### Dose Calculations v2 (1) - radiochem

```NE 301 - Introduction to Nuclear Science
Spring 2012
Classroom Session 9:
Interaction with Matter
 Absorbed Dose (D), Kerma (K)

 Dose Calculations
•Analysis
of Gamma Information (NAA)
•Chemical
Effects of Nuclear Reactions
Reminder




Reset slides
Homework #3 due February 16
Next Tuesday February 14 – 1st Demo Session
 MCA
 Gamma Spectroscopy identification of isotopes
 NAA of samples
2
Energy absorbed per kilogram of matter (J/kg)

Gray:
1 Gy = 1 J/kg


Dose rate = dose/time
Dose = dose rate  time
Kerma (Approx. dose for neutrons)
Kerma





Kinetic Energy of Radiation absorbed per
unit MAss
Kerma is easier to calculate than dose for
neutrons
Kerma and Dose: same for low energy
Kerma over-estimates dose at high energy
 No account for “Bremsstrahlung” radiation loses.
Calculating Dose Rate and Kerma Rate
D[Gy / s]  1.602 10
10
 en ( E ) 
2
2 1
E[ MeV ] 
[cm / g ] [cm s ]
  
en(E)/ =mass interaction coefficient (table C3)
E = particle energy [MeV]
Notice Difference
 = flux [particles/cm2 s]
K[Gy / s]  1.602 10
10
 tr ( E ) 
2
2 1
E[ MeV ] 
[
cm
/
g
]

[
cm
s ]

  
tr(E)/ =mass interaction coefficient (table C3)
E = particle energy [MeV]
 = flux [particles/cm2 s]
Engineering Equations – PLEASE Watch out for units!
Calculating Dose Rate and Kerma Rate
D[Gy / s]  1.602 10
10
 en ( E ) 
2
2 1
E[ MeV ] 
[cm / g ] [cm s ]
  
en(E)/ =mass interaction coefficient (table C3)
E = particle energy [MeV]
Notice Difference
 = flux [particles/cm2 s]
K[Gy / s]  1.602 10
10
 tr ( E ) 
2
2 1
E[ MeV ] 
[
cm
/
g
]

[
cm
s ]

  
tr(E)/ =mass interaction coefficient (table C3)
E = particle energy [MeV]
 = flux [particles/cm2 s]
Engineering Equations – PLEASE Watch out for units!
Dose Calculation Practice
Assume a 57 mCi point source of 137Cs.
137Cs emits a 0.60 MeV gamma with a
frequency of 0.941 per decay. At a
distance of 2 meters from the source,
calculate:
1. “Absorbed Dose” rate in tissue
Dose Calculation Practice – find  first
Sp = 57 mCi
E = 0.6 MeV gamma @ 94.1% of the time
r=200 cm
A  r
Flux  I (r )   (r ) 
e
2
4 r
, total linear attenuation coefficient (or macroscopic
cross section) in air for 0.6 MeV (table C3)
Total linear attenuation coefficient
(or macroscopic cross section) in air
for 0.6 MeV (table C3)
0%
2/
g
cm
2/
g
-1
3.
28
4e
-2
cm
3.
28
9e
-4
cm
0%
cm
0%
8.
04
0e
-2
0%
-1
0%
5
5.
9.
69
e-
4.
2/
g
3.
cm
2.
8.940e-2 cm2/g
9.69e-5 cm-1
3.289e-4 cm-1
3.284e-2 cm2/g
8.040e-2 cm2/g
3.
28
9e
-2
1.

 8.040e  2[cm2 / g ]


   

=9.69e-5 cm-1
Dose Calculation Practice
2

2 cm
 8.040 10

g
Sp = 57 mCi
E = 0.662 MeV gamma @ 94.1% of the time
r=2 m
Linear attenuation coefficient (or macroscopic cross
section) in air for 0.6 MeV (table C3)
 (r ) 
Sp
4 r
2
e
 r

4 r


 r
Sp
2
e
3.7 1010
1 Ci
57 mCi  0.941 3

10 mCi
1 Ci
 (r ) 
4 2002 cm 2
 (r )  3872.4

cm2 s
2

2 cm
=8.040 10

g
diss
s
cm2
g
8.04010
1.205103 3  200 cm
g
cm
2
e
Now this flux incident in TISSUE (H2O)
D[Gy / s]  1.602 10
10
 en ( E ) 
2
2 1
E[ MeV ] 
[cm / g ] [cm s ]
  
What is the (en/ for dose) in tissue for
0.6 MeV (table C3)
-2
3.
