Physics and Engineering of Radiation Detection

2.1. Some Basic Concepts and Terminologies 75

Conservation of electrical charge

Since these laws are directly or indirectly used in computations involved in the
detection and measurement of radiation, therefore we will spend some time under-
standing their basis and learning how they are applied.

E.1 ConservationofEnergy

This law dictates that total energy content of a closed system always remains con-
stant irrespective of the time evolution of the system. Here, by the termclosed
system, it is not meant that the system is completely isolated from anything else in
the world. Rather it represents a system which is notinfluencedby external forces.
Being influenced is certainly a relative term and depends on the accuracy of the
result desired. For example, one can not escape the background electromagnetic
field, which is present everywhere. But for most practical purposes its strength is
too week at the point of collision between two microscopic particles that it can be
safely neglected. In this case we can still apply the law of conservation of linear
momentum to determine the kinematic quantities related to the collision.
At the fundamental level, the law of conservation of energy ensures that temporal
translations do not violate the laws of nature. Since mass and energy are related to
each other through Einstein’s relationE=mc^2 , therefore we can also say that it
is neither possible to completely destroy mass or energy nor it is possible to create
them from nothingness.
Since mass can be converted into energy, therefore with each massive particle an
intrinsic energy content can be associated. We call this quantity itsrest energyto
signify the amount of energy it contains when at rest. For particle interactions it
has been found that the sum of rest energy and the kinetic energy of a closed system
remains constant.

Erest+T=constant

HereErest=m 0 c^2 is the total rest energy of all particles at any instant having
combined rest mass ofm 0. T represents the total kinetic energy of all the particles
at the same instant in time.

E.2 ConservationofMomentum..................

Both linear and angular momenta are conserved for any system not subject to exter-
nal forces. For linear momentum, this law dictates that the total linear momentum
of a closed system remains constant. It represents the fact that the laws of physics
are the same at all locations in space. This law, together with the law of conserva-
tion of energy, is extensively used to determine the kinematic variables related to
particle collisions.
Linear momentum is a vector quantity and therefore one must be careful when
computing the total momentum of the system. One can not just add the momenta,
rather a vector sum must be taken. Mathematically, for the case of collision between
particles, this law requires that

∑

pi=

∑

pf, (2.1.18)