This document discusses concepts related to radiation shielding, including: - How radiation intensity decreases with distance from the source according to the inverse square law. Fluence and flux are defined to describe radiation intensity. - Formulas are provided to calculate flux and exposure rate at varying distances from a point source, taking into account the source strength, photon energy, and attenuation from any shielding material. - Tables of attenuation coefficients are given for various materials to allow for calculations of exposure rate from shielded sources. - Simplified rules of thumb are described for estimating exposure rates from gamma and beta point sources based on source strength, photon energy, and distance from the source.

1. Radiation Shielding
Chapter 7
Section 2 Shielding

2. Radiation Shielding
Objectives
Understand
How radiation is emitted from a
source
The difference between fluence
and flux
How to calculate flux (& fluence) at
a known distance from a point
source
Calculate dose at a point in space
using a dose conversion factor

3. Nature of Radiation Emissions
When a radionuclide
decays, the radiation goes
out from the source in any
direction
This is called isotropic
emission
We measure the strength
of the radiations
(intensity) at some
distance from the source

4. Radiation Intensity
The fluence (Φ) is the
number of photons
moving through a target
area (γ/cm2)
The flux (φ) is the
number of photons
moving through an area
per time (γ/cm2s)

5. Why Calculate Flux?
Fluence and flux tell you:
Photons per area, and
Photons per area & time
If you know:
Energy per photon
Then, you can calculate
Energy deposited per area
and, ultimately, dose

6. Calculating Flux
Need to answer two
questions:
What is the source strength
S0 (in photons/s) or the total
number of disintegrations
(D)?
What is the distance, r, from
the source (at point P)
where you want to calculate
the flux?
r
P

7. Calculating Flux, continued
Consider each photon as it
leaves the source
It moves further away from
others that have been
emitted
Therefore, the flux (γ/cm2s)
decreases

8. Another Way to Look at It
If a source emits 4
photons/s, what is
the flux at 1 cm, 10
cm, and 1m?
Consider the
surface area of the
sphere(s) the
photons are
passing through:

9. Surface Area of a
Sphere
S . A. = 4 π r
2
S.A.1 cm = 12.57 cm2
1 cm
10 cm
100 cm
S.A.10 cm = 1257 cm2
S.A.100 cm = 125,664 cm2

10. Calculating Fluence and Flux,
continued
D
Φ=
4π r 2
S0
φ=
4π r 2
Φ = Fluence γ/cm2
φ = Flux γ/cm2s
D = total number of photons emitted
S0 = source strength (photons/s)
R = distance from source (1, 10, 100 cm)

11. Calculating Fluence and Flux,
continued
If source emits 4 photons/s, S0 = 4,
The φ (flux) is then calculated:
At 1 cm
= 4 γ /12.57cm2s
φ = 0.318 γ/cm2s
At 10 cm
φ = 4 γ /1257 cm2s
φ = 3.18 x 10-3 γ/cm2s
φ
At 100 cm
=4 γ /125,664 cm2s
φ = 3.18 x 10-5 γ/cm2s
φ

12. Calculating Fluence and Flux,
continued
For this same problem, what is the
photon fluence?
Can we calculate it at all?
Why? Why not?

13. Calculating Flux
At any point from the source, the photon intensity
(flux) can also be estimated as:
S0
φ=
2
4π r
But, what happens if we put some photon absorbing
material between the source and our measurement
point?

14. Attenuation Occurs
Remember the “universal” equation (or one
form of it):
−µ x
0
I ( x) = I e
This describes how a beam of photons is
Reduced in intensity by absorbing material
Absorber of thickness x is in the photon path
The source can be said to be “shielded”

15. Source Strength From
Shielded Source
The two equations can be combined to
yield:
φ ( x) shielded = φ unshielded e
So −µ x
=
e
2
4π r
−µ x
The term 1/(4πr2) is called the
geometeric attenuation factor

16. Converting to a Dose Rate
S0
P
Photon intensity can be
converted to dose rate
Called an “uncollided” dose
rate
Use tables of “dose
conversion factors”:
φ ( x) shielded
x
r
So −µ x
=
e
2
4π r
 = k ( E ) E So e−µ x
Du
2
4π r

17. Previous Example, continued
Assume
S0 = 4 photons/s
Photon energy is 0.8 MeV
Shielding material is 0.5 cm Uranium (U)
Calculate the exposure rate at 1, 10, and 100
cm.

