A training overview of basic theory and application of alpha discrimination
1
Outline
y
y
y
y
y
y
y
y
y
y
Enabling Objectives
What is Alpha Spectrometry?
Purpose and Applications
Background—Radon and Aerosol Physics
Alpha Spectrometer
Calibration and Maintenance
Quality Assurance
WIPP Examples
Review
Conclusions
2
Enabling Objectives
y Understand the radioactive decay chains which generate radon
y Understand the alpha and beta radiation that is emitted during the decay process
y Understand radionuclide equilibrium y Understand basics of aerosol physics which effect measurable radon alpha and beta activity
3
Enabling Objectives (2)
y Understand the impact of meteorological conditions on Radon concentration
y Understand basics of instrumentation for measuring alpha spectra.
y Understand basics of signal processing required to generate alpha and beta spectra.
y Understand how dust impacts radionuclide assay and identification
4
Enabling Objectives (3)
y Understand how radon can mask TRU alpha activity
y Understand implications for measuring RAF using alpha and beta spectrometry
y Understand traditional alpha spectrometry performed by WIPP labs
5
What is Alpha Spectrometry?
y Alpha decay of isotopes is similar to gamma decay in that single energy emission takes place.
y Beta decay has a spectrum and is not as simple to discriminate beta emitting isotopes
y Measuring the energy of alpha particles can identify the isotope
y Counting emission rates can assay the isotope in terms of Curies.
6
Beta Spectrometry
y Similar to alpha spectrometry but beta spectra are a continuum
y Beta spectra do not show discrete peaks
y Semi‐log plots are often used to show both at the same time
y Linear scale shows detail of large peaks only
7
Maximum and Average Energy
y The maximum energy tends to have few particles
y The average energy is simply the arithmetic average energy each particle has
y The mean energy is the most likely energy and often is near the average
8
Purpose and Applications of Alpha Spectrometry
y Discrimination of radon progeny from TRU activity.
y Radiochemistry is the best method, but takes days to process.
y Assay of alpha emitting isotopes.
y Used for effluent or contamination assay.
y Best method of assaying radionuclides and distinguishing between NORM and TRU
9
History
y Serially decaying nuclides were first identified by Bateman in 1908 y Impact of radon progeny on health identified in mid 20th century
y Radon gas is breathed out
y Radon progeny can stay in the lungs
y USA background radiation dose now considers radon progeny exposure
10
Radon
y Radon
y Atomic number 86
y Nobel gas (non‐reactive)
y Naturally occurring
y Decays to stable lead via release of alpha or beta particles, which are charged.
y Progeny behave like aerosols
y Both uranium and thorium decay to radium, which decays to radon
y Radium only decays to d
11
Uranium
y Atomic number 92
y Abundance in the earth’s crust: 2.7 ppm by mass
y Dominant isotope U‐238 at 99.3% abundance with half life of 4.5E9 yr
y U‐238 decays to Rn‐222 through Ra‐226
y U‐235 decays to Rn‐219 through Ra‐223
12
Thorium (break)
y Atomic number 90
y Crustal abundance 9.6 ppm by mass
y Only isotope Th‐232 is naturally occurring and radioactive with half life of 1.4E10 yr
y Th‐232 decays to Rn‐220 through Ra‐224
13
Radium y U‐238 eventually decays to produce Ra‐226 y Radon (Rn‐222) is the only decay product of Ra‐226
y Th‐232 eventually decays to produce Ra‐224
y Thoron (Rn‐220) is the only decay product of Ra‐224
y U‐235 eventually decays to produce Ra‐223
y Actinon (Rn‐219) is the only decay product of Ra‐223
y The only natural source of radon on the planet is from radium.
y Without radium, there will be no radon, without radon, there will be no radon progeny.
