4. Radioactive Decay 5

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 Logistics

• Tuesday Clark 331 – 14:30-16:00 • Thursday Clark 331 – 14:30-16:00 Welcome to 12.748 Resources • Material: – Reading lists (journal articles & texts) – Verbal Lectures – Slides presented (on web)* – 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 Grading

• 100% for 3 Assessed Exercises – Handed out on Sept. 21, Oct. 5, and Oct 19 – Due 1 week after handed out – Late policy: 25% of grade deducted per day late (unless documented legitimate reason) Welcome to 12.748 Lecture 1

• Logistics and organisational • Course Objectives and Layout – What you can expect, and what is expected of you – Resources • Introduction to isotopes, radioactivity, and dating Welcome to 12.744/12.754 Objectives

To build a strong, intuitive, and quantitative understanding of the isotopes as tools for understanding earth and ocean processes • You’ll learn – The underlying physical-chemical principles – Stable, radioactive, and radiogenic isotopes – Devise, construct, and solve geochemical mass balances – Understand and use isotope systems as tools Welcome to 12.748 Course Structure 12 Lectures over 7 weeks • Origins of elements, sun, earth, oceans (3) • Measurement techniques (2) • Isotope chemistry and physics (3) • Four case studies (early earth history): 1. Core formation & mantle differentiation 2. Crust formation & extraction 3. Mantle melting & melt extraction 4. Precambrian redox history Welcome to 12.748 Lecture 1

1. Strong nuclear (short range, between nucleons) Strength = 1 2. Electromagnetic (infinite, but shielded) Strength = 10-2 3. Weak nuclear force (very short range, beta decay) Strength = 10-13 4. Gravity (infinite range, cannot be shielded against) Strength = 10-39 Step 0: May the Force be with you 2 most significant advances in modern physics

1. relativity E = mc2 • Matter = energy = gravity • 1 g matter Æ 1014 J ~ 2 x 1013 cal 2. quantum mechanics • Wave/particle, • uncertainty principle, • quantization Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques Isotopes • Atoms consist of: – Electrons in orbit • Define chemical state (ionisation, bonding) • Number/distribution defined by: – Nuclear charge (charge balance) – Shell structure – Nucleus • Protons (charged) – Define the element (chemistry) • Neutrons (neutral) – Add stability and mass •N ~ P Isotopes Most elements have a number of stable isotopes: – Hydrogen has 2 • 1H has 1 proton, 0 neutrons (most abundant) • 2H has 1 proton, 1 neutron – Oxygen has 3 • 16O has 8 protons, 8 neutrons (most abundant) • 17O has 8 protons, 9 neutrons (most rare) • 18O has 8 protons, 10 neutrons (2nd most abundant) – Fluorine has only 1 • 19F (9 protons, 10 neutrons) – Tin has 10 (all with 50 protons, 71-82 neutrons) Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques Cosmic abundance of the elements • Obtained from: – solar spectra – stellar/galactic spectra – meteorite samples – cosmic dust Cosmic abundance of the elements • Note Log Scale and Range • General decrease with mass • Bulge at Fe • Dip at B, Be • ZigZag Pattern • Bulge at Pb Cosmic abundance of the elements Why???

•Ans: – nuclear stability – nucleosynthesis • big bang • galactic and stellar evolution Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques Isotopes • Nuclear “stability” governed by – Quantum mechanical rules – Nuclear forces – Electrostatic charge Isotopes • Nuclear “stability” governed by – Quantum mechanical rules – Nuclear forces – Electrostatic charge • Different elements have varying numbers of stable isotopes • When a nucleus is “unstable” it decays – The more unstable, the quicker it decays • Rates vary from 10-10 seconds to 1012 years Controlling factors on nuclear stability • Number nucleons – the more the merrier • spin pairing – favours even #s – also the abundance of stable isotopes

