Educación familiar y desarrollo de valores

5

INTERACTION OF RADIATION WITH MATTER

In order for health physicists to understand the physical basis for radiation dosime-try and the theory of radiation shielding, they must understand the mechanisms by which the various radiations interact with matter. In most instances, these inter-actions involve a transfer of energy from the radiation to the matter with which it interacts. Matter consists of atomic nuclei and extranuclear electrons. Radiation may interact with either or both of these constituents of matter. The probability of occur-rence of any particular category of interaction, and hence the penetrating power of the several radiations, depends on the type and energy of the radiation as well as on the nature of the absorbing medium. In all instances, excitation and ionization of the absorber atoms result from their interaction with the radiation. Ultimately, the energy that is transferred either to a tissue or to a radiation shield is dissipated as heat.

BETA PARTICLES (BETA RAYS)

Figure 5-1. Experimental arrangement for absorption measurements on beta particles.

approximation of exponential beta absorption is a fortuitous consequence of the shape of the beta-energy-distribution curve; beta and electron absorption do not follow first-order kinetics and hence are not truly exponential functions.) The end point in the absorption curve, where no further decrease in the counting rate is observed, is called therangeof the beta in the material of which the absorbers are made. As a rough rule of thumb, a useful relationship is that the absorber half-thickness (that half-thickness of absorber which stops one-half of the beta particles) is about one-eighth the range of the beta. Since the maximum beta energies for the various isotopes are known, by measuring the beta ranges in different absorbers, the systematic relationship between range and energy shown in Figure 5-3 is established.

Inspection of Figure 5-3 shows that the required thickness of absorber for any given beta energy decreases as the density of the absorber increases. Detailed analyses of experimental data show that the ability to absorb energy from beta particles depends mainly on the number of absorbing electrons in the path of the beta—that is, on the areal density (electrons/cm²) of electrons in the absorber, and, to a much lesser degree, on the atomic number of the absorber. For practical purposes, therefore, in the calculation of shielding thickness against beta particles, the effect of atomic number is neglected. (It should be pointed out that, for reasons to be given later, beta shields are almost always made from low-atomic-numbered materials.) Areal density of electrons is approximately proportional to the product of the density of the absorber material and the linear thickness of the absorber, thus giving rise to the unit of thickness called thedensity thickness.Mathematically, density thicknesstd

is defined as

t_dg/cm²=ρg/cm³×t_lcm. (5.1)

The units of density and thickness in Eq. (5.1), of course, need not be grams and centimeters; they may be any consistent set of units. Use of the density thickness

Figure 5-2. Absorption curve (aluminum absorbers) of²¹⁰Bi beta particles, 1.17 MeV. The broken line represents the mean background count rate.

unit, such as g/cm² or mg/cm² for absorber materials, makes it possible to specify such absorbers independently of the absorber material. For example, the density of aluminum is 2.7 g/cm³. From Eq. (5.1), a 1-cm-thick sheet of aluminum, therefore, has a density thickness of

td =2.7 g

cm³ ×1 cm=2.7 g cm².

If a sheet of Plexiglas whose density is 1.18 g/cm³ is to have a beta absorbing quality very nearly equal to that of the 1-cm-thick sheet of aluminum—that is, 2.7 g/cm²—its linear thickness is found, from Eq. (5.1), to be

t1=td

ρ = 2.7 g/cm²

1.8 g/cm³ =2.39 cm.

Another practical advantage of using this system of thickness measurement is that it allows the addition of thicknesses of different materials in a radiologically meaningful

Figure 5-3. Range–energy curves for beta particles in various substances.(Adapted fromRadiological Health Handbook.Washington, DC: Office of Technical Services; 1960.)

way. The quantitative relationship between beta energy and range is given by the following experimentally determined empirical equations:

E =1.92R^0.725 R≤0.3 g/cm² (5.2)

R=0.407E^1.38 E ≤0.8 MeV (5.3)

E =1.85R+0.245 R≥0.3 g/cm² (5.4)

R=0.542E−0.133 E ≥0.8 MeV (5.5)

where

R=range, g/cm²and

E =maximum beta energy, MeV.

An experimentally determined curve of beta range (in units of density thickness expressed as mg/cm²) versus energy is given in Figure 5-4.

Figure 5-4. Range–energy curve for beta particles and for monoenergetic electrons. (Adapted from Radiological Health Handbook.Washington, DC: Office of Technical Services; 1960.)

W Example 5.1

What must be the minimum thickness of a shield made of (a) Plexiglas and (b) aluminum in order that no beta particles from a⁹⁰Sr source pass through?

Solution

Strontium-90 emits a 0.54-MeV beta particle. However, its daughter, ⁹⁰Y, emits a beta particle whose maximum energy is 2.27 MeV. Since⁹⁰Y beta particles always accompany⁹⁰Sr beta particles, the shield must be thick enough to stop these more-energetic betas. If we substitute 2.27 MeV for E in Eq. (5.5), we find the range of the betas:

R=(0.542×2.27)−0.133=1.1 g/cm².

Alternatively, from Figure 5-4, the range of a 2.27-MeV beta particle is found to be 1.1 g/cm². The density of Plexiglas is 1.18 g/cm³. From Eq. (5.1), the required thickness is found to be

t1= td

ρ = 1.1 g/cm²

1.18 g/cm³ =0.932 cm.

Plexiglas may suffer radiation damage and crack if exposed to very intense radiation for a long period of time. Under these conditions, aluminum is a better choice for a shield. Since the density of aluminum is 2.7 g/cm³, the required thickness of aluminum is found to be 0.41 cm.

The range–energy relationship may be used by the health physicist as an aid in identifying an unknown beta-emitting contaminant. This is done by measuring the range of the beta radiation, calculating the beta particle’s energy, and then using published values of beta energies from the various nuclides to find the radionuclide whose beta energy matches the calculated value.