14
Radon Isotopes
y Radon is found in three isotopic forms:
y Rn‐220 y
y
y
Referred to as thoron
Comes from the decay of naturally occurring Thorium
Half life of less than one minute
y Rn‐222 y Referred to as radon
y Comes from the decay of naturally occurring Uranium
y Half life of almost 4 days
y Rn‐219 (negligible)
y Referred to as actinon
y Comes from the decay of U‐235 y 4 second half life, doesn’t escape its radium matrix
15
Radon Properties
y All isotopes of radon chemically behave the same and have the same chemical properties
y Radon is not reactive y Oxidation number of zero y There are no free electrons in its electron shells
y Passes readily through a HEPA
16
Kinetic theory of Gasses cont
y Pressure is generated from molecules impacting vessel walls.
y Increasing their velocity is done by increasing temperature
y Velocity increase causes an increase in pressure
y Decreasing volume will increase impact rate
17
Kinetic theory of Gas cont.
y Pressure = P, Volume = V, number of molecules =n and temperature = T
y PV=nRT (R=gas constant)
y Increase T, you increase P(at constant V)
y Decrease V at constant T, you increase P
y etc
18
Diffusion
y The random motion of molecules causes mixing by adjacent volumes until a uniform distribution is attained throughout all attached volumes.
y Gaseous diffusion tends to happen much faster than liquid diffusion by volume
19
Gas behavior in a TRUPACT
y All internal containers have a HEPA filter intended to pass H2 but not aerosols (such as Pu)
y Kinetic theory of gas dictates radon will diffuse into volumes outside of drums until an equilibrium (equal volumetric concentration) is attained
20
Radon in a TRUPACT II
y When RAF vacuum is applied to inner lid, vacuum is transferred slowly to drum interior.
y Drum radon at that moment is HEPA filtered so only pure radon should pass.
y Progeny comes only from aged radon outside the drums
21
Gas behavior in the WHB y Gas will diffuse and follow general flow patterns at the same time
y This same process would occur with a Pu aerosol release
y Ventilation flow will occur along with diffusion
y Exhaust will compete with diffusion to remove all contaminants prior to full equilibrium
22
Radon and operations (break) y Is some decay enough?
y What if the TRU has the same beta/alpha ratio as NORM?
y Can we know TRU is below limits?
y Radon can exist at levels of health concern
y Typically at levels 1,000 to 10,000 times > Pu in activity
3000
y = m1 + m2*exp(-m3*x)
2500
2000
m1
m2
m3
Value
892.42
2212.4
0.017969
Error
58.466
48.633
0.0011802
Chisq
R
41888
0.99714
NA
NA
1500
1000
500
y = 2833.6 * e^(-0.0082748x) R= 0.98707
0
0
50
100
150
200
Time (minutes)
23
Radon Decay Chain from Thorium
1.8E+05
1.6E+05
214Po
1.4E+05
1.2E+05
220Rn
55 s
α
212Po
1.0E+05
8.0E+04
6.0E+04
212Bi & 218Po
4.0E+04
212Po
2.0E+04
0.0E+00
2000
3000
4000
5000
6000
7000
8000
9000
Energy (keV)
6.3 MeV
2.2 MeV
β
64.06%
3E‐7 s
α
8.8 MeV
216Po
212Bi
208Pb
.15 s
60.6 min
Stable
α
6.8 MeV
212Pb
10.6 hr
β
35.94%
0.3, 0.6 MeV
α
6.1 MeV
208Tl
3.1 min
β
1.0‐1.8 MeV
24
Radon Decay Chain from Uranium
226Ra
210Po
1600 y
α
4.9MeV
222Rn
0.4‐3.3
MeV
3.82 d
α
1.2
MeV
β
5.5 MeV
218Po
214Bi
3.1 m
19.9 min
α 6 MeV
214Pb
26.8 m
β
0.7, 1.0 MeV
α
β α
5.3
MeV
206Pb
Stable
210Bi
214Po
164.3 μs
7.7
MeV
210Pb
21 y
138 d
5.0 d
β< 0.1 MeV
1.8E+05
1.6E+05
214Po
1.4E+05
1.2E+05
1.0E+05
8.0E+04
6.0E+04
212Bi & 218Po
4.0E+04
212Po
2.0E+04
0.0E+00
2000
3000
4000
5000
6000
Energy (keV)
7000
8000
25
9000
Interim review (break)
y What is the only source of radon?
y What would the time evolution of a pure radon source onto an air filter look like in terms of activity?
y What would a time evolution of aged radon (or thoron) and its progeny activity look like on a filter?
y Why don’t we see radon emissions in our detectors?
y What is secular equilibrium?
y What are the driving forces causing radon emission from our waste packages?
y How does the radon get out of the waste?
y What is diffusion?
