Chapter 7

Section 2 Shielding

Radiation Shielding

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

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

Radiation Intensity

The fluence () is the number of photons moving through a target area (/cm2)

The flux () is the number of photons moving through an area per time (/cm2s)

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

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

Calculating Flux, continued

Consider each photon as it leaves the source

It moves further away from others that have been emitted

Therefore, the flux (/cm2s) decreases

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:

Surface Area of a Sphere

S.A.1 cm = 12.57 cm2

S.A.10 cm = 1257 cm2

S.A.100 cm = 125,664 cm2

24.. rAS

1 cm

10 cm

100 cm

Calculating Fluence and Flux, continued

= Fluence /cm2

= Flux /cm2sD = total number of photons emittedS0 = source strength (photons/s)R = distance from source (1, 10, 100 cm)

20

2

4

4

r

S

r

D

Calculating Fluence and Flux, continued

If source emits 4 photons/s, S0 = 4, The (flux) is then calculated:

At 1 cm = 4 /12.57cm2s = 0.318 /cm2s At 10 cm = 4 /1257 cm2s = 3.18 x 10-3 /cm2s

At 100 cm =4 /125,664 cm2s = 3.18 x 10-5 /cm2s

Calculating Fluence and Flux, continued

For this same problem, what is the photon fluence?

Can we calculate it at all? Why? Why not?

Calculating Flux

At any point from the source, the photon intensity (flux) can also be estimated as:

But, what happens if we put some photon absorbing material between the source and our measurement point?

2

0

4 r

S

Attenuation Occurs Remember the “universal” equation (or one

form of it):

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”

xeIxI 0)(

Source Strength From Shielded Source The two equations can be combined to

yield:

The term 1/(4r2) is called the geometeric attenuation factor

xo

x

unshieldedshielded

er

S

ex

24

)(

Converting to a Dose Rate Photon intensity can be

converted to dose rate Called an “uncollided” dose rate Use tables of “dose conversion

factors”:S0 P

rxo

u

xoshielded

er

SEEkD

er

Sx

2

2

4)(

4)(

x

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.

Photon Energy Flux to Exposure Dose-rate Conversion Factors

1.56 E-062.0

1.62 E-061.8

1.67 E-061.6

1.73 E-061.4

1.78 E-061.2

1.84 E-061.0

1.87 E-060.9

1.90 E-060.8

1.92 E-060.7

1.94 E-060.6

1.96 E-060.5

Conversion Factor, k(E),

R/hr per MeV/cm2 sEnergy (E) in

MeV

Energy of photon being evaluated

Scientific notation commonly used, should be read as:

1.96 x 10-6

These are “look up” values

Total Linear Attenuation Coefficient Factors, (cm-1)

0.334

0.352

0.372

0.397

0.4285

0.468

0.493

0.523

0.557

0.599

0.652

Fe

(7.86)

0.117

0.123

0.131

0.140

0.151

0.166

0.174

0.184

0.196

0.210

0.227

Al

(2.70)*

0.838

0.889

0.949

1.022

1.114

1.233

1.349

1.492

1.705

1.988

2.490

W

(19.3)

0.298

0.314

0.332

0.354

0.382

0.417

0.445

0.479

0.523

0.578

0.666

Sn

(7.31)

0.510

0.544

0.585

0.635

0.699

0.782

0.866

0.971

1.136

1.361

1.746

Pb

(11.34)

0.8792.0

0.9441.8

1.0231.6

1.1211.4

1.2451.2

1.4101.0

1.5840.9

1.8030.8

2.1440.7

2.6180.6

3.4590.5

U

(18.7)

Energy (E)

in MeV

*Normal density () in g/cm3

Total Linear Attenuation Coefficient Factors, (cm-1), continued

0.152

0.160

0.170

0.181

0.196

0.214

0.227

0.243

0.262

0.286

0.317

Barytes Concrete

(3.50)

0.105

0.111

0.118

0.126

0.136

0.149

0.156

0.165

0.175

0.188

0.204

Ordinary Concrete

(2.35)*

0.202

0.213

0.226

0.241

0.260

0.285

0.299

0.317

0.337

0.363

0.395

Ferrophos. Concrete

(4.68)

0.155

0.163

0.173

0.185

0.200

0.219

0.230

0.243

0.259

0.278

0.303

Magnetite Concrete

(3.55)

0.0494

0.0522

0.0554

0.0594

0.0643

0.0707

0.0743

0.0786

0.0835

0.0895

0.0967

Water (1.0)

5.36E-52.0

5.66E-51.8

6.01E-51.6

6.44E-51.4

6.97E-51.2

7.66E-51.0

8.05E-50.9

8.52E-50.8

9.05E-50.7

9.70E-50.6

1.048E-40.5

Air (0.001205)**

Energy (E)

in MeV

*Normal density () in g/cm3

* * Air at 200C, 760 mm Hg

Calculating Exposure

The uncollided flux previously calculated is: At 1 cm, = 0.318 /cm2s At 10 cm, = 3.18 x 10-3 /cm2s At 100 cm, = 3.18 x 10-5 /cm2s

k(E) = 1.9 x 10-6 R/hr per MeV/cm2 s E= 0.8 MeV e-x 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

xou e

r

SEEkD

24)(

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

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:

hr

rad =

ft

Ci E 6.0 D 2

Rule of Thumb #2

For beta radiation, the equation is similar, where the maximum energy of the beta radiation is used.

hr

rad =

ft

Ci E 2 D 2

max

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.