# p # n # n+p #stable ======Even Even Even 156 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 • Number nucleons – the more the merrier • spin pairing • shell– favours structure even #s – “magic numbers” – like atomic shells – popular #s of n or Elements with magic “Z” have p many more isotopes than neighbors – not as pronounced – 208Pb is “doubly magic” Controlling factors on nuclear stability • Number nucleons – the more the merrier • spin pairing – favours even #s • shell structure – “magic numbers” • surface tension – like liquid drop Hence tail-down at low mass (high surface area to volume ratio) Controlling factors on nuclear stability • Number nucleons – the more the merrier • spin pairing – favours even #s • shell structure – “magic numbers” • surface tension – like liquid drop Hence tail-down at high mass • coulomb repulsion … and drift to high-n nuclei – limits ultimate size Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques Modes of Radioactive Decay • Alpha – done by heavy nuclei (e.g., 232Th, 238U, 235U) – involves strong nuclear force – emission of 4He nucleus (a doubly magic nucleus) • ∆ A = 4, ∆ N = 2, ∆ Z = 2 – half-life inversely related to energy: •1024 change in T for 3-fold change in energy • quantum-mechanical tunnelling – mono-energetic (QM) – range ~ 10s of microns – (charged particle) Modes of Radioactive Decay • Alpha •Beta – emission of electron, positron, electron capture – involves weak nuclear force – energy spectrum (QM Î 3 body problem) – emission of neutrino (next best thing to nothing), a V.I.P.* in cosmology and stellar evolution – Range (e ~ microns, neutrino ~ infinite) * Very Important Particle or Very Interesting Puzzle Modes of Radioactive Decay • Alpha •Beta • Gamma – emission of photon – involves electromagnetic force – mono-energetic (QM), spin rules – doesn’t change chemistry or mass – a shell transition in nucleus – results from alpha or beta decay Modes of Radioactive Decay • Alpha •Beta • Gamma • Fission – caused by squishy, big nuclei – wobbly nuclei may break apart naturally or if kicked – split is asymmetric Modes of Radioactive Decay • Alpha •Beta • Gamma • Fission – caused by squooshy, big nuclei – wobbly nuclei may break apart naturally or if kicked – split is asymmetric – characteristic isotopic signatures

Important evidence for past events Radioactive decay

Occurs by 3 mechanisms: α, β, γ α decay results in loss of 2 protons and 2 neutrons β- β decay results from an p X to n transition N β+ β+ decay results from a n to p transition α All of these transitions can lead to γ decay P Chart of the nuclides

http://wwwndc.tokai.jaeri.go.jp/CN/ 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 At the top end, we run out of stability Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating Radioactive decay equations

•dN/dt= -λN • We need to be able λ is the decay constant to convert from (t-1) and is the probability activity to of decay, n is number of concentration and atoms; back again; •dN/dt= -λN dN/dt is known as activity and commonly is depicted by ( brackets) or “A” Example

If (238U) = 2.2 dpm g-1, what is the [238U]?

λ = 1.55 x 10-10 a-1 = 2.95 x 10-16 mins-1 N = 2.2/λ atoms g-1 = 7.45 x 1015 atoms g-1 [U] = N / 6.023 x 1023 mol g-1 = 1.24 x 10-8 mole g-1 = 12.4 nmol g-1 More equations

The integrated form of the activity equation is • The half-life is a useful concept; -λt N = No e

At t = t 1/2, N = No/2 This provides the basis for most radioactive dating methods t 1/2 = (ln 2)/λ Isotopes • Atomic nuclei made of neutrons and protons • Protons determine nuclear charge and atomic chemistry • Each element generally has more than one isotope (same #protons, different #neutrons) • Isotopes differ in mass but not chemistry • Some isotopes are stable, the rest decay Isotopes • Isotopes can be “fractionated” (amounts relatively enhanced/depleted) by physical, chemical or biological processes • Radioactive decay follows fixed rules – Rules and rates don’t change for any physical, chemical or biological reasons • These rates are useful for “clocking” physical, chemical and biological processes Isotope Dating • Several sources of radioisotopes – Primordial • There since the elements were formed • e.g., 40K, 238U, 232Th – Nucleogenic • Produced by the decay of another isotope • E.g., 222Rn, 234Th – Cosmogenic • Produced by cosmic rays smashing stable nuclei • E.g., 10Be, 39Ar – Anthropogenic • Made by bombs, industry, or nuclear fuel reprocessing •E.g, 90Sr, 137Cs, 239Pu Isotope Dating Simple Dating

• Starting with −λt NNe= 0 ⎛⎞N • Take natural log of both sidesln ⎜⎟= −λt ⎝⎠N0 1 ⎛⎞N • And solve for t t = ln ⎜⎟ λ ⎝⎠N0

Assumes you know N0 Isotope Dating Parent Daughter Dating P ⎯⎯λ → D

−λt • Starting with P = Pe0 • Daughter is “dead parent”

DPP= 00−=+ orP DP • And solve for t

11⎛⎞P0 ⎛⎞⎛⎞D + PD 1 t ==ln⎜⎟ ln⎜⎟⎜⎟ =+ ln 1 λλ⎝⎠PP⎝⎠⎝⎠ λ P

You don’t need to know N0 but must be closed system Isotope Dating Isotope Equilibrium • Heaviest isotopes don’t decay to stable ones • Daughter population grows until loss = gain, e.g.

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

AAK238=+ 234 adsorption

i.e., you can solve for K Welcome to 12.748 Lecture 1

1. What is an isotope? 2. Cosmic abundance of the elements 3. Isotope Stability 4. Radioactive Decay 5. Radioactive dating techniques