Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

RADIATION SAFETY GUIDES 361
is 1 g/cm 3 . Since the activity of a radioactive particle is directly proportional to
its mass, we can describe the mean size of a radioactive aerosol by its activity mean
aerodynamic diameter (AMAD) size. In radiation safety standards, particle sizes refer
to the sizes of those particles whose aerodynamic behavior is equivalent to that of
unit density particles.
Thermodynamic Properties
When particle sizes approach the size of air molecules, the random collisions with
the air molecules impart enough energy to the aerosol particles to influence the
motion of the aerosol particles. The resulting random motion of the air molecules
is known as Brownian motion, and is the basis for the diffusion process. (The physics
of Brownian motion was explained by Albert Einstein in the second of his four
revolutionary papers during the annus mirabilis, the “miracle year” of 1905.) The
mean thermal displacement during a time interval t, of particles suspended in a
gaseous medium is independent of the particle density, and is given by
s =
RT Ct
× ; (8.19)
N 3πηd
s is in cm when
R = gas constant = 8.3 × 10 7 ergs/mol/K
T = temperature, K
N = Avogadro’s number = 6.02 × 10 23 molecules/mol
t = time interval, seconds
d = particle size, cm
η = viscosity of the medium = 185 × 10 −6 g/cm/s for standard air
C = Cunningham slip correction factor. This factor corrects for the fact that
the air is not a continuous medium, but consists of discrete molecules.
A particle may thus “slip” between molecules. This slip factor becomes
increasingly important as the particle size approaches the mean free path
of the gas molecules, and
C = 1 + 1.7 λ/d, where λ = mean free path of the gas molecules = 6.7 × 10 −6
cm for air at 25 ◦ C.
Diffusion becomes increasingly important as a particle transport mechanism as the
particle size decreases below 1 μm. The Table 8-6 shows the displacement during
1 second by gravitational settling and by diffusion of a unit density particle of 3
different sizes.
TABLE 8-6. Effect of Particle Size on Displacement Distance by Diffusion and by
Gravitational Settling
PARTICLE SIZE DIFFUSION GRAVITATIONAL SETTLING
(μm) (μm) (μm)
0.1 22.4 0.6
1.0 5.1 29.4
10.0 1.5 2940