26
Radon Decay (and its progeny)
y Different equilibrium factors mean different relative amounts of progeny being attached or unattached
y Thoron progeny have long half lives
y Radon (Uranium) progeny have shorter half lives (~30 min)
1000
800
y = m1 + m2*exp(-m3*x)
m1
600
Value
Error
308.14
29.033
m2
869.97
29.282
m3
0.061464
0.0069686
Chisq
4661.2
NA
R
0.99501
NA
400
200
y = 981.68 * e^(-0.024598x) R= 0.97705
0
0
20
40
60
80
100
Time (minutes)
27
Attached and unattached fractions
y Each time a beta or gamma emission takes place, a new element is created from an old one
y The new element is an ion and interacts through collisions and Coulomb attractions/repulsions
y The ion can interact through dipole interactions when inducing polarization in dust particles in the air.
y This sets up an attractive potential to adhere certain portions of the airborne radionuclides to the dust (organic and mineral) in the air.
y Filter efficiency depends not only on particle size but flow rate
28
Dielectric polarization
y A point charge next to a grounded flat metal conductor will induce a charge distribution on the surface of that conductor to force the lines of flux to be normal to the conductor surface.
y This equates to a phantom source of equal charge behind the surface of the conductor
y If the planar material is a dielectric, only a polarization is induces so the phantom source is normalized smaller in amplitude based on the dielectric constant of the two media on either side of the plane
y This occurs in a more complicated fashion if the separating surface is not a plane (such as a sphere or 29
dust particle)
Equilibrium factors
y A time series average has been reported for outdo0r air as 1/0.9/0.6/0.4 for the radon series Rn222/Po218/Pb214/Bi214 and estimated at 1/0.4/0.3 for the thoron series Pb212/Bi212/Tl218
y The source terms in radon and thoron are dynamic as must then be the progeny
y Plate‐out on surfaces depends on particle size, humidity, surface area in the immediate vicinity, dust loading in the air and material type
y When fresh/filtered air comes in (as in the WHB), progeny must build up and mix with ambient air
30
Radon in a TRUPACT‐II revisited
y Only pure radon gets through the HEPA filters on the interior waste containers
y Progeny has to build up from radon decay in volume sampled by RAF
y Progeny plate out and aerosol attachment physics take place
31
Radon in the Environment
y The equilibrium distribution of radon and its progeny depends on environmental conditions:
y Relative humidity holds, wind disperses, and barometric pressure can either hold or disperse radon and progeny
y Rain and condensed vapor can concentrate radon and progeny
y Dust can capture the progeny and disperse it 32
Radon progeny scrubbing from rain
y Gamma dose rate follows radon progeny
y Dose rates increase on the ground when it rains
y Progeny plates out on surfaces at higher rate
y Fixed and surface removable will be increased on TRUPACT receipts and people passing through portal monitors
33
Equilibrium
y Equilibrium is established when the activity of each progeny are equivalent to the activity of the parent (radon)
y Radon is dynamic, meaning it can be blown away after arising from soil, and is also dependent on environmental conditions such as barometric pressure and soil moisture
y Radon progeny is also dynamic as it can plate out, be suspended or re‐
suspended, attach and detach from aerosols and particles, and be blown away
y So attaining equilibrium all in one Radon leaches
from Soil
Resuspension
rocks!
34
Heat transfer basics (break)
y Conduction
y When two items are in contact and have different temperatures, heat flow will occur.
y Radiation
y Infrared radiation occurs between separated regions of different
temperature
y
This is the same radiation from items which are “red hot” or otherwise glowing from heat
y Convection
y When air is heated through conduction, it rises and is replaced by cooler air. This creates an air current transferring heat from the hotter item.
y The earth is heated through radiation and can cool through convection, conduction and radiation.
y When the air is still, the dominant cooling is through radiation
which interacts with the cooler air, heating it up.
35
Meteorological Dependencies
y Radon typically is more concentrated in the mornings due to temperature inversions.
y The inversion prevents mixing with upper atmosphere air which would dilute surface concentrations
y This gives rise to diurnal variations y CAM spectra tend to follow the radon source term with a small time lag.
