Which process produced most of the nuclei heavier than the iron peak, such as barium, gold and uranium?

Neutron capture, in the slow s-process and the rapid r-process, followed by beta decay

Fusion in the cores of massive stars, which keeps releasing energy as heavier nuclei form

Neutron capture, in the slow s-process and the rapid r-process, followed by beta decay

Cosmic-ray spallation of interstellar nuclei, which builds the heavy elements up from smaller fragments

Big Bang nucleosynthesis during the first few minutes, when all stable nuclei were assembled

Which statement about CI carbonaceous chondrites is correct?

Their non-volatile element abundances match the solar photosphere, although they contain no chondrules

They are the most strongly heated chondrites, of petrologic type 6, and show a well-equilibrated texture

They contain abundant large chondrules set in a continuous network of Fe-Ni metal

Their non-volatile element abundances match the solar photosphere, although they contain no chondrules

They are melted basaltic achondrites derived from the asteroid Vesta and carry igneous textures

A meteorite is composed of olivine crystals set in a continuous network of Fe-Ni metal and contains no chondrules. It is a:

pallasite, a stony-iron meteorite from a differentiated body

eucrite, a basaltic achondrite of the HED group

octahedrite, an iron meteorite with a Widmanstätten pattern of kamacite and taenite

H-group ordinary chondrite with chondrules replaced by metal during metamorphism

Which of the following meteorites come from parent bodies that melted and differentiated?

A eucrite of the HED group, a basaltic achondrite

An octahedrite iron meteorite, an Fe-Ni alloy

A eucrite of the HED group, a basaltic achondrite

An H-group ordinary chondrite of petrologic type 4, unmelted but thermally metamorphosed

An octahedrite iron meteorite, an Fe-Ni alloy

A CM carbonaceous chondrite, aqueously altered but unmelted

Which element is strongly siderophile and is therefore depleted in the silicate Earth because of core formation?

Iridium, one of the platinum-group elements that alloy with metallic iron

Zirconium, a refractory element that forms very stable oxide and silicate minerals

Zinc, which prefers sulphide minerals such as sphalerite in ore deposits

Strontium, which substitutes for calcium in plagioclase and in carbonate minerals

Iridium, one of the platinum-group elements that alloy with metallic iron

Olivine crystallises and is removed from a basaltic melt. How do the concentrations of Ni (compatible) and Rb (incompatible) change in the residual liquid?

Ni falls sharply and Rb rises, because Ni²⁺ replaces Mg²⁺ in olivine while Rb⁺ does not fit

Both rise, because every trace element is concentrated in the liquid as the crystals form and are removed

Ni rises and Rb falls, because the small Ni²⁺ ion is excluded from the olivine lattice while Rb⁺ fits it

Ni falls sharply and Rb rises, because Ni²⁺ replaces Mg²⁺ in olivine while Rb⁺ does not fit

Neither changes, because trace elements do not take part in crystal-melt equilibrium

A basaltic liquid crystallises a plagioclase-rich assemblage with bulk D(Sr) = 1.5 and bulk D(Rb) = 0.05. Use C(L)/C₀ = f^(D − 1), where f is the fraction of liquid remaining. When f falls from 1 to 0.5, the Rb/Sr ratio of the liquid:

rises by a factor of about 2.7, as Rb is enriched about 1.9 times and Sr falls to about 0.71

stays constant, because both elements are lithophile and behave alike

rises by a factor of about 2.7, as Rb is enriched about 1.9 times and Sr falls to about 0.71

rises by a factor of about 1.9, which is the enrichment of Rb alone because Sr is left unaffected by plagioclase

falls by a factor of about 2.7, because the compatible element controls the ratio

Which of the following statements about the Rb-Sr and Sm-Nd systems are correct?

Because Nd is more incompatible than Sm, a partial melt of the mantle has a lower Sm/Nd than its source

Old continental crust typically has a negative ε(Nd) together with a high ⁸⁷Sr/⁸⁶Sr

Because Nd is more incompatible than Sm, a partial melt of the mantle has a lower Sm/Nd than its source

Old continental crust typically has a negative ε(Nd) together with a high ⁸⁷Sr/⁸⁶Sr

The depleted mantle has a higher Rb/Sr than CHUR, so it grows radiogenic Sr faster than the crust does

Sm-Nd ages are easily reset by weathering because Sm and Nd are among the most soluble elements in water

The silicate Earth carries a small excess of radiogenic ¹⁸²W compared with chondrites. Given that ¹⁸²Hf (half-life about 9 Ma) decays to ¹⁸²W, hafnium is lithophile and tungsten is moderately siderophile, what does this indicate?

