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

p.regan@surrey.ac.uk

• 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).