Welcome to 12.748 Lecture 1

• Logistics and organizational • Course Objectives and Layout – What you can expect, and what is expected of you – Resources • Introduction to nuclear structure, isotopes, radioactivity, and dating

Welcome to 12.748 Welcome to 12.748 Logistics Resources • Material: • Tuesday Clark 331 – Reading lists (journal articles & texts) – 14:30-16:00 – Verbal Lectures • Thursday Clark 331 – Slides presented (on web)* – 14:30-16:00 – Lecture notes provided (on web)* You are responsible for all material

* http://www.whoi.edu/sbl/liteSite.do?litesiteid=3055 All in PDF format (slides in 3 X 2 for annotation)

Welcome to 12.748 Welcome to 12.748 Grading Lecture 1

• 100% for 3 Assessed Exercises – Handed out on Sept. 21, Oct. 5, and Oct 19 • Logistics and organisational – Due 1 week after handed out • Course Objectives and Layout – Late policy: 25% of grade deducted per day – What you can expect, and what is expected of late (unless documented legitimate reason) you – Resources • Introduction to isotopes, radioactivity, and dating

1 Welcome to 12.748 Welcome to 12.748 Objectives Course Structure 12 Lectures over 7 weeks To build a strong, intuitive, and quantitative understanding of the isotopes as tools for • Origins of elements, sun, earth, oceans (3) understanding earth and ocean processes • Isotope chemistry and physics (3) • You’ll learn • Measurement techniques (2) – The underlying physical-chemical principles • Four case studies (early earth history): – Stable, radioactive, and radiogenic isotopes 1. Early history of the earth – Devise, construct, and solve geochemical mass 2. U-Series Isotope Dating balances 3. The sedimentary record: Sr and S isotopes – Understand and use isotope systems as tools 4. Cosmogenic Isotopes

Welcome to 12.748 Lecture 1 Lecture 1

1. What is an isotope? • Logistics and organisational • Course Objectives and Layout 2. Cosmic abundance of the – What you can expect, and what is expected of elements you – Resources 3. Isotope Stability • Introduction to isotopes, nuclear stability, 4. Radioactive Decay radioactivity, and dating 5. Radioactive dating techniques

Step 0: May the Force be with you Two Key Underlying Concepts Four fundamental forces of nature The 2 most significant advances in modern 1. Strong nuclear (short range, between physics nucleons) Strength = 1 2. Electromagnetic (infinite, but shielded) 1. relativity E = mc2 Strength = 10-2 (fine structure constant) • Matter = energy = gravity 3. Weak nuclear force (very short range, •1 g matter Æ 1014 J ~ 2 x 1013 cal -13 beta decay) Strength = 10 2. quantum mechanics 4. Gravity (infinite range, cannot be shielded • Wave/particle duality -39 against) Strength = 10 • uncertainty principle and complementarity • Quantization and spin

2 • Atoms consist of: Isotopes Isotopes – Electrons in orbit • Define chemical state (ionization, bonding) Most* elements have a number of stable isotopes: • Number/distribution defined by: – Hydrogen has 2 – Nuclear charge (charge balance) • 1H has 1 proton, 0 neutrons (most abundant) – Shell structure • 2H has 1 proton, 1 neutron – Nucleus – Oxygen has 3 • Protons (charged) • 16O has 8 protons, 8 neutrons (most abundant) – Define the element (chemistry) • 17O has 8 protons, 9 neutrons (most rare) – P = e for neutral atom • 18O has 8 protons, 10 neutrons (2nd most abundant) • Neutrons (neutral) – Add stability and mass – Fluorine has only 1 19 •N ~ P • F (9 protons, 10 neutrons) – Tin has 10 (all with 50 protons, 71-82 neutrons)

*Technetium has no stable isotopes, 98Tc ~ 4.2 Ma

12.748 Cosmic abundance of the elements Lecture 1 • Obtained from: – solar spectra 1. What is an isotope? – stellar/galactic 2. Cosmic abundance of the spectra elements – meteorite samples 3. Isotope Stability – cosmic dust 4. Radioactive Decay 5. Radioactive dating techniques

Cosmic abundance of the elements Cosmic abundance of the elements

• Note Log Scale and Range Why??? • General •Ans: decrease with – nuclear stability mass – nucleosynthesis • Bulge at Fe • big bang • Dip at B, Be • galactic and stellar evolution • ZigZag Pattern • Bulge at Pb