Core formation happened while ¹⁸²Hf was alive: W went to the core and Hf stayed to make ¹⁸²W in the mantle

Core formation was completed after ¹⁸²Hf had become extinct, so the mantle kept all of its radiogenic ¹⁸²W

A late veneer delivered ¹⁸²W-rich chondritic material to the mantle after the core had formed

Tungsten is lithophile and hafnium is siderophile, so Hf went into the core while W stayed in the mantle

Core formation happened while ¹⁸²Hf was alive: W went to the core and Hf stayed to make ¹⁸²W in the mantle

Arc magmas are enriched in Ba and Sr relative to Nb and Ta. Which explanation is correct?

Slab-derived aqueous fluids carry the mobile LILE (Ba, Sr) but not the immobile HFSE (Nb, Ta), which stay in the slab

Ba and Sr are high field strength elements and are carried efficiently by slab-derived aqueous fluids into the mantle wedge

Nb and Ta are volatile elements that escape as gas during the eruption of the arc magma at the surface

Ba and Sr are siderophile elements added to the arc mantle by leakage from the core

Field relations show that a granite crystallised at about 2,700 Ma, and its zircons lost lead in a single episode. They define a discordia with an upper intercept at 2,700 Ma and a lower intercept at 600 Ma on the concordia curve. What does the lower intercept date?

The single episode of lead loss, such as a metamorphic event, about 600 Ma ago

The crystallisation of the granite, since zircon begins to grow at the lower intercept

The present day, because lead loss is always a recent process

The single episode of lead loss, such as a metamorphic event, about 600 Ma ago

The age of the Earth, since every chord is extrapolated back to the origin of the curve

Which conditions are required for a Rb-Sr whole-rock isochron to give the crystallisation age of a rock suite?

The samples are cogenetic and began with the same initial ⁸⁷Sr/⁸⁶Sr

The Rb-Sr system has stayed closed since crystallisation

The samples show a measurable spread in ⁸⁷Rb/⁸⁶Sr

The samples are cogenetic and began with the same initial ⁸⁷Sr/⁸⁶Sr

The samples all have the same ⁸⁷Rb/⁸⁶Sr today, so that they plot as one tight cluster

The Rb-Sr system has stayed closed since crystallisation

The samples show a measurable spread in ⁸⁷Rb/⁸⁶Sr

Cosmochemistry, Element Distribution, Planetary Differentiation and Radiogenic Isotopes

This chapter answers the first half of the Geochemistry heading of Part B1 (Advanced topics in Geology) of the Geology and Geophysics (GG) paper: “Nucleosynthesis and cosmic abundance of elements; Classification and components of meteorites; Geochemical affinities and distribution of major, minor and trace elements in crust, mantle, and core; Planetary differentiation and geochemical evolution of the earth; Radiogenic (long-lived) isotopic evolution (Rb-Sr, Sm-Nd, U-Th-Pb) of the crust and the mantle, mantle reservoirs”. It teaches how the elements were made, what meteorites record, how Goldschmidt’s classes and the partition coefficient decide where an element goes, how the Earth separated into core, mantle and crust, and what the Rb-Sr, Sm-Nd and U-Th-Pb systems tell us about ages and mantle reservoirs. The numericals are isochron ages, epsilon-Nd, U-Pb ages and batch melting, with every constant stated in the question.

1. Nucleosynthesis and the cosmic abundance of the elements

The Big Bang made only hydrogen and helium (about 75 and 25 percent by mass) with traces of deuterium, ³He and lithium. Every heavier element was made later, inside stars. Hydrogen burning (the proton-proton chain, and the CNO cycle in heavier stars) makes helium; helium burning fuses three ⁴He nuclei into ¹²C (the triple-alpha process); massive stars then burn carbon, neon, oxygen and silicon in turn and stop at the iron-peak nuclei (Fe, Ni). Each stage is hotter and shorter than the last, and a massive star ends as a core-collapse supernova.

Beyond the iron peak, fusion no longer releases energy, so heavier nuclei are built by neutron capture. In the s-process (slow, in evolved low-mass AGB stars) each capture is followed by beta decay, so the path hugs the valley of stability and builds Sr, Ba and Pb. In the r-process (rapid, in neutron-star mergers and some supernovae) many neutrons are captured before any decay, which makes much of the Au and Pt and all of the U and Th. Li, Be and B are fragile, are destroyed inside stars, and are made mainly by cosmic-ray spallation of heavier nuclei.

Abundance falls steeply with mass number up to the iron peak and then flattens; hydrogen and helium make up about 98 percent of the mass of the solar system.
Elements of even atomic number are more abundant than their odd-numbered neighbours (the Oddo-Harkins rule), which is why rare earth patterns are smooth once normalised to chondrite.
Li, Be and B lie far below their neighbours, and peaks at the neutron numbers 50, 82 and 126 (near Sr, Ba and Pb) mark neutron capture.

