Rad i at i o n Basi cs

C o okie pho to : Public domain .

22. S 902 – D I Y G eiger C ount ers P rof . M ic hael S hort

 Y ou hav e f our highly radioac t iv e c ook ies :

α β γ n

 Y ou m us t :

P ut one in your pocket H old one in your hand E at one G ive one t o a “f riend”

O ld 2 2.01 Fi nal Exam Quest i o n

 W hat do y ou do?

Co okie pho to : Pub lic domain . 2

M o t i vat i o n

 I nt roduc e ioniz ing radiat ion bas ic s

 E s t ablis h c om m on not at ion and t erm inology

 U nders t and t y pes of radiat ion

 I nt uit iv ely unders t and range of radiat ion

 D eriv e and us e nuc lear reac t ion equat ions , half liv es of c om m on is ot opes

T y p es o f Io ni zi ng Rad i at i o n

 A lpha ( α) – Heliu m nucleu s +2

– H eav y , c harged

± 1

 B eta ( β ) – A fr ee electr o n or positr on

– Li ght, c harged

 Gam m a ( γ) – A nuclea r ph o ton ( l ight )

– N o mas s , no c harge

 Neutr on ( n ) – A fr ee neutr on

– H eav y , no c harge

Rang es o f Io ni zi ng Rad i at i o n

P aper

Plastic

Steel

Lead

alpha beta beta

gamma

Image by MIT OpenCourseWare.

R elat i ve Ener g y Dep o si t i o n

Which do you think deposi ts the +2

m ost ener g y?

± 1

Wher e? ( Over what r ange ? )

Which type( s) is/ar e safer outside the body?

Which type( s) is/ar e safer inside the body?

 Y ou hav e f our highly radioac t iv e c ook ies :

α β γ n

 Y ou m us t :

P ut one in your pocket H old one in your hand E at one G ive one t o a “f riend”

O ld 2 2.01 Fi nal Exam Quest i o n

 W hat do y ou do?

Co okie pho to : Public domain . 7

 A tom s ar e deter m i n e d by the num be r of pr oton s

– Exa m p le : He liu m A L W A YS h a s t wo p r o t o n s

 T wo specia l types:

Io ns, Iso t o p es

– Ion

• S a m e # pr ot ons & neut r ons

• Dif f er ent # elec t r ons ( c har ge)

– Isotope

• S a m e # pr ot ons

• Dif f er ent # neut r ons ( m as s )

4 He

4 He

4 He +

3 He

Iso t o p i c No t at i o n

𝐴 𝑁𝑎𝑚 𝑒

Image No t a t i o n T empl at e

𝟗𝟗 𝟐𝟐𝟐𝟐 𝟎𝟎 𝟗𝟗 𝟐𝟐𝟐𝟐

𝟗𝟗𝟗𝟗

𝟗𝟗 𝟐𝟐𝟐𝟐 + 𝟒𝟒 𝟗𝟗 𝟐𝟐𝟐𝟐 + 𝟒𝟒

𝟗𝟗𝟗𝟗

𝟔𝟔𝟎𝟎 𝐶𝑜 𝟎𝟎 = 𝟔𝟔𝟎𝟎 𝐶𝑜

No t at i o n Examp les

1 𝟐𝟐𝟐𝟐 + 1

𝟐𝟐𝟐𝟐

𝟒𝟒 𝐻 𝑒 + 𝟗𝟗 =

1 𝟐𝟐𝟐𝟐 𝐶𝑠 + 1

𝟒𝟒 𝐻 𝑒 + 𝟗𝟗 = 𝛂

St able Iso t o p es

http://atom.kaeri.re.kr/

 S table isotopes do not under g o s p ont a neous

r adio a ctive decay

 Which ar e stable? Consult the T abl e o f Nuclide s

Courtesy of K orea Atomic Energy Research Institute. Used with p ermiss ion.

 Look closer at one section

 W hic h is ot opes of c hlor ine ar e s t able?

S a me n e u t r o n n u mb e r ( N)

St able Iso t o p es, At o mi c W ei g ht

http://atom.kaeri.re.kr/

S am e ato m i c n u mb e r ( Z )

St able Iso t o p es, At o mi c W ei g ht

http://atom.kaeri.re.kr/

 Look closer at one section

 W hic h is ot opes of c hlor ine ar e s t able? I n whic h per c ent ages ?

 Look closer at one section

 W hic h is ot opes of c hlor ine ar e s t able? I n whic h per c ent ages ?

