Physics and Engineering of Radiation Detection

2.1. Some Basic Concepts and Terminologies 67

Example:

Determine the relative change in flux ofγ-rays when the distance from the

source is changed from 5mto 20min air.

Solution:

The flux at 5mfrom the source is given by

Φ 1 = A

1

r^2

= A

1

52

whereAis the proportionality constant. Similarly the flux at 20mfrom the

source is

Φ 2 =A

1

202

The relative change in flux is then given by

δΦ=

Φ 1 −Φ 2

Φ 1

× 100

=

1

52 −

1

202

1

52

× 100

=93.7%.

2.1.B CrossSection

Particle interactions have been very successfully handled by quantum mechanics
and there is no reason to believe that these theoretical foundations are not accurate
descriptions of natural phenomena. However, these theories have physical and math-
ematical explanations that sometimes defy our common sense and therefore become
difficult to comprehend and visualize. Wave-particle duality that we discussed in
the preceding chapter is one such concept. Another important concept is Heisen-
berg’s uncertainty principle, which states that there is always some uncertainty in
determining any two properties of a particle simultaneously. For example, according
to this principle, it is impossible to find the exact energy of a particle at an exact
moment in time or to find its exact momentum at an exact position. Mathematically
this concept is represented by

∆E.∆t ≥

2 π

(2.1.2)

∆p.∆x ≥

2 π

. (2.1.3)

Here ∆ represents uncertainty in energyE,timet,momentump, or positionx.

=h/ 2 πis the so called reduced Planck’s constant and is commonly pronounced
h-barorh-cut.
These concepts, together with Planck’s explanation of black body spectrum and
Einstein‘s derivation of the photoelectric effect (discussed later in this chapter) led