N
A
= Avogadro’s number
m = mass of the sample
m
*
= mass of one atom
N = number of atoms in the sample
m = N m
*
If N = N
A
, then m = M, the molar mass; and M = N
A
m
*
.
n = number of moles of atoms in the sample
n = m / M
and
n = N / N
A
.
(Note that combining these gives
m / N
=
M / N
A
.)
V = volume of the sample
d = m / V
=
M
/
V
m
, where V
m
is molar volume, V
m
= V / n.
V
*
= volume of one atom = (4/3)
π
r
3
, where
r
is the atomic radius.
The volume of the N atoms in the sample is obtained by multiplying V
*
by N.
Observe that N V
*
is not the volume of the sample, since the sample contains some
empty space in addition to the atoms.
The fraction of the sample that is occupied by atoms is
f
=
N V
*
/ V
and is called
the packing fraction.
N
cell
= number of unit cells in the sample
x
cell
= number of atoms in a unit cell
m
cell
= mass in a unit cell
V
cell
= volume of a cubic unit cell = a
3
, where
a
is the length of a side of a cubic unit
cell (also called the edge length).
For a simple cubic unit cell, a = 2r ; for a bodycentered cubic or bcc unit cell,
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 Fall '07
 Zbaida
 Atom, Mole

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