Chemistry Reference
In-Depth Information
For collinear momentums, one solution exists for
p
1
in Figure 3.10 on the momentum
sphere and the gain of translational energy of the target particle, ε
gain
T
(
m
2
)
can be easily
calculated
4
·
m
1
·
m
2
ε
gain
T
(
m
2
)
=
ε
T
(
m
1
)
·
2
.
(3.87)
(
m
1
+
m
2
)
The maximum gain of translational energy of the target particle is achieved for equal
mass of the collision partners (
m
1
=
m
).
The
inelastic collisions
are characterized by the loss of translational energy and
its transfer into internal energy of the target particle. In the total translational energy
balance equation (3.88) this loss of translational energy has to be compensated by
the factor α
2
m
2
=
1. Together with the total momentum conservation (3.84) the derived
momentum sphere (3.89) is characterized by a reduced radius of the sphere (γ
2
<
<
1),
see Figure 3.11.
Translational energy balance equation:
·
(
2
2
m
1
=
p
1
)
p
1
p
2
2
m
2
α
2
2
m
1
+
.
(3.88)
Momentum sphere:
m
2
m
1
+
m
2
·
p
1
2
p
1
−
m
2
·
p
1
2
m
1
m
1
+
γ
2
·
=
(3.89)
α
2
1
.
m
1
m
2
m
1
m
2
with γ
2
=
·
+
−
(3.90)
The strongest loss of translational energy of the impinging particle,
ε
loss
T
(
m
1
)
,is
achieved for collinear momentums, which provides γ
=
0 and α
min
=
m
1
/(
m
1
+
m
2
)
,
respectively
m
2
m
1
+
ε
loss
T
ε
T
(
(
m
1
)
=
m
1
)
·
m
2
.
(3.91)
p
1
ϑ
p
2
m
2
m
1
+
m
1
m
1
+
m
2
p
1
΄
p
1
΄
m
2
m
2
m
1
+
γ
p
1
΄
m
2
FIGURE 3.11
The momentum sphere illustrates the inelastic collisions (γ
2
<
1) between
two particles for the condition
m
1
>
m
2
.