3 12.748 Isotopes Lecture 1 • Nuclear “stability” governed by 1. What is an isotope? – Quantum mechanical rules 2. Cosmic abundance of the – Nuclear forces elements – Electrostatic charge 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques

Isotopes Controlling factors on nuclear stability • Nuclear “stability” governed by • Number nucleons – the more the merrier – Quantum mechanical rules • spin pairing – Nuclear forces – favours even #s – Electrostatic charge – also the abundance of stable isotopes • Different elements have varying numbers of stable isotopes # p # n # n+p #stable • When a nucleus is “unstable” it decays ======– The more unstable, the quicker it decays Even Even Even 156 • Rates vary from 10-10 seconds to 1012 years Also means spin pairing distinguishes Even Odd Odd 50 between n & p Odd Even Odd 48 Odd Odd Even 5

Controlling factors on nuclear stability Controlling factors on nuclear stability • Number nucleons – the more the merrier • spin pairing – favours even #s

• shell structure – “magic numbers” – like atomic shells – popular #s of n or p 2, 8, 14, 20, 28,… Elements with magic “Z” have – 208Pb is “doubly many more isotopes than neighbors magic”: Pb @ end of Not as pronounced as atomic shell structures decay chains (more forces & issues at work here…)

4 Controlling factors on nuclear stability Controlling factors on nuclear stability • Number nucleons • Number nucleons – the more the merrier – the more the merrier • spin pairing • spin pairing – favours even #s – favours even #s

• shell structure • shell structure – “magic numbers” – “magic numbers” • surface tension • surface tension – like liquid drop – like liquid drop Hence tail-down at low mass • coulomb repulsion Hence tail-down at high mass (high surface area to volume ratio) … and drift to high-n nuclei – limits ultimate size

12.748 Modes of Radioactive Decay Lecture 1 • Alpha – done by heavy nuclei (e.g., 232Th, 238U, 235U) – involves strong nuclear force 1. What is an isotope? – emission of 4He nucleus (a doubly magic nucleus) • ∆ A = 4, ∆ N = 2, ∆ Z = 2 – half-life inversely related to energy: 2. Cosmic abundance of the •1024 change in T for 3-fold change in energy • quantum-mechanical tunnelling elements – mono-energetic (QM) – range ~ 10s of microns 3. Isotope Stability – (charged particle) 4. Radioactive Decay 5. Radioactive dating techniques

Alpha Decay Modes of Radioactive Decay • Alpha • Gamma – Quantized transitions lead to mono-energetic – emission of photon radiation – involves electromagnetic force – Gamma decay from – mono-energetic (QM), spin rules excited states – doesn’t change chemistry or mass – a shell transition in nucleus – results from alpha or beta decay Bouncing > 6 MeV alpha particles off the daughter nucleus doesn’t induce the reverse reaction! Why???

5 Modes of Radioactive Decay Modes of Radioactive Decay • Alpha • Alpha • Gamma • Gamma •Beta •Beta – emission of electron, positron, electron – emission of electron, positron, electron capture capture – involves weak nuclear force – involves weak nuclear force – energy spectrum in particles (NOT – energy spectrum (QM Î 3 body problem) monoenergetic) – emission of neutrino (next best thing to nothing), a V.I.P.* in cosmology and stellar evolution Must be a 3 body decay! – Range (e ~ microns, neutrino ~ infinite)

* Very Important Particle or Very Interesting Puzzle

Modes of Radioactive Decay Modes of Radioactive Decay • Alpha • Alpha •Beta •Beta • Gamma • Gamma •Fission •Fission – caused by squishy, big nuclei – caused by squooshy, big nuclei – wobbly nuclei may break apart naturally or – wobbly nuclei may break apart naturally or if kicked if kicked – split is asymmetric – split is asymmetric – characteristic isotopic signatures

Important evidence for past events

The mysterious case of Oklo The mysterious case of Oklo

• 235U/238U ratio remarkably • Other isotope signatures invariant globally (fixed consistent with nuclear by initial isotope ratio and fission different half-lives) • Except: in one location in Oklo mine in Gabon, where ratio was anomalously low

