Environmental Engineering Reference
In-Depth Information
3.6 The Lennard-Jones potential energy function is often used to represent the
interaction between a pair of atoms:
ε
r
0
r
6
,
12
2
r
0
r
U(r)
=
−
where
r
is the separation of the atomic centres. Show that the equilib-
rium separation is
r
0
and that the depth of the potential is
ε
.Sketcha
graph of
U(r)
. If the system of two atoms has a maximum vibrational
kinetic energy
K
max
, use your graph to indicate the range of allowed sep-
arations.
3.7 A proton makes a low-energy, head-on, collision with an unknown parti-
cle and rebounds straight back along its path with 4/9 of its initial kinetic
energy. Assuming that the collision is elastic and that the unknown particle
is originally at rest, calculate the mass of the unknown particle.
