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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
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!
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)