Looked like spent nuclear fuel rods! And presence of Tc daughters…

6 The mysterious case of Oklo Radioactive decay

• U concentrated by groundwater redox changes – Hexavalent/tetravalent solubilization changes Occurs by 3 mechanisms: α, β, γ • 235U abundance ~10X higher 2 Ga ago α decay results in loss of 2 • Water acts as neutron moderator protons and 2 neutrons β- – Slower neutrons better induce fission β decay results from an p X to n transition N β+ • Started 1.7 Ga ago β+ decay results from a n to p transition α • Ran for ~ 150 Ka All of these transitions can • Produced about 100 KW lead to γ decay • Temperatures ~ 50-200 C P

Chart of the nuclides The further away an isotope is from the “line of stability”, the faster it decays

¾500 Ma or “stable” ¾1 Month ¾10 Minutes ¾0.1 Sec

http://wwwndc.tokai.jaeri.go.jp/CN/

At the top end, we run out of 12.748 stability Lecture 1 1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques

Consider downloading Isotope Explorer from http://isotopes.lbl.gov/toi.html

7 Radioactive decay equations Example

If (238U) = 2.2 dpm g-1, what is the [238U]? • dN/dt = -λN • We need to be able to λ is the decay constant convert from activity to -1 concentration and back λ = 1.55 x 10-10 a-1 (tm ) and is the probability of decay, n is again; = 2.95 x 10-16 mins-1 number of atoms; N = 2.2/λ atoms g-1 • dN/dt = -λN = 7.45 x 1015 atoms g-1 dN/dt is known as activity t = mean life 23 -1 m [U] = N / 6.023 x 10 mol g and commonly is (time it takes for population to -8 -1 depicted by ( brackets) decay to 1/e of original) = 1.24 x 10 mole g or “A” = 12.4 nmol g-1

Isotope Dating More equations • Several sources of radioisotopes – Primordial • There since the elements were formed The integrated form of the • The half-life is a useful activity equation is • e.g., 40K, 238U, 232Th concept; – Nucleogenic N = N e-λt • Produced by the decay of another isotope o • E.g., 222Rn, 234Th At t = t 1/2, N = No/2 – Cosmogenic This provides the basis for • Produced by cosmic rays smashing stable nuclei most radioactive dating t = (ln 2) t = (ln 2)/λ • E.g., 10Be, 39Ar methods 1/2 m – Anthropogenic • Made by bombs, industry, or nuclear fuel reprocessing • E.g, 90Sr, 137Cs, 239Pu

Isotope Dating Sources of radioisotopes Simple Dating • Some are produced by more than one: 3 – e.g., H is cosmogenic (~4 Kg) and • Starting with NNe= −λt anthropogenic (bombs ~400 Kg) 0 – e.g., 14C is cosmogenic, anthropogenic ⎛⎞N (bombs), and 14C/12C diluted by fossil fuels • Take natural log of both sidesln ⎜⎟= −λt ⎝⎠N0 1 ⎛⎞N • And solve for t t = ln ⎜⎟ λ ⎝⎠N0 Assumes you know N 0 e.g, radiocarbon dating

8 Isotope Dating Parent Daughter Dating λ PD⎯⎯→ Isotope Equilibrium −λt • The heaviest isotopes don’t • Starting with PPe= 0 immediately decay to stable ones • Daughter is “dead parent” • Daughter population grows until loss = gain, e.g. D =−P P or P =+ D P 00 Adaughter= Aparent • And solve for t

11⎛⎞PDPD0 ⎛+ ⎞ 1 ⎛ ⎞ t ==ln⎜⎟ ln⎜⎟⎜⎟ =+ ln 1 λλ⎝⎠PP⎝⎠⎝⎠ λ P

You don’t need to know N0 but must be closed system

e.g, 3H-3He dating, 40K-40Ar dating

Isotope Dating Isotope Dating Isotope Disequilibrium Isotope Disequilibrium • Chemistry of isotopes in chain • Chemistry of isotopes in chain are unequal (e.g. U & Th) are unequal (e.g. U & Th) • If you “break” the chain, then • If the system is “in balance” daughters will grow in at a then certain rate Production= Loss

AAK238=+ 234 adsorption

i.e., you can solve for K

12.748 Isochron Dating Lecture 1 • Largely used in rocks • In a medium where there are varying ratios 1. What is an isotope? of parent/daughter – Due to partitioning in minerals 2. Cosmic abundance of the elements – Or phase separation (vesiculation) 3. Isotope Stability • If closed system, get linear P/D relationship 4. Radioactive Decay – Slope gives time – Intercept gives initial P/D 5. Radioactive dating techniques

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