Cosmic abundances come from the solar photosphere and from CI chondrites, which match the photosphere for every element except the volatiles (H, C, N, O, noble gases) and Li; they are normalised to 10⁶ atoms of Si. The Earth is not cosmic in composition: it lost most of its hydrogen, helium and other volatiles.

🎯 Why the iron peak?

Binding energy per nucleon rises with mass to a maximum near ⁵⁶Fe and ⁶²Ni. Fusing nuclei lighter than this releases energy; fusing heavier ones consumes it. A massive star that has built an iron core has no further fusion fuel, so the core collapses.

2. Meteorites: classification and components

Meteorites are fragments of asteroids (a few come from the Moon and Mars) and preserve the early solar system. The first division is whether the parent body melted: chondrites are unmelted and primitive, while achondrites, stony-irons and irons come from bodies that melted and differentiated.

Meteorite classes
Class	Group	Defining features	What it tells us
Chondrite	Carbonaceous (CI, CM, CV, CO)	Chondrules and matrix, but none in CI; CI holds water-bearing minerals and organic matter	CI matches the solar photosphere: the cosmic reference
Chondrite	Ordinary (H, L, LL)	Olivine, pyroxene, Fe-Ni metal, troilite; H, L, LL grade total iron from high to low	Commonest falls; heated in their asteroid parent
Chondrite	Enstatite (EH, EL)	Enstatite, Fe-Ni metal, unusual sulphides	Formed in very reduced conditions
Achondrite	HED, SNC, lunar, others	No chondrules; igneous textures	HED come from the asteroid Vesta, SNC from Mars
Stony-iron	Pallasite, mesosiderite	Pallasite: olivine crystals in Fe-Ni metal; mesosiderite: silicate-metal breccia	Metal and silicate of differentiated bodies
Iron	Hexahedrite, octahedrite, ataxite	Fe-Ni alloy (kamacite, taenite); octahedrites show the Widmanstätten pattern	Metal cores of melted, differentiated bodies

A chondrite has four building blocks. Chondrules are millimetre-sized silicate droplets that melted and cooled quickly in the solar nebula. CAIs (calcium-aluminium-rich inclusions) are refractory minerals such as corundum, hibonite, spinel and melilite, and are the oldest dated solids, at about 4.567 Ga. The fine-grained matrix carries the volatile-rich material, and metal and sulphide grains (kamacite, taenite, troilite) complete the set. The petrologic type (1 to 6) records the parent body’s history: type 3 is the least altered, types 1 and 2 show increasing aqueous alteration, and types 4 to 6 increasing thermal metamorphism.

📖 How the age of the Earth was found

In the 1950s Clair Patterson showed that lead in meteorites, including troilite of the iron meteorite Canyon Diablo, and terrestrial lead lie on one Pb-Pb isochron giving about 4.55 Ga for the Earth. Work on CAIs later refined the solar system to about 4.567 Ga.

⚠️ Chondrite, chondrule, achondrite

A chondrite is a rock, a chondrule is a droplet inside it, and an achondrite is a melted meteorite without chondrules. The classes are defined by history and bulk composition, not by chondrules alone: CI chondrites contain no chondrules yet are still chondrites, because they are unmelted and have solar composition.

3. Goldschmidt’s geochemical classification and substitution rules

V. M. Goldschmidt grouped the elements by the phase they prefer when a planet differentiates into metal, sulphide, silicate and gas.

Goldschmidt’s geochemical classes
Class	Preference	Examples	Where they sit
Lithophile	Oxygen: silicates and oxides	Si, Al, Mg, Ca, Na, K, Ti, Rb, Sr, Ba, REE, Zr, Hf, Nb, Ta, Th, etc.	Crust and mantle
Siderophile	Metallic iron	Fe, Ni, Co, Mo, Re, Au, platinum-group elements	Mostly in the core; depleted in the mantle
Chalcophile	Sulphur: sulphides	Cu, Zn, Pb, Ag, Cd, Hg, As, Sb, etc.	Sulphide minerals and ore deposits
Atmophile	Gas phase	H, N, noble gases	Atmosphere and hydrosphere

Which crystal site an element enters follows Goldschmidt’s rules of substitution. Ions whose radii differ by less than about 15 percent substitute freely. A charge difference of one unit is allowed if a coupled substitution restores balance (Na⁺Si⁴⁺ for Ca²⁺Al³⁺ in plagioclase). When two ions compete for a site, the one with the higher charge-to-radius ratio (ionic potential) is taken up first, so Mg²⁺ enters early olivine before Fe²⁺ and the larger ion is left to later crystals. Ni²⁺, slightly smaller than Mg²⁺, substitutes for it in olivine and is taken up early.