28
4e
-2
3.
28
9e
-2
0%
cm
2/
g
0%
cm
2/
g
0%
cm
2/
g
0%
8.
94
0e
4.
cm
2/
g
3.
cm2/g
cm2/g
cm2/g
cm2/g
-2
2.
8.939e-2
8.940e-2
3.289e-2
3.284e-2
8.
93
9e
1.
Flux incident in TISSUE (H2O)
Table C.3:
en(E)/ =3.284e-2 cm2/g
D[Gy / s]  1.602 10
10
in H2O
 en ( E ) 
2
2 1
E[ MeV ] 
[cm / g ] [cm s ]
  
D[Gy/s]  1.602 1010  0.6 MeV   3.284 102 cm2 / g   3872.4 cm2 s 1 
2. Quality factor for gamma is 1, so Dose Equivalent rate is:
H [Sv/s]  1.18e  8 Gy/s 1= 1.18e  8 Sv/s = 1.18e  6 rem/s 
=1.18  rem/s=4.2 mrem/hr
Time to reach 5 rem (annual limit for radiation workers)?
Not much? But isn’t 57 mCi a lot?
Well, let’s see distance…
Redo dose at 2 cm? i.e. working with
the source?
16
2 cm Dose Calculation Practice

cm2
 8.040 10

g
2
Sp = 57 mCi
E = 0.6 MeV gamma @ 94.1% of the time
r=2 cm
Linear attenuation coefficient (or macroscopic cross
section) in air for 0.6 MeV (table C3)
 (r ) 
Sp
4 r
2
e
 r

4 r


 r
Sp
2
e
3.7 1010
1 Ci
57 mCi  0.941 3

10 mCi
1 Ci
 (r ) 
4 22 cm 2
 (r )  3.95 107

cm 2 s
2

2 cm
=8.040 10

g
diss
s
cm 2
g
8.04010
1.205103 3 2 cm
g
cm
2
e
2 cm flux incident in TISSUE (H2O)
Table C.3:
en(E)/ =3.284e-2 cm2/g
D[Gy / s]  1.602 10
10
in H2O
 en ( E ) 
2
2 1
E[ MeV ] 
[cm / g ] [cm s ]
  
D[Gy/s]  1.602 1010  0.662   3.284 102 cm2 / g   3.95e7 cm2 s 1
D[Gy/s]  1.4e  4 Gy/s = 0.014 rad/s  3600 s = 50 rad/hr
LD50=300 rem, so Lethal Dose in few hours!
Distance matters!
According to the
committee V (BEIR V)
The risk of cancer death is 0.08% per rem (0.0008/rem) for doses received rapidly
(acute)
Might be 2-4 times less than that (0.04% per rem) for doses over a long period (chronic)
These risk estimates are an average for all ages, males and females, and all forms of
cancer. There is a great deal of uncertainty associated with the estimate.
BEIR VII risk estimates for fatal cancer are similar to the values from BEIR V, but they
also estimated incidence rates, which were about 50% of the fatal cancer rate.
Risk from radiation exposure has been estimated by other scientific groups. The other
estimates are not the exact same as the BEIR V estimates, due to differing methods of
risk and assumptions used in the calculations, but all are close.
19
Cancer Risk Estimates
Using the linear no-threshold risk model, the 1990 BEIR* V report
provided the following estimate:
The average lifetime risk of death from cancer following an acute dose
equivalent to all body organs of 0.1 Sv (10 rem) is estimated to be
0.8%. This increase in lifetime risk is about 4% of the current baseline
risk of death due to cancer in the United States. The current baseline
risk of cancer induction in the United States is approximately 25%.
Another way of stating this risk:
A dose of 10 mrem creates a risk of death from cancer of
approximately 1 in 1,000,000.
* The National Academy of Sciences Committee on the Biological
(the BEIR Committee)
20
naturally found in:
water, soil, vegetation