𝑀𝑎 𝑠 𝑠 𝐶𝑙 =

Courtesy of Korea Atomic Energy Research Institute. Used with permission.

+

= 3 5 . 46 𝑎 𝑚𝑢

St able Iso t o p es, At o mi c W ei g ht

http://atom.kaeri.re.kr/

Li terat ure v al ue: 35 . 453 ± 0. 00 2 𝑎 𝑚𝑢

14

M o r e Feat ur es o f t he Nucli d e T able

http://atom.kaeri.re.kr/

Courtesy of K orea Atomic Energy Research Institute. Used with p ermiss ion.

 E xcess m ass

 Y ields ener get ic s and nuc lear r eac t ion inf or m at ion

 S tability

 Y ields half lif e and s pec if ic ac t iv it y inf or m at ion

 P ar ent nuclide s

 Y ields nuc lear r eac t ion m ec hanis m inf or m at ion

M o r e Feat ur es o f t he Nucli d e T able

http://atom.kaeri.re.kr/

 E xcess m ass

 Y ields ener get ic s and nuc lear r eac t ion inf or m at ion

 S tability

 Y ields half lif e and s pec if ic ac t iv it y inf or m at ion

 M ode of decay

 Y ields nuc lear r eac t ion

Courtesy of K ore a Atomic Energy Research Institute. U sed with p ermiss ion. m ec hanis m inf or m at ion

Next T hr ee T o p i cs

 W rit ing nuc lear reac t ions

 Q uant if y ing energet ic s of reac t ions

 P redic t ing radiat ion t y pe and energy

 F ission – S plitting atom s

T oday’ s focus

Nuclear R eact i o ns

– T h e r m a l e n e r g y is co lle ct e d f r o m kin e t ic e n e r g y ( r e co il e n e r g y) o f f issio n p r o d u ct s

 F usion – Com bin i n g atom s

– T h e r m a l e n e r g y is co lle ct e d f r o m m u lt ip le so u r ce s

18

Nuclear R eact i o n P r i nci p les

 CONS E R V E ( alm ost) E V E R Y T HING

 M as s ( num ber of nuc leons )

 Char ge

 E ner gy

 NO T nec es s ar ily pr ot ons and neut r ons

 E xam ple : T r itium decay 𝛼 + 2

𝟐𝟐 𝐻 → 𝟐𝟐 𝐻 𝑒 + ? ? ? 𝛽 ±

𝛾𝛾

Nuclear R eact i o n P r i nci p les ( β )

 CONS E R V E ( alm ost) E V E R Y T HING

 M as s ( num ber of nuc leons )

 Char ge

 E ner gy

 NO T nec es s ar ily pr ot ons and neut r ons

 E xam ple : T r itium decay

𝟐𝟐 𝐻 → 𝟐𝟐 𝐻 𝑒 + + 𝛽 − + 𝐸 𝑟𝑥 𝑛

 What is E rx n ? What else is m issing?

𝟐𝟐 𝐻 → 𝟐𝟐 𝐻 𝑒 + + 𝛽 − + 𝐸 𝑟𝑥 𝑛

 T otal E rx n : Look at dif fer en ce s in excess m ass

𝑄𝑄

= ∆ 𝑃 − ∆ 𝐷

Nuclear R eact i o n Ener g et i cs ( β )

 T he Q value gives this am oun t

 P ar ents ( P ) ar e all specie s on the left side

 Daugh te r s ( D ) ar e all on the r ight side

𝟐𝟐 𝐻 → 𝟐𝟐 𝐻 𝑒 + +

~0

+ 𝐸 𝑟𝑥 𝑛

Nuclear R eact i o n Ener g et i cs ( β )

http://atom.kaeri.re.kr/

𝑸

Courtesy of K orea Atomic Energy Research Institute. Used with p ermiss ion.

= ∆ 𝑃 − ∆ 𝐷 = 1 𝟒𝟒 . 𝟗𝟗 𝟐𝟐𝟎𝟎 − 1 𝟒𝟒 . 𝟗𝟗 𝟐𝟐1 = 𝟎𝟎 . 𝟎𝟎 1𝟗𝟗 𝑀 𝑒 𝑉 22

𝟐𝟐 𝐻 → 𝟐𝟐 𝐻 𝑒 + + 𝛽 − + 𝐸 𝑟𝑥 𝑛

 T otal E rx n : Look at dif fer en ce s in excess m ass

𝑸

= ∆ 𝑃 − ∆ 𝐷 = 1 𝟒𝟒 . 𝟗𝟗 𝟐𝟐𝟎𝟎 − 1 𝟒𝟒 . 𝟗𝟗 𝟐𝟐1 = 𝟎𝟎 . 𝟎𝟎 1𝟗𝟗 𝑀 𝑒 𝑉

Nuclear R eact i o n Ener g et i cs ( β )

 Not all ener g y goes to the beta par ticle

 A v er age bet a ener gy : 5. 7 ke V

 S om e, not all, goes t o t he daught er nuc lide' s r ec oil

 Wher e does the r est go?

