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How do We Age the Earth?
or
‘Measurement of Environmental
Radioactivity’
Paddy Regan
Dept. of Physics, University of Surrey, Guildford,
UK
&
Radioactivity Group, National Physical Laboratory,
Teddington
• Scientific methods for estimating the age of the
earth? (Literature surveys and radiometric dating).
• Which isotopes and how you do it ?
• What is NORM…where does it come from ?
• How do measure NORMs ?
• Why do you want to measure it ?
• An example (Map of Qatar)
Nuclear and Atomic Physics Module, MSc in Radiation
and Environmental Protection, University of Surrey
Tutorial Question (2012)
(equation to work this out given later…..)
…ageing the earth using the available literature…
Famous example is Archbishop Ussher,
Annals of the Old Testament, Deduced From the First Origins of the World
Bishop James Ussher (1581-1656)
Others also tried
similar methods to
age the Earth,
including Isaac
Newton and
Johannes Kepler.
…new information / discoveries… a Chronology of Chronologies…
• Comte de Buffon (1779) - Believes earth is slowly cooling, from the rate compared to
a small globe, estimated ~75,000 years.
• James Hutton (1795) - ‘The Theory of the Earth (1795)’ Geological evolution of the
earth’s crust, rock strata formed in layers?
• Lord Kelvin aka William Thompson (1862) - Earth had formed between 20 and 40
million years, estimated from time to cool and heat assuming heat generated by
gravitational contraction and scientific estimates of earth’s heat conduction (2 nd law of
thermodynamics etc.)
• Rutherford and Soddy (1903) - Explanation of radioactivity of Uranium (U); earth’s
internal heat could come from radioactivity. Half-lives for decays could be billions of
years. Rutherford suggests use of helium (alpha particles) in rocks to age them.
• Boltwood (1907) - ratios of U to Lead to get age of rocks > 109 years.
e.g. L. Badash, ‘The Age of the Earth Debate’ Scientific American, August 1989 p
90ff
What is NORM?
• Naturally Occurring Radioactive Materials
• Two main sub-groups…
– Cosmogenic (from cosmic ray interactions)
• 14C (from 14N(n,p)14C), 7Be, 26Al
– Primordial (i.e. very old)
• Single nuclei (e.g., 40K)
• Decay chains (232Th, 235U, 238U/226Ra)
Natural decay
‘chains’.
Sequences of and
decaying radioisotopes
from Uranium (Z=92) or
Thorium (Z=90)
to Lead (Z=82).
On earth since formed.
Isotope ratios
(e.g., 235U/238U) also used
to estimate earth age..
Laws of radioactive decay defined: A(t) =Ao exp (-t)
A(t) = number of decays per unit time at time t =‘activity’
What if the ‘daughter’ nucleus is also
radioactive?
..if 2 >> 1 (T1/21 >> T1/2
2) then A2≈A1
and
Secular Equilibrium…
If there is a ‘long’ decay half-life beginning a radioactive
decay chain (e.g., 238U), the activity or
(number of atoms which decay per second) of all of the
successive daughter decays tends to the activity of the
long-lived parent.
i.e. measuring the
Activity, A(t), of any
member of the 238U
decay chain can be
used to estimate
amount of 238U present
in the sample from
A=N:
We can measure A(t) &
know , therefore we
can estimate N, number
of atoms present.
•Radiation occurs in nature…the earth is ‘bathed’ in radiation from a variety of sources.
•Humans have evolved with these levels of radiation in the environment.
Naturally Occurring Radioactive Materials
These include Uranium-238, which has radioactive half-life of 4.47 billion years.
238U decays via a series of alpha and beta decays (some of which also emit gamma rays). These create radionuclides including:
• Radium-226• Radon-222• Polonium-210
Calculation of age of rocks from 206Pb to 238U ratios
(assumes secular equilibrium)
where is ln2 /T1/2 and
T1/2 is the decay half-life
of 238U (~4.5x109 years).which solves to
(can do the same for 235U : 207Pb ratios in the same
samples…)
•Radiation occurs in nature…the earth is ‘bathed’ in radiation from a variety of sources.
•Humans have evolved with these levels of radiation in the environment.
Naturally Occurring Radioactive Materials
These include Uranium-238, which has radioactive half-life of 4.47 billion years.
238U decays via a series of alpha and beta decays (some of which also emit gamma rays). These create radionuclides including:
• Radium-226• Radon-222• Polonium-210
(all of which are emitters).
Other NORM includes 40K (in bones!)
Can also use other (primordial) isotope ratios…• 40K decay to 40Ar.
– T1/2 for 40K is 1.2x109 years.
– Taking mass ratios using mass spectrographs in rock inclusions, can date the rock
using the equation:
– The factor 0.109 is due to the ‘branching ratio’ in the decay of 40K, i.e., only 10.9% of
the time does it decay to 40Ar (see later).
• 87Rb - 87Sr.
• 147Sm -143Nd (alpha decay)
‘signature’
1461 keV
gamma
Interesting aside: 40K decays by all three forms of
‘beta’ decay, + and electron capture (ec) to 40Ar; & - to 40Ca.
Signature of decay of 40K is the 1461 keV gamma ray.
Why are primordial nuclei
so long lived?
The alpha particle quantum mechanically ‘tunnels’
through a ‘Coulomb energy barrier’ to escape the
mother nucleus. The width of this energy barrier
depends on the energy released in alpha decay (Q≈
E).
The relationship between Q and tunnelling
probability and hence the decay lifetime is the
Geiger-Nuttall rule.
See H. Geiger & J.M.Nuttall Philosophical Mag. 22
(1911) p613-621. ‘The ranges of a particles from
various radiaoctive substances and a relation
between range and period of transformation’
How (and why) do you
measure the gamma rays from
NORMs?
Nuclear Data Evaluations:
RISING array @ GSI
(105 germanium detectors)
Note, also otherradioactivities might be presentwhich don’t emitsignaturegamma rays.
Examples are:
14C from cosmic ray interactions &
90Sr fission reside fromweapons tests / fission fallout.
Gamma-ray spectra show clearly the levels and nature of the Naturally Occurring Radioactive Material (NORM) in, for example, beach sand.
D.Malain, PhD thesis, University of Surrey (2011)
‘background (2 days) ‘sand sample (2 days)
Making a Radiological Map of
Qatar• Arabic Gulf state,
• Oil Rich (oil industry all around)
• To host World Cup (2022)
How do we use the Activity Concentration measurements?
The gamma dose rate (D) in units of nGy/hour in the
outdoor air can be estimated using dose conversion coeffs…
A = measured specific activity concentration (Bq/kg)
Gy = unit of radiation dose = 1 Joule / kg (1 Sv = Wr x
1Gy)
226Ra 232Th 40K
This leads to calculation of effective annual doses from
NORM (in mSv/year) = 0.00123D assuming an outdoor
occupancy of 20%.
Other useful calculated properties?
1) Radium equivalent activity, Raeq:
On assumption that 370 Bq/kg of 226Ra (max permissable Raeq)
or 259 Bq/kg of 232Th
or 4810 Bq/kg of 40K produce the same gamma-ray dose.
2) External Hazard Index (Hex):
Hex should be <1 for an
‘insignificant radiation hazard).
Summary
• Very old NORMs such as 238U, 232Th, 40K are everywhere.
• Do they cause additional biological harm?
• Need to measure the levels and types of radiation / nuclei
present to make a scientific assessment of this.
• Provision of measurement of background levels is also
important regarding non-proliferation and remediation
following nuclear power decommissioning / nuclear accidents.
• Useful in ageing the earth (to around 4.5 x109 years).