4. Partition coefficients and the distribution of elements in crust, mantle and core

The partition coefficient D = C(mineral)/C(melt) measures how an element divides between crystal and melt. Compatible elements have D > 1 (Ni, Cr and Co go into olivine and spinel); incompatible elements have D < 1 (K, Rb, Cs, Ba, Th, Nb, Ta and the light REE stay in the melt). The incompatible ones split into LILE (large, low charge: K, Rb, Cs, Sr, Ba, mobile in fluids) and HFSE (small, highly charged: Zr, Hf, Nb, Ta, Ti, Th, immobile in fluids). For batch melting the melt has C(L)/C₀ = 1/[D + F(1 − D)], where F is the melt fraction and D the bulk coefficient; for D close to 0 this is about 1/F, so 10 percent melting enriches an incompatible element about tenfold. For fractional crystallisation the liquid follows C(L)/C₀ = f^(D − 1), where f is the fraction of liquid left.

Where the elements are
Reservoir	Share of Earth’s mass	Composition	Geochemical character
Crust	Under 1 percent	Continental bulk andesitic (about 60 wt% SiO₂), oceanic basaltic; O, Si, Al, Fe, Ca, Na, K, Mg make up about 98 wt%	Holds a disproportionate share of K, Rb, Ba, Th and U
Mantle	About two-thirds	Peridotite (olivine, pyroxenes, spinel or garnet); MgO about 38 wt%	Depleted in incompatibles (crust extraction) and siderophiles (core formation)
Core	About one-third (32 percent)	Fe-Ni alloy with a few percent Ni and light elements (S, Si, O, C, H)	Liquid outer core, solid inner core; lighter than pure Fe-Ni

⚠️ Compatibility belongs to a mineral-melt pair

An element is not compatible or incompatible in the abstract. Sr is incompatible when a mantle peridotite melts (D < 1) but compatible in plagioclase-rich crystallisation (D > 1), and Eu²⁺ follows Sr into plagioclase. Always ask which mineral and which melt.

5. Planetary differentiation and the geochemical evolution of the Earth

The Earth accreted from planetesimals within a few tens of millions of years of the oldest solids. Heat from impacts, from short-lived ²⁶Al (half-life about 0.7 Ma) and ⁶⁰Fe, and later from U, Th and ⁴⁰K melted much of it, and a giant impact late in accretion formed the Moon. Dense Fe-Ni metal sank to make the core, leaving the bulk silicate Earth (BSE: primitive mantle plus crust). Siderophile elements followed the metal and are depleted in the BSE, moderately for Ni and Co and very strongly for Au, Ir and the other platinum-group elements.

Two observations time and test this. In the Hf-W system (¹⁸²Hf decays to ¹⁸²W with a half-life of about 9 Ma; Hf is lithophile and W is moderately siderophile) W went into the core and Hf stayed in the mantle, so the excess of ¹⁸²W in the silicate Earth over chondrites shows that the core formed while ¹⁸²Hf was still alive, within a few tens of millions of years. Second, the highly siderophile elements in the mantle are far more abundant than metal-silicate equilibrium predicts, which is explained by a late veneer of chondritic material added after the core had formed.

Partial melting then moves incompatible elements upward. Basaltic melts built the first crusts, subduction-related magmatism and later reworking built the continents, and the residue, depleted mantle, has low Rb/Sr and high Sm/Nd. Degassing supplied the atmosphere and oceans; atmospheric argon is mostly radiogenic ⁴⁰Ar from the decay of ⁴⁰K in the solid Earth.

🎯 Why chondritic ratios?

In the BSE the ratios among refractory lithophile elements (Ca/Al, Sm/Nd, Lu/Hf) stay at chondritic values, because neither condensation nor core formation separated them. That is the justification for CHUR, the chondritic uniform reservoir used as the reference in neodymium isotopes.

6. Radiogenic isotopes: the decay law, isochrons and Rb-Sr

A parent decaying with constant λ obeys N = N₀e^(−λt), with half-life t½ = ln 2/λ. The radiogenic daughter made in time t is D* = N(e^(λt) − 1), where N is the parent present now. Dividing by a stable isotope of the daughter element, D(s), removes the dependence on sample size: (D/D(s)) = (D/D(s))₀ + (N/D(s))(e^(λt) − 1). This is a straight line. A set of cogenetic samples of one age plots as an isochron whose slope is e^(λt) − 1 and whose intercept is the initial ratio.

A valid isochron needs cogenetic samples that began with the same initial ratio, a system that has stayed closed since formation, and a real spread in the parent/daughter ratio.
The slope gives the age, t = ln(1 + slope)/λ; the intercept gives the initial ratio, which fingerprints the source (mantle or crust).

