents one eighth of a sphere. There is a
half sphere in the middle of each face. Thus there
are four atoms in one unit cell.
If the unit cell type, the length of an edge, and the
density of the crystal are known, then the volume,
mass and radius of individual atoms may be
calculated.
Problem: Silver crystallizes in a face-centered cubic
crystal lattice. The length of one edge of the unit
cell is 408.6 picometers. The density of silver metal
is 10.50 g/cm3
. What is the mass of a silver atom?
Use volume in the density formula to calculate the
mass of a unit cell.
Dividing the mass of a unit cell by the number of
atoms in the unit cell allows calculation of the mass
of a single atom.
Problem: What is the radius of a silver atom?
Allow the length of the unit cell edge (d) to be the
base of a right triangle. The value for the
hypotenuse of this right triangle, which contains four
atomic radii, can be calculated using the
Pythagorean theorem.
Dividing the resulting value by 4 yields the atomic
radius of a silver atom.
A knowledge of unit cell arrangement permits
calculation of values for mass and radius for other
standard crystal arrangements.
The simple cubic unit cell has a single atom in the
unit cell. The cell edge (d) / atomic radius (r)
relationship is d = 2 • r.
The body-centered unit cell contains two atoms.
The cell edge / atomic radius relationship is
√ 3 • d = 4 • r.
The face-centered unit cell contains four atoms.
The cell edge / atomic radius relationship is
√ 2 • d = 4 • r.
In the face-centered cubic (fcc) lattice shown, each
corner represents one eighth of a sphere. There is a
half sphere in the middle of each face. Thus there
are four atoms in one unit cell.
If the unit cell type, the length of an edge, and the
density of the crystal are known, then the volume,
mass and radius of individual atoms may be
calculated.
Problem: Silver crystallizes in a face-centered cubic
crystal lattice. The length of one edge of the unit
cell is 408.6 picometers. The density of silver metal
is 10.50 g/cm3
. What is the mass of a silver atom?
Use volume in the density formula to calculate the
mass of a unit cell.
Dividing the mass of a unit cell by the number of
atoms in the unit cell allows calculation of the mass
of a single atom.
Problem: What is the radius of a silver atom?
Allow the length of the unit cell edge (d) to be the
base of a right triangle. The value for the
hypotenuse of this right triangle, which contains four
atomic radii, can be calculated using the
Pythagorean theorem.
Dividing the resulting value by 4 yields the atomic
radius of a silver atom.
A knowledge of unit cell arrangement permits
calculation of values for mass and radius for other
standard crystal arrangements.
The simple cubic unit cell has a single atom in the
unit cell. The cell edge (d) / atomic radius (r)
relationship is d = 2 • r.
The body-centered unit cell contains two atoms.
The cell edge / atomic radius relationship is
√ 3 • d = 4 • r.
The face-centered unit cell contains four atoms.
The cell edge / atomic radius relationship is
√ 2 • d = 4 • r.
simple cubic: d=2r
body centered cubic: (sqrt3)d=4r
face centered cubic: (sqrt2)d=4r
simple cubic: d=2r
body centered cubic: (sqrt3)d=4r
face centered cubic: (sqrt2)d=4r
What is the difference between a simple cubic, a face-centered cubic, and a body-centered cubic unit cell?
They differ in the number, arrangement, and spacing of atoms. (B)
In a face centered cubic crystal lattice, each corner atom is shared between how many cells?
eight (D)
Each corner has an atom shared with eight other cells. So each corner contributes 1/8 of an atom.
What is the total number of atoms contained in a simple cubic cell?
one (A)
As in the face-centered cubic cell, each corner atom is shared among eight cells. So each cell contains 1/8 of each corner atom multiplied by eight corners, or one atom.
