Lecture 12 Radioactive Isotopes

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Lecture 12 Radioactive Isotopes
Decay Equations Half Lives Useful Radiotracers in
Oceanography Secular Equilibrium
E H Chpt 5
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Radioisotopes and decay Definitions and
Units Parent Original Radioactive Atom Daughter
The Product of Decay Decay Chain A Series of
Decays
Types of Decay DP DN DAtomic
Wt. Alpha a He2 -2 -2
-4 Beta b e- 1 -1 0 (n
? P e-) Gamma g excess energy
Decay is independent of chemistry and T and
P. Decay is only a property of the nucleus (see
Chart of Nuclides)
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The chart of the nuclides - decay
b decay
X
X
a decay
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Mathematical Formulation of Decay
Decay Activity (A) decays per time (dpm or dps)
A l N l decay constant (t-1)
N of atoms or concentration (atoms
l-1) Units Becquerel (Bq) 1 dps Curie 3.7
x 1010 Bq Activity of 1 gram of 226Ra
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Decay Equations Decay is proportional to the of
atoms present (first order)
AN where N 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 No is the number of parent
atoms present at time zero. Integration leads
to or
or
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Decay Curve
Both N and A decrease exponentially
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Half Life The half life is defined as the time
required for half of the atoms initially present
to decay. After one half life Thus
? t1/2 ln (2) ? t1/2 0.693
? t1/2 so
Math note -ln(1/2) - (ln 1 ln 2)
- ( 0 ln 2) ln2 0.693
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Mean Life Average Life of an Atom
t
1 / l
t 1.44 t1/2
Q. Why is the mean life longer than the half life?
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Isotopes used in Oceanography
steady 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.
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238U decay products in the ocean
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Parent-Daughter Relationships
Radioactive Parent (A) Stable Daughter (B) A ? B
e.g. 14C ? 15N (stable)
Production of Daughter Decay of Parent
2-box model
l A
A
B
Example 14C ? 15N (stable) t1/2
5730 years
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Radioactive Parent (A) Radioactive Daughter (B)
2-box model
A ? B ?
lA
lB
A
B
l A
l B
source
sink
mass balance for B
solution
solution after assuming NB 0 at t 0
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Three Limiting Cases
1) t1/2(A) gt t1/2(B) or lA lt lB one
important case 2) t1/2(A) t1/2(B) or lA lB
e.g. 226Ra ? 222Rn 3)
t1/2(A) lt t1/2(B) or lA gt 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???
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Secular equilibrium t1/2 daughter 0.8 hr t1/2
parent ?
parent
daughter
Activity (log scale)
! Daughter grows in with half life of the
daughter!
time (hr)
t1/2
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Example
Grow in of 222Rn from 226Ra
After 5 half lives activity of daughter 95
of activity of parent
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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. 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
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There is considerable exposure due to
artificially produced sources!
Possibly largest contributor is tobacco which
contains radioactive 210Po which emits 5.3 MeV a
particles with an half life of T1/2138.4days.
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Was Litvinenko (a former Russian spy) killed by
210Po?? A case study of 210Po Toxicity of
Polonium 210 Weight-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 500C. 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 Sievert which is a unit of dose
equivalent). The committed effective dose
equivalent 210Po is 0.51 µSv/Bq if ingested, and
2.5 µSv/Bq if inhaled. Since 210Po has an
activity of 166 TBq per gram (1 gram produces
1661012 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).
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Body burden limitThe 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 a-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.