3 𝐻 → 3 𝐻 𝑒 +

+ 𝛽 − +

0 𝝂

+ 𝐸 𝑟𝑥 𝑛

Nuclear R eact i o n Ener g et i cs ( β )

 An antine u tr in o car r ie s away the excess ener g y

 Char g e le ss, essentia ll y m assless par ticle s

 E xtr em ely har d to detect!

 How did we know of their existence ? M issi n g ener g y in the r eaction ba l a n ce !

 Neutr in o ( ν )

 C hargel es s , n e a r ly m a ssle ss p a r t icle

 A nti- neu tr in o ( ν � )

 A nti par ti c l e equi v al e nt of the neutr i no

C h e re n k o v ra d i a ti o n ri n g s p ro d u c e d b y

O t her T y p es o f Rad i at i o n

http://www-s k.icrr.u -t okyo.ac.jp/sk/gallery/wme/sk_01h -w m.jpg

http://www.ps.uci.edu/~tomba/sk/tscan/pictures.html

Courtesy of Kamioka Observatory, ICRR (Institute for Cosmic Ray Research), The University of Tokyo. Used with permission.

© Tomasz Barszczak. All rights reserved. This content is

Su p e r K am i o kan d e n e u tri n o d et ect o r , Jap an

excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

 S om etim es beta decay leave s the nucleu s in an

excited state

 T his ener g y can be lost thr ough gam m a em ission , br ing in g the nucle us to the gr oun d state

 E xam ple : Cobalt- 60

D enotes excited

state

𝟔𝟔𝟎𝟎 𝐶𝑜

→ 𝟔𝟔𝟎𝟎 ∗ 𝑁𝑖 + + 𝛽 − +

0 𝝂

Nuclear R eact i o n P r i nci p les ( γ )

𝟔𝟔𝟎𝟎 ∗ 𝑁𝑖 + →

𝟔𝟔𝟎𝟎 𝑁𝑖 + + γ

26

Nuclear R eact i o n P r i nci p les ( γ )

http://atom.kaeri.re.kr/

 How to deter m i n e gam m a ener g y levels?

 Use ener g y level diagr a m s

 Inter nal conver sio n ( IC)

 Excit e d st a t e kicks o u t a n in n e r -sh e l l e le ct r o n

 E xam ple : Cobalt- 6 0 m o st likely m echan ism

𝟔𝟔 𝟎𝟎 𝐶 𝑜 → 𝟔𝟔 𝟎𝟎 ∗ 𝑁𝑖 + + 𝛽 − +

0 𝝂 β

𝟔𝟔 𝟎𝟎 𝟗𝟗 . 𝟐𝟐1 𝑀 𝑒 𝑉 𝑁𝑖 + → 𝟔𝟔 𝟎𝟎 𝟗𝟗 . 1 𝟔𝟔 𝑀 𝑒 𝑉 𝑁𝑖 +𝟗𝟗 + 𝑒 − IC

Nuclear R eact i o n P r i nci p les ( γ )

𝟔𝟔 𝟎𝟎 𝟗𝟗 . 1 𝟔𝟔 𝑀 𝑒 𝑉 𝑁𝑖 +𝟗𝟗 →

𝟔𝟔 𝟎𝟎 1 . 𝟐𝟐𝟐𝟐 𝑀 𝑒 𝑉 𝑁𝑖 + 𝟗𝟗 →

𝟔𝟔 𝟎𝟎 1 . 𝟐𝟐𝟐𝟐 𝑀 𝑒 𝑉 𝑁𝑖 + 𝟗𝟗 + γ γ

𝟔𝟔 𝟎𝟎 𝑁𝑖 + 𝟗𝟗 + γ γ

29

 Resul ting radiation spectrum can be complex

 Example: Cesi um - 137

Nuclear R eacti on Princ iples ( γ )

Graph © Wiley-VCH, from J. Turner, Atoms, Radiation, and Radiation Protection (2007). All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Courtesy of Korea Atomic Energy Research Institute. Used with permission.

