Physics and Engineering of Radiation Detection

80 Chapter 2. Interaction of Radiation with Matter

If an electron is accelerated through a potentialV (as in x-ray machines), the
maximum energy it can attain is given by

Emax=eV, (2.2.2)

whereeis the unit electronic charge. The maximum energy of the Bremsstrahlung
in the form of photons that this electron can emit will then also be equal toeV,
that is
Ebrems≤Emax=eV. (2.2.3)

Since Bremsstrahlung is emitted in the form of photons having energyE=hν=
hc/λtherefore we can write the above equation as

h

c

λ

≤ eV

⇒λ ≥

hc

eV

. (2.2.4)

Hence we can associate a minimum wavelengthλminwith the process below which
there will be no Bremsstrahlung photons emitted.

λmin=

hc

eV

(2.2.5)

λminis also called thecutoff wavelengthfor Bremsstrahlung.

Example:

Compute the cutoff Bremsstrahlung wavelength for an electron moving under

the influence of a potential of 40kV.

Solution:

We will use equation 2.2.5 to compute the cutoff wavelength.

λmin =

hc

eV

=

(6. 626 × 10 −^34 )(2. 99 × 108 )

(1. 602 × 10 −^19 )(40× 103 )

m

=30. 91 fm

2.2.E CherenkovRadiation.......................

We know that velocity of a particle in a medium depends, among other things, also
on the nature and density of the medium. The same is true for light particles,
or photons. There is no theory in physics that demands that light has constant
velocity in all types of media. The special theory of relativity only says that the
velocity of light is independent of the frame of reference, not that it is constant
everywhere. In water, for example the velocity of light is significantly lower than
c=2. 99 × 108 ms−^1 , which is the velocity of light invacuumand is supposed to be
constant invacuum.