18. Photon Energy Flux to Exposure Doserate Conversion Factors
Energy of
photon being
evaluated
Energy (E) in
MeV
Conversion Factor,
k(E),
R/hr per MeV/cm2 s
0.5
1.96 E-06
0.6
1.94 E-06
0.7
1.92 E-06
0.8
1.90 E-06
0.9
1.87 E-06
1.0
1.84 E-06
1.2
1.78 E-06
1.4
1.73 E-06
1.6
1.67 E-06
1.8
1.62 E-06
2.0
1.56 E-06
Scientific
notation
commonly
used, should be
read as:
1.96 x 10-6
These are
“look up”
values

19. Total Linear Attenuation Coefficient
Factors, µ (cm-1)
Energy (E)
in MeV
Al
(2.70)*
Fe
(7.86)
Sn
(7.31)
W
(19.3)
Pb
(11.34)
U
(18.7)
0.5
0.227
0.652
0.666
2.490
1.746
3.459
0.6
0.210
0.599
0.578
1.988
1.361
2.618
0.7
0.196
0.557
0.523
1.705
1.136
2.144
0.8
0.184
0.523
0.479
1.492
0.971
1.803
0.9
0.174
0.493
0.445
1.349
0.866
1.584
1.0
0.166
0.468
0.417
1.233
0.782
1.410
1.2
0.151
0.4285
0.382
1.114
0.699
1.245
1.4
0.140
0.397
0.354
1.022
0.635
1.121
1.6
0.131
0.372
0.332
0.949
0.585
1.023
1.8
0.123
0.352
0.314
0.889
0.544
0.944
2.0
0.117
0.334
0.298
0.838
0.510
0.879
*
Normal density (ρ) in g/cm3
µ

20. Total Linear Attenuation Coefficient
Factors, µ (cm-1), continued
Energy (E)
in MeV
Ordinary
Concrete
(2.35)*
Barytes
Concrete
(3.50)
Magnetite
Concrete
(3.55)
Ferrophos.
Concrete
(4.68)
Water
(1.0)
Air
(0.001205)**
0.5
0.204
0.317
0.303
0.395
0.0967
1.048E-4
0.6
0.188
0.286
0.278
0.363
0.0895
9.70E-5
0.7
0.175
0.262
0.259
0.337
0.0835
9.05E-5
0.8
0.165
0.243
0.243
0.317
0.0786
8.52E-5
0.9
0.156
0.227
0.230
0.299
0.0743
8.05E-5
1.0
0.149
0.214
0.219
0.285
0.0707
7.66E-5
1.2
0.136
0.196
0.200
0.260
0.0643
6.97E-5
1.4
0.126
0.181
0.185
0.241
0.0594
6.44E-5
1.6
0.118
0.170
0.173
0.226
0.0554
6.01E-5
1.8
0.111
0.160
0.163
0.213
0.0522
5.66E-5
2.0
0.105
0.152
0.155
0.202
0.0494
5.36E-5
Normal density (ρ) in g/cm3
**
Air at 200C, 760 mm Hg
*

21. 
Du = k ( E ) E
So
4π r
2
e
−µ x
Calculating
Exposure
The uncollided flux previously calculated is:
At 1 cm, φ = 0.318 γ/cm2s
At 10 cm, φ = 3.18 x 10-3 γ/cm2s
At 100 cm, φ = 3.18 x 10-5 γ/cm2s
k(E) = 1.9 x 10-6 R/hr per MeV/cm2 s
E= 0.8 MeV
e-µx is e-1.803*0.5 = 0.41
So, the exposure rate is:
1.98 x 10-7 R/hr at 1 cm; 1.98 x 10-9 R/hr at 10 cm;
1.98 x 10-11 R/hr at 100 cm

22. Calculating Flux From
Complex Geometries
Point Kernel method
Source broken into many
small kernels
Contribution from each
kernel evaluated for a
common point
Contributions are
summed
P

23. Rule of Thumb #1
Some equations to memorize
For estimating dose rate from a
gamma point source where the
distance is in feet, and the source
strength is in Ci, and the energy of
the gamma is expressed in MeV,
then:
6.0 Eγ Ci rad

=
Dγ ≈
2
hr
ft

24. Rule of Thumb #2
For beta radiation, the equation is
similar, where the maximum
energy of the beta radiation is
used.
2 E max Ci rad

=
Dβ ≈
2
hr
ft

25. Rules of Thumb,
continued
It is important to note that if a
nuclide decays by multiple
emissions (betas or gammas) that
they have to be accounted for in
the calculation. You can estimate
the dose from each separately and
sum the total.