36
Radon Concentrations
y Radon typically is more concentrated in the mornings due to temperature inversions.
y The inversion prevents mixing with upper atmosphere air which would dilute surface concentrations. y Humidity and dust loading effect unattached fraction
y When windy conditions are present, thoron to radon ratios tend to be higher. Why?
y When you walk your dog to what are you more likely to be exposed radon or thoron and why? 37
Radon and Aerosol Physics
y When radon or its progeny decay, the result is an ion which will be attracted to ambient dust through because they are both charged particles.
y Impaction will result in some ions stripping or giving charge to ambient particles or being attached
y This results in both free and attached components of the progeny.
y Attached fraction tends to be in the respirable range
y Particles can stay in the lung constantly irradiating living tissue – tumors, cancers
38
Radon Discrimination
y Radon progeny has multiple discrete alpha emissions y This progeny can and does plate out on surfaces generating surface removable alpha activity
y Discrimination of TRU and radon progeny alpha activity requires either alpha spectroscopy or radiochemical separation.
y Radiochemistry often takes multiple days, but is very good at discriminating TRU from radon progeny and the only validated assay method for this discrimination
39
CAM Alarms
y The most common cause of a false CAM alarm occurs when a large shift in radon concentration has occurred (such as when an atmospheric temperature inversion has just lifted) Why?
y RADOS CAMs have two set points.
y FASs are counted twice with decay time in between
40
Alpha Spectrometry System
Displays spectrum and allows for analysis of peaks
Solid State Detector
Vacuum Pump
Detector
Electronics
PC Analysis Software
Sample
Optional‐Used for Higher Resolution
Filter, swipe or other medium
Amplifier, MCA, and other signal changing electronics
41
Alpha Particle Interaction
y An alpha particle has approximately 4000 times more mass than orbital electrons in matter.
y High energy alphas tend to travel in straight lines
y It is not highly likely that they will come close to a nucleus
y Initial energy deposition is almost constant
42
Alpha Spectrometry
y Requires measuring the energy of each alpha particle detected.
y Typically done with solid state detectors but can be done with ion chambers.
y Solid state detectors include GeLi, NaI, HPGe
y Total ionizations created are correlated with incident particle energy
y The energy of the alpha particle identifies the radionuclide 43
Detector Output 1.8E+05
1.6E+05
214Po
1.4E+05
1.2E+05
1.0E+05
8.0E+04
6.0E+04
212Bi & 218Po
4.0E+04
212Po
2.0E+04
0.0E+00
2000
3000
4000
5000
6000
7000
8000
9000
Energy (keV)
From http://www.laserfocusworld.com/display_article/31182/12/none/none/News/Pho
tomultiplier‐tubes‐count‐photons
44
Pulse Height Histogram
y An ion chamber collects the amount of charge generated in its controlled volume
y The height of the pulse determines how much activity you have in your sample
y By placing a single count at a given amplitude for each time a charge is collected at that amplitude, the histogram is built up.
y The resultant histogram is the alpha spectrum
y This is your sample assay
45
What happens with low counts?
Preliminary radon spectrum (short count time)
Aged radon with long count time (only Thoron progeny)
46
What happened to the iSolo? (break)
WIPP Measurements
iSolo blank Rn loaded filter with filter (dpm) source (dpm)
% TRU detected
384
409
84%
439
505
103%
521
747
152%
510
98
20%
558
83
17%
528
327
67%
481
129
26%
409
449
624
WHC (Hanford) Measurements
Table 6 (WCH‐172 Rev. 0) 308W Hood TH/U/Ra/Rn Test
Percent detected, Radon Count Time post sample (min) compensated
length
40
33.1%
10
50
20.3%
10
60
26.3%
10
100
51.9%
30
Table 7 (WCH‐172 Rev. 0)
Source/Nuclide
Pu/Am
Unat 47 mm
Pu‐239
Unat
Unat
Unat
Unat
Pu‐239
Pu‐239
Pu‐239
Percent detected, Radon compensated Sample ID
93.50%
1
90.2%
2
95.50%
3
43.9%
4
8.1%
5 (30 min)
15.3%
6 (30 min)
72.7%
8
132%
9
117%
10
176%
12
47
TRU Region of interest
y Noise sources
y Counting
y Relative Activity
y Algorithm assumptions
y
y
Spectral shape
Activity levels
y Sample size
y Sample geometry
y Relative activities
From DRAFT Standard N42.50 - Performance Specifications for Instrumentation Systems
Designed to Measure Radon Progeny in Air, Final Draft
48
Do not use iSolo printout values
y Attribute all counts in the TRU ROI to being actual TRU
y Result is very conservative because no credit is given to 6 MeV tails into TRU ROI
y Result is very useful as only 10 to 15 % of alpha activity now can be partly due to TRU
49
New paradigm in control limits
y 20 dpm α
TRU
y 200 dpm β (90Sr)
y 1000 dpm NORM
y Only gross α & β on iSolo
50
Basics of algorithms (i.e., CAM Alarms) y Constant spectral shape assumption
y Constant activity assumption
y Changes assumed due only to Pu content
y Time resolution limited
y Sensitivity related to time resolution
51
Radon Masking Effects
92 cpm estimate
3.4 cpm estimate
50
75
100
125
150
175
200
225
y Spectra acquired from used PAS filters having a small TRU count rate contribution present due to a source being placed behind the filter (Figure 1). y The upper spectra had a total accumulation time of 3.5 minutes whereas the lower spectrum had a 16 minute accumulation time. y No amplitude normalization was used, intensity similarities reflect radon progeny activity on the filters.
