Definitions and types of decay Derivation of decay e quations Half l ives and mean lives Secular Equilibrium Useful radiotracers in oceanography E amp H Chpt 5 The chart of the nuclides decay ID: 534389
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Slide1
Lecture 6 Radioactive Isotopes
Definitions and types of decayDerivation of decay equationsHalf lives and mean livesSecular EquilibriumUseful radiotracers in oceanography
E & H
Chpt
5Slide2
The chart of the nuclides - decay
Q. 230Th90 How many protons / neutrons? Slide3
Full Chart of the Nuclides
1:1 lineValley of StabilityFor
230
Th N/P = 1.55Slide4
Radioisotopes and decay
Definitions and UnitsParent – Original radioactive atomDaughter – The product of decayDecay Chain – A series of sequential decays from one initial parentDecay is independent of chemistry and T and P.Decay is only a property of the nucleus (see Chart of Nuclides)
Types of Decay
D
P
D
N
D
Atomic
Wt.
Alpha
a
He2+ -2 -2 -4Beta b e- + 1 -1 0 (n → P+ + e-)Gamma g “packets of excess energy”
MeasurementsSlide5
The chart of the nuclides
– decay pathwaysX
b
decay
X
a
decaySlide6
Mathematical Formulation of Decay
Decay Activity (A) = decays per time (e.g. minutes (dpm) or second (dps))A = l
N
l
= decay constant (t
-1
)
N = # of atoms or concentration (atoms l
-1
)
Remember 1 mol = 6.02 x 10
23
atomsUnits:Becquerel (Bq) = 1 dps (the official SI unit)Curie (Ci) = 3.7 x 1010 Bq = Activity of 1 gram of 226RaNamed after Pierre CurieSee this link for the history:
http://www.orau.org/ptp/articlesstories/
thecurie.htmSlide7
Decay
Equations (essential math lessons)Decay is proportional to the # of atoms present (first order)dN/dt = - N = ANwhereN = the number of atoms of the radioactive substance present at time t = the first order decay constant (time-1)
The number of parent atoms at any time t can be calculated as follows.
The decay equation can be rearranged and integrated over a time interval.
where
N
o
is the number of parent atoms present at time zero. Integration leads to
or
orSlide8
Decay Curve
Both N and A decrease exponentiallySlide9
Half Life
The half life is defined as the time required for half of the atoms initially present to decay. After one half life: From the decay equation = t1/2 ln (2) = t1/2 0.693 = t1/2so
Math note:
-ln(1/2) = - (ln 1 – ln 2)
= - ( 0 – ln 2)
= + ln2 = 0.693Slide10
Mean Life = Average Life of an Atom
t
= 1 /
l
= (1/0.693)
t
1/2
t
= 1.44
t
1/2
Q. Why is the mean life longer than the half life?Slide11
Isotopes used
in Oceanographysteady state transient
U-Th series are shown on the next
page. These tracers have a range
of chemistries and half lives.
Very useful for applications in
oceanography.Slide12
Two forms of Helium3He2 from beta decay of 3H
1 (called tritium) and primordial from the mantle3H1 = 3He2 + b4He2 the product of alpha decay from many elements (especially in U-Th series)How would you expect their distributions to vary in the ocean?Slide13
Example distributions of 3He
from mid-ocean ridge crestJohn Lupton (NOAA) et al (various)Slide14
Q.
Why is the inside of the earth hot?Q. What is the age of the earth? 6000 years or 4.5 x 109 yearsSlide15
238
U decay products in the oceanQ. What controls the concentration of 238U in SW?109 y24 d105
y
10
4
y
1600 y
3 d
22 y
U – conservative
Th
– particle reactive
Ra – intermediate (like Ca)
Rn = conservativePb – particle reactiveSlide16
Parent-Daughter Relationships
Radioactive Parent (A)Stable Daughter (B)A → B e.g. 14C → 15N (stable)Production of Daughter = Decay of Parent
A
B
l
A
2-box model
Example:
14
C →
15
N (stable)
t
1
/2
= 5730
years
l
= 0.693 / t
1/2Slide17
Radioactive Parent (A)
Radioactive Daughter (B)A → B → lA
l
B
source
sink
A
B
l
A
l
B
solution after assuming N
B
= 0 at t = 0
2-box model
mass balance for B
solution:Slide18
Three Limiting Cases
1) t1/2(A) > t1/2(B) or lA < lB one important example:2) t
1/2
(A) =
t
1/2
(B) or
l
A
=
l
B
e.g. 226Ra → 222Rn3) t1/2(A) < t1/2(B) or lA > lB 1600yrs 3.8 days
Case #1: long half life of parent = small decay constant of parent
SECULAR EQUILIBRIUM
Activity of daughter
equals activity of
parent!
