Shie lding and Ra nge Rad iati on Pr otect ion
T ime Distan ce
Shielding
V a ul t B oy cha ra cte r f rom Fal l o u t ga m e se r i e s © B e the sda
G ame St u d i o s . A ll r ig hts re se r ve d. Thi s conte nt i s excl ude d from our Creative Commons license. For more information,
P ubl i c dom ai n i m age see ht tp://ocw.mit.edu/help/faq -fa ir - u se/ .
22. S9 02 – DIY Geiger Counte rs Prof. Michael Short
Qu e sti o n:
W ha t i s V a ul t B oy doi ng? Vault Boy character from Fallout g ame series © Bethesda Game Stud ios.
All rights reserved. This content is excluded from our Creat ive Commons
license. For more information, see http://ocw.mit.edu/help/faq -f air -u se / . 2
M o ti vati o n
U nder s t and how t i me and di s t anc e dec r eas e ex pos ur e r at e t o r adi at i on
D er i v e r ul es of l ogar i t hmi c at t enuat i on
C har ac t er i z e di f f er ent mat er i al s i n t er ms of t hei r s hi el di ng ef f i c ac y
D es i gn i deal , ec onomi c al r adi at i on s hi el di ng
3
D o se and T i m e
I hope t hi s one i s sel f - expl anat or y!
4
D o se and D i stanc e
A ssum i ng a poi nt sour ce of r adi at i on:
Intensit y at surface of s phere
I 9
Sphere area
A= 4 r 2 Source strength
S
I = S
I 4
4 r 2
I
r
2r
3r
In v erse square la w: Doubling the distance from source, the energy is spread o v er four times the area, so intensit y falls to one-fourth.
Image by MIT OpenCourseWare. After Hyperphysics .
5
T he sol i d angl e subt ended by t he obj ect of i nt er est det er m i nes dose r at e
D o se and D i stanc e
T he sol i d angl e subt ended by t he obj ect of i nt er est det er m i nes dose r at e
Label photo courtesy of Brook Clarke. Used with permission.
Geiger tube photo courtesy of Jeff Keyzer on Flickr.
What i s t he “ obj ect of i nt er est ?”
H ow do you det er m i ne i f a sour ce i s a “ poi nt sour ce?”
6
D o se and D i stanc e
T he sol i d angl e subt ended by t he obj ect of i nt er est det er m i nes dose r at e
Label photo courtesy of Brook Clarke. Used with permission.
Geiger tube photo courtesy of Jeff Keyzer on Flickr.
I f your obj ect ’ s ( or your ) sol i d angl e ( pr oj ect ed ar ea) on a spher e of r adi us r i s sm al l , and t he sour ce i s sm al l i n com par i son, i t s ar ea appr oxi m at es t he ar ea pr oj ect ed ont o t he spher e
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D o se and D i stanc e
http://en.wikipedia.org/wiki/Steradian
T he sol i d angl e subt ended by t he obj ect of i nt er est det er m i nes dose r at e
Label photo courtesy of Brook Clarke. Used with permission.
O ne st er adi an
Pu b lic domain im ages.
I f your obj ect ’ s ( or your ) di st ance f r om t he spher e
i s l ar ge, and i t s ar ea i s sm al l , t hen 𝑟 ≫ ℎ , and
you can appr oxi m at e obj ect ar ea as spher e ar ea
8
D o se and D i stanc e Cal c u l ati o n
Label photo courtesy of Brook Clarke. Used with permission.
Geiger tube photo courtesy of Jeff Keyzer on Flickr.
T hi s sour ce has 5 μ C i of act i vi t y , and our SBM - 20 t ube i s 1m aw ay:
𝐵𝑞
3 .7 ∙ 10 1 0
𝐶𝑖
5 ∙ 10 − 6 𝐶𝑖
4 𝜋 𝑆 𝑟
5 𝜇 𝐶𝑖
𝛾𝛾 − 𝑟 𝑎𝑦 𝑠
𝐼 =
4 𝜋 𝑆 𝑟
=
= 1. 47 ∙ 10 4
𝑆 𝑟 − 𝑠
I gnor i ng shi el di ng of ai r , t he t ube w al l , et c. :
𝐴 ≈ 0 . 01𝑚 × 0 . 1 08𝑚 ≈ 0 . 001 08 𝑚 2
T u b e d i ag ram © so u rce u n k n o w n . A l l ri g h ts re se rv e d . T h i s con te n t i s excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq -f air -u se/ .
9
D o se and D i stanc e Cal c u l ati o n
Label photo courtesy of Brook Clarke. Used with permission.
Geiger tube photo courtesy of Jeff Keyzer on Flickr.
I gnor i ng shi el di ng of ai r , t he t ube w al l , et c. :
T u b e d i ag ram © so u rce u n k n o w n . A l l ri g h ts re se rv e d . T h i s con te n t i s excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq -f air -u se/ .
