ME 125NT
Intro to Nanotechnology
Due: 5/8/2008
1
Solution Set 5
Problem 6.14 in book
We can look at the band structure of an element to get an idea of how many electrons per
atom participate in conduction.
We can also determine this number based on the free
electron density, the atomic mass, and the mass density of the material.
(a)
Calculate the free electron density of lithium.
The Fermi energy is 4.72 eV.
(b)
Derive a formula for the number of atoms per unit volume.
(c)
Calculate the number of atoms per unit volume of lithium (535 kg/m
3
, 6.9 g/mol)
using the formula you derived in part (b).
(d)
Determine the number of free electrons per lithium atom.
(e) What is the electron configuration for Li?
Explain whether your answer to (d) makes
sense according to this configuration.
The free electron(s) of Li is in which sublevel?
ANSWER
A)
( )
( )
( )
×
×
×
=

2
3
19
3
2
34

2
3
31

J
10
56
7
3
2
s
/
kg
m
10
6.626
kg
10
9.11
2
8
.
n
e
π
=
4.7 × 10
28
electrons/m
3
B)
The number of atoms per unit volume =
[kg/mol]
])
[kg/m
])(
[atoms/mol
(N
3
A
A
ρ
, where
N
A
is
Avogadro’s number,
ρ
is the density of the material and
A
is the atomic mass.
C)
=
×
[kg/mol]
0069
0
])
[kg/m
35
5
])(
[atoms/mol
10
(6.022
3
23
.
4.67 × 10
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 Spring '08
 PENNATHUR
 Atom, Electron, Quantum dot, free electron, energy state

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