RadioactivityRadioactive (unstable) nuclei are generally believed to be man made, however many unstable isotopes are produced in large quantities by “natural” occurring processes.

The decay always follows the same pattern described by radioactive decay law

Radioactive Decay Laws

dNdt

N

dNN

dt

N t N t e t

= − ⋅

= − ⋅

= ⋅ − ⋅

λ

λ

λ( ) ( )0

λ: decay constant

N: number of radio-isotopes

N(t0)=N0: initial number of radio-isotopes

Radioactive substance

Half-Life of Radio-Isotope

N t N e t( ) = ⋅ − ⋅0

λtime (days) 131I (%)0 100.00001 91.74112 84.16423 77.21324 70.83625 64.98596 59.61887 54.69498 50.17779 46.033510 42.231715 27.444620 17.835125 11.590330 7.532140 3.180950 1.343460 0.567370 0.239680 0.101290 0.0427

100 0.0180

decay curve

0

20

40

60

80

100

0 10 20 30 40 50

time [days]

N(t)

[%

]

T1/2

131IT1/2= 8.04 d

Half-Life & Decay Constant

N T N N e

T

TT

T( )

ln

ln ln

12

0 0

12

12

12

122

2 2

12= = ⋅

= ⋅

= =

− ⋅λ

λ

λλ

The decay constant λis inverse proportional

to the half-life T1/2

Half-life of a radioactivesubstance determines a

time-scale clock

Radioactive Clocks

dating isotopes

0

20

40

60

80

100

0 10000 20000 30000 40000

time [years]

activ

ity

[%]

226Ra14CT1/2(14C)=5730 y

T1/2(226Ra)=1600 y

Example: If your 22920 yearold sample (4 half-lives) originally had 1000 14C isotopes, how many 14C isotopes are left today?

[ ]N y e

y yN y

y( [ ])

ln [ ] .( [ ])

[ ]22920 1000

2 5730 121 1022920 62

22920

4 1

= ⋅

= = ⋅

=

− ⋅

− −

λ

λ

Units for scaling the decay

[ ] ⎥⎦⎤

⎢⎣⎡⋅==

sdecays

dtdNCi 10107.31Classical Unit: 1 Curie [Ci]

[ ] ⎥⎦⎤

⎢⎣⎡==

sdecay

dtdNBq 11Modern Unit: 1 Becquerel [Bq]

The so-called dosimetry units (rad, rem) determine the amount of damage radioactive radiation can do to the human body. They depend on the kind and nature of the incident radiation

(X-rays, γ-rays, α-particles, β-particle, or neutrons).It also depends on the energy loss of the particular radiation and the associated ionisation effects in the human body material.

Units for measuring the impact

Dose: DEm

=Amount of energy E deposited by radiation into body part of mass m. unit Rad or Gray

Equivalent Dose:Radiation independent doseQ is normalization factorUnit Rem or Sievert

Photons: Q=1Neutrons: E<10keV Q=5Neutrons: E>10keV Q=15Protons: Q=5Alphas : Q=20

DQH ⋅=http://en.wikipedia.org/wiki/Dosimetry

Internal γ GlowingOn average, 0.27% of the mass of the human body is potassium K of which 0.021% is radioactive 40K

with a half-life of T1/2=1.25·109 [y]. Each decay releases an average of Eavg= 0.5 MeV β- and γ-radiation,

which is mostly absorbed by the body but a small fraction escapes the body.

Calculate, how many radioactive 40K atoms are in your body system!

Example: 40K in your body

[ ] [ ]

[ ]

[ ]particlesNkg

mN

gparticlesmN

Nparticlesm

gmm

atomsKg

m.m.m

m.mm

K

bodyK

body

K

Kbody

bodyK

bodyKK

bodyK

body

20

15

7237

2340

740

1083.6 :body 80for

gramm. in massbody theneed you, calculate to

/1054.8

401067.510023.6

1067.5

10023.6of 40

10675000210 :body theinK e radioactiv of mass

00270 :body thein K potassium of mass :body theof mass

40

40

40

4040

40

⋅=

⋅=

=⋅⋅⋅⋅

≡⋅⋅=

⋅≡

⋅⋅=⋅=∗

⋅=∗

∗

−−

−

Calculate the absorbed body dose over an average human lifetime of t = 70 y for this source of internal exposure.