Channel number
52
RAF
y If 3 dpm (1 cpm) falls in the TRU ROI on an RAF count, concern is warranted.
y NUREG 1400 gives a re‐
suspension factor of 0.01, whereas we use a factor of 0.001, meaning that 3000 dpm of surface removable activity is credible within the TRUPACT
y 4 dpm was enough to ID a leaky drum from an RAF
y What would you do if you saw one or more counts on an RAF in the TRU ROI?
y What if you saw no counts in the peak channel location but many on either side?
53
Signal Detection at low activity
y When radon or TRU has low activity, few counts are seen and the signal grows fuzzy
y Channels with zero counts can occur even in the peak channel location. y It is best to have sample with more activity on it than very little activity because you can’t always see peaks clearly when there is only a little activity on a sample being analyzed.
54
Efficiency and Energy
y Efficiency requires using the whole peak (not just a channel or two).
y Use of only one channel for an assay measurement drastically reduces efficiency
y Energy requires one or more channels at known discrete energies
55
Quality of Signal is Important
y Low activity samples produce “noisy” spectra y Noise is relative
y Produced by electronics, background, and other factors
y The signal to noise ratio is the true metric for quality
y Filter loading, geometry and overlapping signals can degrade quality
y Desire higher signal, lower noise
y Can be done with longer counts or more sensitive instrumentation or more sample activity
56
Full Width at Half Maximum
y Used to determine the resolution of the spectrum
y Is the width of the peak at half its maximum height
y The smaller it is, the better the spectrum.
y See next slide for examples of good and bad spectra.
57
58
Particulate deposition on filters
y There are four primary particle deposition mechanisms on filter media
y The dominant mechanisms are impaction and interception for aerosols >0.2 um.
y Diffusion is the dominant mechanism <0.2 um
http://www.cdc.gov/niosh/docs/2003‐136/2003‐136c.html#fig3
59
Filter efficiency
y Not all filters behave the same
y Typically filters have higher efficiency when wet
y You can even charge the filter to increase efficiency
http://www.cdc.gov/niosh/docs/2003‐136/2003‐136c.html#fig3
60
Efficiency tends to increase with loading
y As the filter loads with particulate, the efficiency tends to increase
y Does not address flow, spectra or DP
http://www.cdc.gov/niosh/docs/2003‐136/2003‐136c.html#fig3
61
Sample Preparation
y If high resolution is needed, impurities must be removed from the sample.
y Impurities include filter media, dust and any chemical constituents not being assayed.
y Impurities make assay very difficult
y Assay can be affected by water content and dust loading due to masking of the alpha emissions
y Alpha spectroscopy has its limitations.
y Sometimes only radiochemistry can be used to identify TRU activity
y There is no simple go/no go system for identifying TRU activity when radon and its progeny are present.
62
Calibration and Maintenance
y Detectors must be calibrated y
y
y
y
and properly maintained.
Some detectors may have to be replaced if exposed to light or salt or humidity over time.
Calibration requires NIST traceable calibrated sources in the same configuration as samples to be assayed.
Equipment must operate properly to achieve accurate assay.
RCT must know if equipment is operating properly and if the sample is appropriate for alpha spectroscopy
63
Quality Assurance
y Rigorous QA is required for regulatory compliance activities which rely on radiological assay. – how certain are you that your alpha spec interpretation is correct?
y Could your analysis be defended in court and accepted?
y Accurate and complete documentation must demonstrate each component relied upon for accuracy and precision is working properly and was properly considered in the analysis.
y If it was not written down, then it did not occur.
