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 ( )

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 > 10 9 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) 14 C (from 14 N(n,p) 14 C), 7 Be, 26 Al – Primordial (i.e. very old) Single nuclei (e.g., 40 K) Decay chains ( 232 Th, 235 U, 238 U/ 226 Ra)

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., 235 U/ 238 U) also used to estimate earth age..

Laws of radioactive decay defined: A(t) =A o 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 (T 1/2 1 >> T 1/2 2 ) then A 2 ≈A 1 and

Secular Equilibrium… If there is a ‘long’ decay half-life beginning a radioactive decay chain (e.g., 238 U), 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 238 U decay chain can be used to estimate amount of 238 U 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. 238 U 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 206 Pb to 238 U ratios (assumes secular equilibrium) where is ln2 /T 1/2 and T 1/2 is the decay half-life of 238 U (~4.5x10 9 years). which solves to (can do the same for 235 U : 207 Pb 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. 238 U 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 40 K (in bones!)

Can also use other (primordial) isotope ratios… 40 K decay to 40 Ar. –T 1/2 for 40 K is 1.2x10 9 years. –Taking mass ratios using mass spectrographs in rock inclusions, can date the rock using the equation: –The factor is due to the ‘branching ratio’ in the decay of 40 K, i.e., only 10.9% of the time does it decay to 40 Ar (see later). 87 Rb - 87 Sr. 147 Sm Nd (alpha decay)

‘signature’ 1461 keV gamma Interesting aside: 40 K decays by all three forms of ‘beta’ decay,  + and electron capture (ec) to 40 Ar; &  - to 40 Ca. Signature of decay of 40 K 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) p ‘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 GSI (105 germanium detectors)

Note, also other radioactivities might be present which don’t emit signature gamma rays. Examples are: 14 C from cosmic ray interactions & 90 Sr fission reside from weapons 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) 226 Ra 232 Th 40 K This leads to calculation of effective annual doses from NORM (in mSv/year) = D assuming an outdoor occupancy of 20%.

Other useful calculated properties? 1) Radium equivalent activity, Ra eq : On assumption that 370 Bq/kg of 226 Ra (max permissable Ra eq ) or 259 Bq/kg of 232 Th or 4810 Bq/kg of 40 K produce the same gamma-ray dose. 2) External Hazard Index (H ex ): Hex should be <1 for an ‘insignificant radiation hazard).

Summary Very old NORMs such as 238 U, 232 Th, 40 K 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 x10 9 years).