𝐴 ≈ 0. 01𝑚 × 0. 1 08𝑚
≈ 0. 001 08 𝑚 2
O ne S t er adi an ( Sr ) on a 1m r adi us spher e i s 1m 2 :
1. 47 ∙ 10 4 𝛾𝛾 − 𝑟 𝑎𝑦 𝑠
𝑆 𝑟 − 𝑠
Φ ̇ =
𝛾𝛾 − 𝑟 𝑎𝑦 𝑠
0. 00 10 8 𝑚 2
= 15 . 88
𝑠
1 𝑆 𝑟
𝑚 2
10
R epea t t h e Q ues t io n :
W hat i s V aul t B oy doi ng?
Vault B oy ch aracter from Fallou t gam e series © B ethesda Game S tudio s . A ll rights r eserved. T his c ontent i s excluded from ou r Creative C ommons license. For m ore in formation,
W hat i s V aul t B oy doi ng?
H e i s est i m at i ng a sol i d angl e!
Vault B oy ch aracter from Fallou t gam e series © B ethesda Game S tudio s. A ll rights r eserved. T his c ontent i s excluded from ou r Creative C ommons license. For m ore in formation, see h ttp://ocw.mit.edu/help/faq -f air -u s e / .
R epea t t h e Q ues t io n :
12
W hat A bo u t S hi e l d i ng ?
T u r n er , p . 188 ( 2007)
Sa y N gam m a r ay s r eac h a di s t anc e x w i t hout i nt er ac t i on. D ef i ne a c ons t ant of pr opor t i onal i t y r el at i ng t he num ber t hat
x
dx
N o
N(x)
i nt er ac t i n a di s t anc e dx :
𝑑𝑁 = −µ 𝑁𝑑 𝑥
Thi s c ons t ant
( µ )
i s t he l i near
at t enuat i on c oef f i c i ent . S ol v e t he di f f er ent i al equat i on t o get :
Image by MIT OpenCourseWare. After Turner (2007).
𝑥
𝑁 = 𝑁 0 @ 𝑥 = 0 𝑐 = 𝑙𝑛 𝑁 0
𝑑𝑁
𝑁
= − 𝜇 𝑑𝑥 ln 𝑁 = − 𝜇 𝑥 + 𝑐 𝑁
= 𝑁 0
𝑒 − 𝜇𝑥
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At t en ua t io n C o ef f icien t s
T u r n er , p . 190 ( 2007)
N ot e µ has uni t s of c m -1 , y et t abl es gi v e v al ues i n uni t s of 𝑐𝑚 2
M ust m ul t i pl y by t he m at er i al densi t y !
𝑔𝑔
Source: Morgan, K . Z., and J. E. Turner , eds . Principles of Radiation Protection . Wiley, 1 967 .
© Jo hn Wiley & Sons. All rights reserved. This conten t is e xcluded from ou r Creative
Commo ns licens e. For more in formation, see h ttp://ocw.mit.edu/help/faq -f air - u se / . 14
Addit iv e At ten ua t io n C o ef f icien t s
H ow do y ou deal w i t h m ul t i com ponent m at er i al s?
𝑥
C om pos i t es , al l oy s , f oam s , c onc r et e…
𝑥
𝑁
= 𝑁 0
−
𝜇
𝜌
𝑒
𝜌 𝑥 𝑁
= 𝑁 0 𝑒
𝑛
− ∑
𝑖= 1
𝜌 𝑖 𝑥
𝜇
𝜌
𝑖
E ach com ponent i com bi nes addi t i vel y i n t he exponent i al
𝜇
𝜌
N ow , w her e t o f i nd val ues of ?
N I S T ( N at i onal I nst i t ut e of S t andar ds and T echnol ogy ) m ai nt ai ns an act i ve dat abase!
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Ex am p l e : Che ap S hi e l d i ng
What m akes better shi elding, plasti c or bacon grease?
P ublic domain im ages.
A bout t he sam e! W hy ??? 16
Ex am p l e : Che ap S hi e l d i ng
W hat m akes bet t er shi el di ng, concr et e or l eaded gl ass?
P ublic domain im ages.
I t depends on t he ener gy ! 17
W hat A bo u t Ene r g y D e g r ad ati o n?
T u r n er , p . 188 ( 2007)
Y ou can i gnor e t hi s f or “ good geom et r i es” and gam m as
x
Narrow Beam
d
Detector
R d<<R
Image by MIT OpenCourseWare.
A ssum e t hat al l gam m as w hi ch i nt er act l eave t he beam 18
T hi nk i ng A bo u t the L ab
H ow w i l l y ou det er m i ne how m any gam m as i nt er act w i t h y our G ei ger count er ?
Label photo courtesy of Brook Clarke. Used with permission.
Ai r A i r G as es W ho C ar es
P l a st i c B r a ss Br a s s
19
20
MIT OpenCourseWare http://ocw.mit.edu
22. S902 Do-It-Yourself (DIY) Geiger Counters
January IAP 2015
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