DATE:
October 16, 2011
DUE:
October 21, 2011
ENG45, Solution to homework set #3.
1.
Weak interactions. We can write the van der Waals’ interaction energy between two
atoms separated by the distance
r
, in the following three ways
V
(
r
) = 4
E
1
parenleftBigg
parenleftbigg
σ
1
r
parenrightbigg
12

parenleftbigg
σ
1
r
parenrightbigg
6
parenrightBigg
(1)
=
E
2
parenleftBigg
parenleftbigg
σ
2
r
parenrightbigg
12

2
parenleftbigg
σ
2
r
parenrightbigg
6
parenrightBigg
(2)
=
K
R
r
12

K
A
r
6
(3)
where
E
1
and
E
2
are energies,
σ
1
and
σ
2
are distances, and
K
A
and
K
R
are constants
with units necessary for the equalities above.
a. Determine the SI units of
K
R
and
K
A
such that expression (3) makes sense.
If the terms have units of energy (and they do), then we have
[
K
A
] = [
Jm
6
]
and
[
K
R
] = [
Jm
12
]
.
b. Write the interatomic force
F
(
r
)
associated with the energy expressed in the
form (1).
F
(
r
) =

∂V
∂r
= 24
E
1
σ
1
parenleftBigg
2
parenleftbigg
σ
1
r
parenrightbigg
13

parenleftbigg
σ
1
r
parenrightbigg
7
parenrightBigg
(4)
c. Write the interatomic force
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 Fall '11
 jensen
 Energy, kA, KR

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