Rb-Sr: ⁸⁷Rb decays to ⁸⁷Sr by beta emission with λ = 1.42 × 10⁻¹¹ yr⁻¹ (half-life about 49 Ga), and the plot is ⁸⁷Sr/⁸⁶Sr against ⁸⁷Rb/⁸⁶Sr. Rb⁺ follows K⁺ (micas, K-feldspar) and Sr²⁺ follows Ca²⁺ (plagioclase). Rb is more incompatible than Sr, so melts and crust have high Rb/Sr and the depleted mantle low Rb/Sr. The crust therefore grows radiogenic Sr quickly (old continental crust is well above 0.71), while MORB sits near 0.703 and the solar system began at about 0.699.

Worked example. Two cogenetic whole rocks have (⁸⁷Rb/⁸⁶Sr, ⁸⁷Sr/⁸⁶Sr) = (1.0, 0.7150) and (4.0, 0.7450). The slope is (0.7450 − 0.7150)/(4.0 − 1.0) = 0.0100, so t = ln(1.0100)/(1.42 × 10⁻¹¹) = 7.0 × 10⁸ yr, about 700 Ma. The intercept is 0.7150 − 0.0100 × 1.0 = 0.7050, the initial ratio: a value above the mantle’s 0.703 can hint at a crustal contribution to the source.

⚠️ A mixing line can masquerade as an isochron

Both axes of the Rb-Sr plot share the denominator ⁸⁶Sr, so mixing two components gives a straight line, and its slope has no age meaning. Mineral isochrons also record cooling, not crystallisation: biotite closes to Rb-Sr at only about 300 °C. Always check that the samples are cogenetic and the system closed.

7. Sm-Nd and the epsilon notation

Sm-Nd: ¹⁴⁷Sm decays to ¹⁴³Nd by alpha emission with λ = 6.54 × 10⁻¹² yr⁻¹ (half-life about 106 Ga), normalised to ¹⁴⁴Nd. Sm and Nd are neighbouring rare earths, so Sm/Nd changes little in weathering and metamorphism and the system dates mafic rocks and Archean terrains well. In melting Nd is the more incompatible, so melts and crust get low Sm/Nd and the depleted mantle high Sm/Nd: the opposite sense to Sr. The reference is CHUR: today ¹⁴³Nd/¹⁴⁴Nd = 0.512638 and ¹⁴⁷Sm/¹⁴⁴Nd = 0.1967, with CHUR(t) = 0.512638 − 0.1967(e^(λt) − 1).

The deviation from CHUR is expressed as ε(Nd)(t) = [ (¹⁴³Nd/¹⁴⁴Nd)(sample, t) ÷ (¹⁴³Nd/¹⁴⁴Nd)(CHUR, t) − 1 ] × 10⁴, with the sample ratio taken at the time t of interest. Positive ε means a source with long-term Sm/Nd above chondritic (depleted mantle; MORB is strongly positive), negative ε a crustal or enriched source (old continental crust is strongly negative). The model age T(CHUR) = (1/λ) ln[1 + ((¹⁴³Nd/¹⁴⁴Nd)(S) − 0.512638)/((¹⁴⁷Sm/¹⁴⁴Nd)(S) − 0.1967)] is the time when the sample’s Nd matched CHUR, an estimate of when its source left the mantle.

The three long-lived systems
System	Decay and λ (yr⁻¹)	Normalising isotope	In melting	Continental crust
Rb-Sr	⁸⁷Rb → ⁸⁷Sr, 1.42 × 10⁻¹¹	⁸⁶Sr	Rb more incompatible: melt has high Rb/Sr	High ⁸⁷Sr/⁸⁶Sr
Sm-Nd	¹⁴⁷Sm → ¹⁴³Nd, 6.54 × 10⁻¹²	¹⁴⁴Nd	Nd more incompatible: melt has low Sm/Nd	Negative ε(Nd)
U-Pb	²³⁸U → ²⁰⁶Pb, 1.55125 × 10⁻¹⁰; ²³⁵U → ²⁰⁷Pb, 9.8485 × 10⁻¹⁰	²⁰⁴Pb	U more incompatible than Pb: upper crust has high U/Pb	Radiogenic Pb isotopes in the upper crust

8. U-Th-Pb, Pb-Pb ages and the mantle reservoirs

U-Th-Pb has three chains (the third, ²³²Th → ²⁰⁸Pb, has λ = 4.9475 × 10⁻¹¹ yr⁻¹) and a stable reference, ²⁰⁴Pb. The two uranium chains give two clocks. On the concordia diagram (²⁰⁶Pb/²³⁸U against ²⁰⁷Pb/²³⁵U) concordant ages lie on the curve; zircons that lost lead lie on a chord, the discordia, whose upper intercept is the crystallisation age and whose lower intercept dates the lead loss. Zircon takes in U but rejects Pb when it forms, so it is the standard U-Pb mineral. The Pb-Pb age uses ²⁰⁷Pb/²⁰⁶Pb = (1/137.88)(e^(λ235·t) − 1)/(e^(λ238·t) − 1), where 137.88 is the present ²³⁸U/²³⁵U; it does not depend on the U/Pb ratio and so survives recent U loss.

