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Lecture 12 Radioactive Isotopes Decay Equations Half Lives Useful Radiotracers in Oceanography Secular Equilibrium E & H Chpt 5 Radioisotopes and decay Definitions and Units Parent – Original Radioactive Atom Daughter – The Product of Decay Decay Chain – A Series of Decays

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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


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)


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)


Becquerel (Bq) = 1 dps

Curie = 3.7 x 1010 Bq = Activity of 1 gram of 226Ra


Decay Equations

Decay is proportional to the # of atoms present (first order)

= AN


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




Decay Curve

Both N and A decrease exponentially


Half Life

The half life is defined as the time required for half of the

atoms initially present to decay.

After one half life:


=  t1/2

ln (2) =  t1/2

0.693 =  t1/2


Math note:

-ln(1/2) = - (ln 1 – ln 2)

= - ( 0 – ln 2)

= + ln2 = 0.693


Mean Life = Average Life of an Atom


= 1 / l

t = 1.44 t1/2

Q. Why is the mean life longer than the half life?


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



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



Example: 14C → 15N (stable)

t1/2 = 5730 years


Radioactive Parent (A)

Radioactive Daughter (B)

2-box model

A → B →






l B



mass balance for B


solution after assuming NB = 0 at t = 0


Three Limiting Cases

1) t1/2(A) > t1/2(B) or lA < lB one important case

2) t1/2(A) = t1/2(B) or lA = lB e.g. 226Ra → 222Rn

3) 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


Activity of daughter

equals activity of


Are concentrations also equal???


Secular equilibrium

t1/2 daughter = 0.8 hr

t1/2 parent = 




(log scale)

! Daughter grows

in with half life of

the daughter!


time (hr)



Grow in of 222Rn

from 226Ra

After 5 half lives

activity of daughter =

95% of activity of parent


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:


There is considerable exposure due to artificially produced sources!

Possibly largest contributor is tobacco which contains radioactive 210Po which emits 5.3 MeV aparticles with an half life of T1/2=138.4days.


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 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 = 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 166×1012 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).


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 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.