Are concentrations also equal???Slide19
Q.
Are concentrations also equal???
Example:
226
Ra and
222
RnSlide20
Secular
equilibrium (hypothetical)t1/2 daughter = 0.8 hrt1/2 parent = time (hr)
Activity
(log scale)
daughter
t
1/2
Parent
d
oesn’t change
★
!
Daughter grows
in with half life of
the daughter!
Total
Activity
(
parent+daughter
)
★
Activity
of parent
and daughter
equal at
secular equilibriumSlide21
Grow in of
222Rnfrom 226RaExample:
After 5 half lives
activity of daughter =
95% of activity of parent
Another way to plotSlide22
Example: Rate of grow in
Assume we have a really big wind storm over the ocean so that all the inert gas 222Rn is stripped out of the surface ocean by gas exchange. The activity of the parent of 222Rn, 226Ra, is not affected by the wind. Then the wind stops and 222Rn starts to increase (grows in) due to decay.Q. How many half lives will it take for the activity of 222Rn to equal 50% (and then 95%)of the 226Ra present?Answer: Use the following equation to calculate the activity A at time tSlide23
Radon is a health hazzard!Radon source strength from rocksWhy are some zones high (red)?Slide24
There is considerable exposure due to artificially produced sources!
Possibly largest contributor is tobacco which contains radioactive
210
Po which emits 5.3 MeV
a
particles with an half life of T
1/2
=138.4days.Slide25
Was Litvinenko (a former Russian spy) killed by
210Po?? A case study of 210PoToxicity of Polonium 210Weight-for-weight, polonium's toxicity is around 106 times greater than hydrogen cyanide (50 ng for Po-210 vs 50 mg for hydrogen cyanide). The main hazard is its intense radioactivity (as an alpha emitter), which makes it very difficult to handle safely - one gram of Po will self-heat to a temperature of around 500°C. It is also chemically toxic (with poisoning effects analogous with tellurium). Even in microgram amounts, handling 210Po is extremely dangerous, requiring specialized equipment and strict handling procedures. Alpha particles emitted by polonium will damage organic tissue easily if polonium is ingested, inhaled, or absorbed (though they do not penetrate the epidermis and hence are not hazardous if the polonium is outside the body).Acute effectsThe lethal dose (LD50) for acute radiation exposure is generally about 4.5 Sv. (Sv = Sievertwhich is a unit of dose equivalent). The committed effective dose equivalent
210
Po
is 0.51 µSv/Bq if ingested, and 2.5 µSv/Bq if inhaled. Since
210
Po has an activity of
166 TBq per gram (1 gram produces 166×10
12
decays per second),
a fatal 4-Sv dose can be caused by ingesting 8.8 MBq (238 microcurie),
about 50 nanograms (ng), or inhaling 1.8 MBq (48 microcurie), about 10 ng.
One gram of
210Po could thus in theory poison 100 million people of which 50 million would die (LD50).Slide26
Body burden limit
The maximum allowable body burden for ingested polonium is only 1,100 Bq (0.03 microcurie), which is equivalent to a particle weighing only 6.8 picograms. The maximum permissible concentration for airborne soluble polonium compounds is about 10 Bq/m3 (2.7 × 10-10 µCi/cm3). The biological half-life of polonium in humans is 30 to 50 days. The target organs for polonium in humans are the spleen and liver. As the spleen (150 g) and the liver (1.3 to 3 kg) are much smaller than the rest of the body, if the polonium is concentrated in these vital organs, it is a greater threat to life than the dose which would be suffered (on average) by the whole body if it were spread evenly throughout the body, in the same way as cesium or tritium.Notably, the murder of Alexander Litvinenko in 2006 was announced as due to 210Po poisoning. Generally, 210Po is most lethal when it is ingested. Litvinenko was probably the first person ever to die of the acute α-radiation effects of 210Po , although Irene Joliot-Curie was actually the first person ever to die from the radiation effects of polonium (due to a single intake) in the late 1950s. It is reasonable to assume that many people have died as a result of lung cancer caused by the alpha emission of polonium present in their lungs, either as a radon daughter or from tobacco smoke.