Ocean-island basalts sample mantle reservoirs that differ from the depleted MORB mantle (DMM: low ⁸⁷Sr/⁸⁶Sr, positive ε(Nd)). HIMU has very high ²⁰⁶Pb/²⁰⁴Pb (high ²³⁸U/²⁰⁴Pb, μ) with lowish ⁸⁷Sr/⁸⁶Sr, read as recycled oceanic crust (St Helena). EM1 has low ¹⁴³Nd/¹⁴⁴Nd and low ²⁰⁶Pb/²⁰⁴Pb, read as recycled pelagic sediment or lower crust. EM2 has the highest ⁸⁷Sr/⁸⁶Sr, read as recycled terrigenous sediment or upper crust (Samoa). A shared, moderately depleted component (FOZO or PREMA) is also recognised.

🧠 Crust: Sr up, Nd down

Melting puts Rb and Nd (the more incompatible partners) into the crust. Crust therefore has high Rb/Sr, which grows high ⁸⁷Sr/⁸⁶Sr, and low Sm/Nd, which grows low ¹⁴³Nd/¹⁴⁴Nd and negative ε(Nd). The depleted mantle is the mirror image, so oceanic basalts plot on a negatively sloping mantle array in ε(Nd) against ⁸⁷Sr/⁸⁶Sr.

