Physics and Engineering of Radiation Detection

614 Chapter 11. Dosimetry and Radiation Protection

Example:

Calculate the exposure received in 2 hours at a distance of 3cmfrom a 10

mCicobalt-60 source.

Solution:

The gamma constant for cobalt-60 is 13.2Rcm^2 mCi−^1 h−^1. To calculate the

exposure we substitute this and the given values in equation 11.2.14.

X =Γ

λdNt

r^2

=13. 2

(10)(2)

32

=29. 3 R (11.2.15)

Note that sinceλdNcorresponds to the activity of the material therefore we

did not need individual values ofλdandN.

Since exposure can not be used for particles other than photons therefore another
quantity calledabsorbed dosehas been introduced. It is defined as the average energy
dE ̄absorbed in an infinitesimal volume elementdVper unit densityρof the medium.

D=

1

ρ

lim

V→ 0

dE ̄

dV

(11.2.16)

Note that this definition has less parameters than the definition of exposure and
therefore is much easier to measure and compare. The parameter that needs a bit
of attention here is the volume element, which according to the definition should be
infinitesimally small. The question is how small is infinitesimally small. The answer
lies in the physical limit of signal to noise ratio set by the statistics of charge pair
production. We know that the production of charge pairs is a statistical process with
the standard deviation given by

√

Nfor the production ofN charge pairs. Now,
the production of charge pairs is, among other things, dependent on the availability
of molecules and therefore to the volume element itself. Hence the volume element
should not be too small to cause high fluctuations in the charge pair production. Of
course the fluctuations also depend on the energy flux of the radiation and therefore
one can not generally say how big the volume element should be for all cases.
Whatever the volume is, one can in general express the absorbed dose in terms
of energy absorbed per unit mass, that is

D=

dE ̄

dM

, (11.2.17)

wheredM=Vρis the mass of the sample. From this definition it is evident that
the SI units for absorbed dose areJ/kg. This is generally known as agrayand
represented by the symbolGy.
Radiation quantities and conversion factors relating to dosimetry are listed in
Table 11.2.4.