64
WIPP Examples
y Radon at intake shaft – less at y
y
y
y
y
station A
WIPP salt is a big filter
Shaft scraping with galloway released fallout when Station A detected small amounts of Plutonium
Plutonium in environment due to Gnome site explosion which released fallout nearby
Challenge is to discriminate between Plutonium from waste versus from the environment.
Radon at WIPP is typical for the US averaging 0.1 to 0.4 pCi/L
65
Review Part 1
y What is the initial decay product of all radium isotopes?
y What is final decay product of all radium isotopes?
y What kinds of radioactivity comes from radon progeny?
y What are some meteorological parameters that effect radon progeny distributions?
y What is the difference between attached and unattached progeny?
y What effect does a temperature inversion have on radon and its progeny?
66
Review Part 2
y What is an alpha spectrometer?
y What is a pulse height distribution? What does it tell you?
y When is your sample not appropriate for alpha spec?
y What does dust and salt on an air filter do to the alpha spectrum?
y How can radon mask TRU alpha activity?
y What do a few counts on an RAF in the TRU ROI imply?
67
Conclusions
y Alpha assay has many similarities to gamma assay
y Radon discrimination is a problem that has been with the nuclear community since the Manhattan project.
y Radon progeny have predicable qualities that can be leveraged in mitigation solutions
y Current state of the art method of discerning radon from TRU is radiochemistry
68
Photo Credits
Citation
http://toxipedia.org/download/attachments/3604/radon.png
http://www.rtca.com/images/radon_enters_bg1.jpg
http://www.nucleonica.net/wiki/index.php/Help:Decay_Engine
http://www.cemrc.org/depts/rag.html
http://www.kendalhang.btinternet.co.uk/clipart_ih/Dust.gif
http://www.orchd.com/environmentalHealth/indoorAir/radon/images/radon_movement.jpg
http://redkid.net/generator/snoopy/pigpen.jpg
http://nsspi.tamu.edu/NSEP/basic_rad_detection/index.php?course=0600
http://www.hko.gov.hk/radiation/ermp/kp_lab_eng/ass_content.htm?flash=1
http://www.canberra.com/products/1210.asp
http://www4.uwm.edu/radon/radon2.jpg
http://www.radonatlantic.com/images/radon.jpg
http://arq.lanl.gov/source/orgs/nmt/nmtdo/AQarchive/02spring/gifs/RadTechs.gif
http://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Nougat_Gnome_Marker.jpg/300px‐Nougat_Gnome_Marker.jpg
http://www.motabaqah.com/Conformity/uploadedImages/LABS/Calibration_Lab/Services/measurement(1).jpg
http://www.wipp.energy.gov/Photo_Gallery_Images/CH_photos/CH2.jpg
http://www.lightandmatter.com/html_books/0sn/ch13/figs/fwhm.png
69
Photo Credits (2)
http://www.nationalparkstraveler.com/files/storyphotos/Pitchblende_via_Wikipedia_Commons.jpg
http://depletedcranium.com/fiestaware55.jpg
http://www.eia.doe.gov/cneaf/nuclear/page/images/intro_fig3.jpg
http://www.orau.org/ptp/collection/consumer%20products/mantle2.jpg
http://www.galleries.com/minerals/silicate/thorite/thorite.jpg
http://www.orau.org/PTP/collection/consumer%20products/weldingrod.jpg
http://www.ead.anl.gov/project/images/progprojphotos/norm.jpg
http://www.nature.com/nature/journal/v407/n6806/images/407897aa.0.jpg
http://www.sandia.gov/LabNews/LN04‐09‐99/images/wipp4_pix.jpg
http://www.hedgeco.net/blogs/wp‐content/uploads/2008/07/courtroom.jpg
http://wayofthewest.files.wordpress.com/2009/06/pen‐to‐paper.jpg
http://4engr.com/images/thumb/52854a9ef3ec667bb1bb9667578ccb74.jpg http://www.nuc.berkeley.edu/dept/Courses/NE‐162/Lecture7‐hchp.ppt.
70
Photo credits (3)
y http://en.wikipedia.org/wiki/File:Translational_motio
n.gif
y http://en.wikipedia.org/wiki/File:Diffusion.svg
y http://www.cdc.gov/niosh/docs/2003‐136/2003‐
136c.html#fig3
y http://www.cdc.gov/niosh/docs/2003‐136/2003‐
136c.html#fig3
71