Key takeaways

Light elements come from the Big Bang, elements up to the iron peak from stellar fusion, and heavier ones from s- and r-process neutron capture; Li, Be and B come from spallation. CI chondrites define cosmic abundance, normalised to 10⁶ Si atoms.
Chondrites are unmelted (chondrules, matrix, CAIs, metal; petrologic types 1 to 6); achondrites, stony-irons and irons come from melted bodies. CAIs at about 4.567 Ga are the oldest solids.
Goldschmidt’s classes are lithophile, siderophile, chalcophile and atmophile. Substitution follows radius, charge and ionic potential; D = C(mineral)/C(melt) splits elements into compatible and incompatible, and batch melting gives C(L)/C₀ = 1/[D + F(1 − D)].
The Earth differentiated into a Fe-Ni core (about 32 percent of its mass), a peridotite mantle and a thin crust; siderophiles went to the core, Hf-W dates core formation to a few tens of millions of years, and a late veneer explains mantle platinum-group elements.
An isochron has slope e^(λt) − 1 and intercept equal to the initial ratio; it needs cogenetic, closed-system samples with a spread in parent/daughter, and a mixing line can imitate it. Rb-Sr: λ = 1.42 × 10⁻¹¹ yr⁻¹.
Crust has high Rb/Sr (high ⁸⁷Sr/⁸⁶Sr) and low Sm/Nd (negative ε(Nd)); the depleted mantle is the opposite. ε(Nd)(t) compares a sample with CHUR(t) in parts per 10⁴; concordia, discordia and Pb-Pb ages come from the two uranium chains. HIMU, EM1 and EM2 are enriched OIB reservoirs.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Which process produced most of the nuclei heavier than the iron peak, such as barium, gold and uranium?
1. Fusion in the cores of massive stars, which keeps releasing energy as heavier nuclei form
2. Neutron capture, in the slow s-process and the rapid r-process, followed by beta decay
3. Cosmic-ray spallation of interstellar nuclei, which builds the heavy elements up from smaller fragments
4. Big Bang nucleosynthesis during the first few minutes, when all stable nuclei were assembled
Show answer
Answer: B — Neutron capture, in the slow s-process and the rapid r-process, followed by beta decay
Beyond the iron peak fusion absorbs energy, so heavier nuclei are built by neutron capture in the s-process (slow, in AGB stars) and the r-process (rapid, in neutron-star mergers and some supernovae). Fusion in massive stars is the tempting alternative but stops at the iron peak. Spallation makes only Li, Be and B and gives fragments of lower mass, and the Big Bang made only H, He and traces of Li.
Which statement about CI carbonaceous chondrites is correct?
1. They are the most strongly heated chondrites, of petrologic type 6, and show a well-equilibrated texture
2. They contain abundant large chondrules set in a continuous network of Fe-Ni metal
3. Their non-volatile element abundances match the solar photosphere, although they contain no chondrules
4. They are melted basaltic achondrites derived from the asteroid Vesta and carry igneous textures
Show answer
Answer: C — Their non-volatile element abundances match the solar photosphere, although they contain no chondrules
CI chondrites are unmelted, water-altered (petrologic type 1) and, although they have no chondrules, match the solar photosphere for non-volatile elements, which is why they define the cosmic reference. The tempting error is that chondrite means chondrules present; type 6 would mean thermal metamorphism rather than aqueous alteration, and the HED achondrites come from Vesta.
A meteorite is composed of olivine crystals set in a continuous network of Fe-Ni metal and contains no chondrules. It is a:
1. pallasite, a stony-iron meteorite from a differentiated body
2. eucrite, a basaltic achondrite of the HED group
3. octahedrite, an iron meteorite with a Widmanstätten pattern of kamacite and taenite
4. H-group ordinary chondrite with chondrules replaced by metal during metamorphism
Show answer
Answer: A — pallasite, a stony-iron meteorite from a differentiated body
Silicate (olivine) mixed with Fe-Ni metal in roughly comparable proportions is the definition of a stony-iron, and olivine in metal is the pallasite. An octahedrite is the tempting alternative because it is also Fe-Ni, but it is metal only, with no olivine. A eucrite is a basaltic silicate rock with little metal, and an ordinary chondrite would show chondrules.
Which of the following meteorites come from parent bodies that melted and differentiated?
1. A eucrite of the HED group, a basaltic achondrite
2. An H-group ordinary chondrite of petrologic type 4, unmelted but thermally metamorphosed
3. An octahedrite iron meteorite, an Fe-Ni alloy
4. A CM carbonaceous chondrite, aqueously altered but unmelted
Show answer
Answer: A — A eucrite of the HED group, a basaltic achondrite; C — An octahedrite iron meteorite, an Fe-Ni alloy
Eucrites are igneous (basaltic) rocks from a melted body, and iron meteorites are the metallic cores of melted, differentiated bodies. Ordinary and carbonaceous chondrites are primitive: heating (type 4) or water (CM) altered them, but they never melted and kept their chondrules and near-solar composition.
Which element is strongly siderophile and is therefore depleted in the silicate Earth because of core formation?
1. Zirconium, a refractory element that forms very stable oxide and silicate minerals
2. Zinc, which prefers sulphide minerals such as sphalerite in ore deposits
3. Strontium, which substitutes for calcium in plagioclase and in carbonate minerals
4. Iridium, one of the platinum-group elements that alloy with metallic iron
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Answer: D — Iridium, one of the platinum-group elements that alloy with metallic iron
Platinum-group elements such as iridium have a very strong affinity for iron metal and went into the core, leaving the mantle strongly depleted. Zirconium and strontium are lithophile (they stay in silicates and oxides), and zinc is chalcophile, preferring sulphide rather than metal.
Olivine crystallises and is removed from a basaltic melt. How do the concentrations of Ni (compatible) and Rb (incompatible) change in the residual liquid?