30

Nuclear R eact i o n P r i nci p les ( γ )

http://atom.kaeri.re.kr/

Courtesy of K orea Atomic Energy Research Institute. Used with p ermiss ion. 31

 Relative ly heavy isotope s can em it a heliu m nucleu s ( alpha par ticle)

 E xam ple : A m er icium - 241

𝟗𝟗𝟒𝟒 1 𝐴 𝑚 → 𝟗𝟗 𝟐𝟐𝟐𝟐 ∗ 𝑁𝑝 −𝟗𝟗 + α + 2

𝟗𝟗 𝟐𝟐𝟐𝟐 ∗ 𝑁𝑝 − 𝟗𝟗 →

𝟗𝟗 𝟐𝟐𝟐𝟐 𝑁𝑝 − 𝟗𝟗 + γ

Nuclear R eact i o n P r i nci p les ( α )

32

Nuclear R eact i o n P r i nci p les ( α )

http:// en.wikipedia.org/wiki/Americium

Use s o f Am e r iciu m :

© MD111 on Flickr. License CC B Y -S A. This content i s excluded from our Creative

Commo ns license. For more information, see http://ocw.mit.edu/help/faq -f air - u se/ . 33

Nuclear R eact i o n P r i nci p les ( α )

http://atom.kaeri.re.kr/

Ho w' s t h i s d e ca y ch a in ?

Courtesy of Korea Atomic Energy Research Institute. Used with permission. 34

H alf L i fe

 T im e it takes for half of an isotope to decay

 T he decay constant r elates this to an expon e ntia l for m of the sam e r ule

Image by MIT OpenCourseWare. 35

 Define an activity in ter m s of decays per second

𝑑 𝑁

𝐴 = −

𝑑 𝑡

= 𝜆𝑁 𝐴 = 𝐴 0 @ 𝑡 = 0

 S olve the or din a r y dif fer en tia l equatio n :

𝑑𝑁

𝑡 = 0

𝑁 = −𝜆 ∗ 𝑑 𝑡 ln 𝑁 = −𝜆 𝑡 + 𝑐 ln 𝑁 0 = 𝑐

ln 𝑁 = −𝜆 𝑡 + ln 𝑁 0

𝑁

𝑙𝑛

𝑁 0

= −𝜆 𝑡 𝑁 = 𝑁 0

𝑒 − 𝜆𝑡

H alf L i fe

 λ descr ibe s how quickly the num b er of atom s N

chang e s by a factor of e

𝑑 𝑁

𝐴 = − 𝑑 𝑡 = 𝜆𝑁 𝐴 = 𝐴 0 @ 𝑡 = 0

𝑁 = 𝑁 0

𝐴

𝑒 −𝜆𝑡

= 𝐴 0

𝑒 − 𝜆𝑡

Fi nd the hal f l i fe ( T ) :

𝑁

𝑁 0

= 1 = 𝑒 − 𝜆𝑇 ln 0. 5 = − 𝜆𝑇 𝑇

2

0. 693

=

𝜆

H alf L i fe

M easur i ng Act i vi t y

 A ctivity is m easur e d in B ecquer e l s ( Bq )

1 𝐵𝑞 = 1 𝐷𝑖 𝑠𝑖 𝑛𝑡 𝑒 𝑔𝑟 𝑎𝑡 𝑖𝑜 𝑛 𝑝 𝑒𝑟 𝑠 𝑒𝑐 𝑜𝑛 𝑑

 A m or e conveni e n t unit is the Cur ie ( Ci )

1 𝐶𝑖 = 3. 7 × 10 10 𝐵𝑞

 Y ou will often see r educe d un i ts ( m Ci, µCi) o n r eal devices and sour ces

 O n e Cu r ie is a l ot o f r a d ia t io n ! ! !

Act i vi t y o n So ur ces and De vi ces

en.wikipedia.org/wiki/Americium www. prc68.com/I/Rad_Det.shtml

© MD111 on Flickr. License CC B Y -SA . This content i s excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq -fa ir -us e/ .

Label photo courtesy of Brooke Clarke. Used with permission. 39

T hi nki ng Ahead fo r t he L ab

 How do you m easur e the activity of a sour ce?

 How do you accoun t for older sour ces?

 What else will m ake m easur i n g the activity of a sour ce dif ficult?

 I n o t h e r wo r d s, wh a t a r e p o ssib le so u r ce s o f e r r o r and/or c onfus i on?

40

41

MIT OpenCourseWare http://ocw.mit.edu

22. S902 Do-It-Yourself (DIY) Geiger Counters

January IAP 2015

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .