In this chapter on collisions, we shall have occasion to distinguish between elastic and inelastic
An elastic collision is one in which there is no loss of translational kinetic energy.
is, not only must no translational kinetic energy be degraded into heat, but none of it may be
converted to vibrational or rotational kinetic energy.
It is well known, for example, that if a ball
makes a glancing (i.e. not head-on) elastic collision with another ball of the same mass, initially
stationary, then after collision the two balls will move off at right angles to reach other.
But this is
so only if the balls are smooth.
If they are rough, after collision the balls will be spinning, so this
result – and any other results that assume no loss of translational kinetic energy
will not be valid.
When molecules collide, they may be set into rotational and vibrational motion, and in that case the
collision will not be elastic in the sense in which we are using the term.
If two atoms collide, one
(or both) may be raised to an excited electronic level.
Some of the translational kinetic energy has
then been converted to potential energy.
If the excited atom subsequently drops down to a lower
level, that energy is radiated away and lost from the system.
Superelastic collisions are also
If one atom, before collision, is in an excited electronic state, on collision it may make a
radiationless downwards transition, and the potential energy released is then converted to
translational kinetic energy, so the collision is superelastic.
None of this is intended to mean that
elastic collisions are impossible or even rare.
In the case of collisions involving macroscopic
bodies, such as smooth, hard billiard balls, collisions may not be 100% elastic, but they may be
close to it.
In the case of low-energy (low temperature) collisions between atoms, there need be no
excitation to excited levels, in which case the collision will be elastic.
Some subatomic particles, in
particular leptons (of which the electron is the best-known example), are believed to have no
internal degrees of freedom, and therefore collisions between them are necessarily elastic.
In laying out the principles involved in collisions between particles, we need not suppose that the
particles actually "bang into" – i.e. touch – each other.
For example most of the principles that we
shall be describing apply equally to collisions between balls that "bang into" each other and to
phenomena such as Rutherford scattering, in which an alpha particle is deviated from its path by a
gold nucleus without actually "touching" it.
Of course, if you think about it at an atomic level,
when two billiard balls collide, the atoms don't actually "touch" each other; they are repelled from
each other by electromagnetic forces, just as the alpha particle and the gold nucleus repelled each
other in the Rutherford-Geiger-Marsden experiment.