[ ]

∗ = = ⋅ ⋅

∗ = ⋅ = ⋅

= ⋅⋅

⋅ ⋅ ⋅ ⋅

= ⋅ = ⋅ = ⋅

= ⋅

−

− −

−

Dose DEm

t A KEm

Activity A K N T N

D y g mMeV

m

D MeV kg J kg Gy

with eV J

absorbed

body

avg

body

K K

bodybody

: ( )

: ( ) ln

[ ]ln

( . [ ] ). [ ]

. . [ / ] . [ ]

: [ ] . [ ]

40

401 2

15 1

10 2 2

19

40 402

702

4 88 1005

9 47 10 15 10 15 10

1 1602 10

λ

1.25 10 [y]9 8.54

[ ] [ ] [ ]

[ ] [ ]JeVwith

GykgJkgMeVD

19

2211

10602.11:

1063.2/1063.2/1066.1

−

−−

⋅=

⋅=⋅=⋅=

Exposure to other natural or man-made radioactivity

Tobacco contains a-emitter 210Po with T1/2=138.4 days. Through absorption in bronchial system smoking adds 280 mrem/year to the annual dose of US population

Sources of Natural Radioactivity

Spectrum of CR

Cosmic Rays origin from:• solar flares;• distant supernovae;

Cosmic Ray Bombardment

Low energy CR

High energy CR

14C Enrichment in Environment14C is produced by interaction of cosmic rays with 14N in theatmosphere. Fall out of 14C and implementation into bio-materialby photosynthesis. Decay countingmay start after bio-material is dead.

Convection establishes a Convection establishes a homogeneous distribution homogeneous distribution of of 1414C in the atmosphere!C in the atmosphere!

Some Reminder?

[ ]

[ ]

The piece of carbon has a mass of M 25 g. This translates into the number of carbon atoms:12

=

= ⋅ =

=⋅

⋅

C

N( CN nuclei mole

A g moleM

. [nuclei mole]g mole

g

A12

236 022 1012

25

)[ ]

[ ]

1 mole of material has a mass of A [g]!e.g. 1 mole 12C ≡ 12 g; 1 mole 56Fe ≡ 56 g;1 mole 197Au ≡ 197g; 1 mole of 208Pb ≡ 208 g1 mole AlO3 ≡ 27 g + 3·16 g = 75 g

1 mole of any kind of material contains NA= 6.022·1023 particles (Avogadro’s number)

N(12C) = 1.25 ·1024 atoms

You find in the ruins of a lost city - in acold forgotten fireplace - a 25g piece of charcoal. How much carbon is in there?

14C-Dating, how old is the piece of charcoal?

[ ] [ ] [ ]

[ ]

λ

λ

λλ

= =⋅ ⋅

= ⋅

= ⋅

⇒ = ⋅ ⋅ ⋅ = ⋅

= ⋅ =

= ⋅ ⇒ = =⋅

− −

−

− ⋅− −

ln ..

.

) . [ ];) . . . [ ]

) min]

( )ln

( ) ln

.;

2 0 6935730 315 10

384 10

125 10125 10 13 10 163 10

370

370250

384 10

1 27

12 1

12 24

14 12 14 24 12 12

014

0

0

12 1

T y s ys

N( C atomsC C N( C atoms

A N( C [decays

A t A e t

AA t

stt

number of C atoms in wood: if has been constant

initial activity:

12

= 3250[ ]y

You analyze some weak activity of A(t)=dN/dt=250 decays/min, this gives you the clue for determining its age.The atmospheric ratio is:

14

121213 10

CC

= ⋅ −.

Sources of Natural Terrestrial MaterialNatural alpha decay chains from long-lived heavy radioisotopes• Uranium Series: 238U 206Pb +8a• Actinium Series: 235U 207Pb +7a• Thorium Series: 232Th 208Pb +6a• Neptunium Series: 241Pu 209Pb +8a

There are several long-lived a-emittersin the chain: 234U230Th, 226Ra!

Natural Radioactivity in the US

Long lived 40K Radioactivity40K has a half-life of T1/2=1.28·109 yearsits natural abundance is 0.0118 % 40K

40Ar 40Ca

β+ β-

γ

40Ar40K

Potassium-Argon dating method

Radiation Effects of Nuclear Bomb TestsBeside shock, blast, and heat a nuclear bomb generates high intensity flux of radiation in form of γ-rays, x-rays, and neutrons as well as large abundances of short and long-lived radioactive nuclei which contaminate the entire area of the explosion and is distributed by atmospheric winds worldwide.

T1/2=5730y

Effective half-life ~5-10 y(photosynthesis)

131I Fallout from Nevada Tests

Summary

Natural (and also anthropogenic) radioactivity provides a unique tool;

• characteristic decay patterns allow to analyze the content of the material

• characteristic decay times allow to introduceradioactive clocks for dating the material