1. Both rise, because every trace element is concentrated in the liquid as the crystals form and are removed
2. Ni rises and Rb falls, because the small Ni²⁺ ion is excluded from the olivine lattice while Rb⁺ fits it
3. Ni falls sharply and Rb rises, because Ni²⁺ replaces Mg²⁺ in olivine while Rb⁺ does not fit
4. Neither changes, because trace elements do not take part in crystal-melt equilibrium
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Answer: C — Ni falls sharply and Rb rises, because Ni²⁺ replaces Mg²⁺ in olivine while Rb⁺ does not fit
Ni²⁺ (about 0.69 Å) is close in size to Mg²⁺ (about 0.72 Å) and has a high D for olivine, so the liquid is stripped of Ni, while the large Rb⁺ ion has D close to zero and accumulates in the liquid. The idea that all trace elements rise ignores partitioning; the idea that Ni rises reverses the substitution rule.
A basaltic liquid crystallises a plagioclase-rich assemblage with bulk D(Sr) = 1.5 and bulk D(Rb) = 0.05. Use C(L)/C₀ = f^(D − 1), where f is the fraction of liquid remaining. When f falls from 1 to 0.5, the Rb/Sr ratio of the liquid:
1. stays constant, because both elements are lithophile and behave alike
2. rises by a factor of about 2.7, as Rb is enriched about 1.9 times and Sr falls to about 0.71
3. rises by a factor of about 1.9, which is the enrichment of Rb alone because Sr is left unaffected by plagioclase
4. falls by a factor of about 2.7, because the compatible element controls the ratio
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Answer: B — rises by a factor of about 2.7, as Rb is enriched about 1.9 times and Sr falls to about 0.71
Rb: 0.5^(0.05 − 1) = 0.5^(−0.95) = 1.93. Sr: 0.5^(1.5 − 1) = 0.5^0.5 = 0.707. The ratio changes by 1.93/0.707 = 2.73, about 2.7 times higher. Ignoring the loss of Sr gives only 1.9, which is the tempting slip; the compatible Sr leaves the liquid, so Rb/Sr cannot fall.
Which of the following statements about the Rb-Sr and Sm-Nd systems are correct?
1. Because Nd is more incompatible than Sm, a partial melt of the mantle has a lower Sm/Nd than its source
2. Old continental crust typically has a negative ε(Nd) together with a high ⁸⁷Sr/⁸⁶Sr
3. The depleted mantle has a higher Rb/Sr than CHUR, so it grows radiogenic Sr faster than the crust does
4. Sm-Nd ages are easily reset by weathering because Sm and Nd are among the most soluble elements in water
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Answer: A — Because Nd is more incompatible than Sm, a partial melt of the mantle has a lower Sm/Nd than its source; B — Old continental crust typically has a negative ε(Nd) together with a high ⁸⁷Sr/⁸⁶Sr
Melting concentrates the more incompatible partner (Rb, Nd) in the melt, so melts and crust have low Sm/Nd, which grows low ¹⁴³Nd/¹⁴⁴Nd and negative ε(Nd), and high Rb/Sr, which grows high ⁸⁷Sr/⁸⁶Sr. The depleted mantle has the opposite, a low Rb/Sr, so it grows Sr slowly. Rare earths are among the least mobile elements in weathering, which is why Sm-Nd is robust.
The silicate Earth carries a small excess of radiogenic ¹⁸²W compared with chondrites. Given that ¹⁸²Hf (half-life about 9 Ma) decays to ¹⁸²W, hafnium is lithophile and tungsten is moderately siderophile, what does this indicate?
1. Core formation was completed after ¹⁸²Hf had become extinct, so the mantle kept all of its radiogenic ¹⁸²W
2. A late veneer delivered ¹⁸²W-rich chondritic material to the mantle after the core had formed
3. Tungsten is lithophile and hafnium is siderophile, so Hf went into the core while W stayed in the mantle
4. Core formation happened while ¹⁸²Hf was alive: W went to the core and Hf stayed to make ¹⁸²W in the mantle
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Answer: D — Core formation happened while ¹⁸²Hf was alive: W went to the core and Hf stayed to make ¹⁸²W in the mantle
Hf stays in the mantle while W partly follows the metal, so the mantle acquired a high Hf/W ratio. If that happened while ¹⁸²Hf was alive, the mantle’s ¹⁸²Hf decayed to ¹⁸²W and left an excess, so the core formed within a few half-lives, tens of millions of years. Formation after extinction would leave no anomaly, which is the tempting reading, and chondrites are the low-¹⁸²W reference rather than the source of an excess.
Arc magmas are enriched in Ba and Sr relative to Nb and Ta. Which explanation is correct?
1. Slab-derived aqueous fluids carry the mobile LILE (Ba, Sr) but not the immobile HFSE (Nb, Ta), which stay in the slab
2. Ba and Sr are high field strength elements and are carried efficiently by slab-derived aqueous fluids into the mantle wedge
3. Nb and Ta are volatile elements that escape as gas during the eruption of the arc magma at the surface
4. Ba and Sr are siderophile elements added to the arc mantle by leakage from the core
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Answer: A — Slab-derived aqueous fluids carry the mobile LILE (Ba, Sr) but not the immobile HFSE (Nb, Ta), which stay in the slab
Large, low-charge LILE such as Ba and Sr dissolve readily in aqueous fluids released by the dehydrating slab, whereas small, highly charged HFSE such as Nb and Ta are immobile in them, giving the Nb-Ta trough of arc magmas. Ba and Sr are LILE, not HFSE, and they are lithophile, not siderophile; Nb and Ta are refractory and not volatile.
Two cogenetic whole-rock samples plot at (⁸⁷Rb/⁸⁶Sr, ⁸⁷Sr/⁸⁶Sr) = (2.0, 0.7290) and (8.0, 0.8010). Take λ(⁸⁷Rb) = 1.42 × 10⁻¹¹ yr⁻¹ and use the exact relation slope = e^(λt) − 1. The isochron age, in Ma to the nearest 10 Ma, is ____.
Numerical answer — type the value.
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Answer: 840
Slope = (0.8010 − 0.7290)/(8.0 − 2.0) = 0.0720/6.0 = 0.01200. Then t = ln(1.01200)/(1.42 × 10⁻¹¹) = 0.011929/(1.42 × 10⁻¹¹) = 8.40 × 10⁸ yr = 840 Ma. (The intercept 0.7290 − 0.0120 × 2.0 = 0.7050 is the initial ratio.) Using slope/λ instead of the exact logarithm would give 845 Ma, which is why the exact relation is specified.
A granite crystallised 2,000 Ma ago with an initial ¹⁴³Nd/¹⁴⁴Nd of 0.510252. For CHUR take the present ¹⁴³Nd/¹⁴⁴Nd = 0.512638 and ¹⁴⁷Sm/¹⁴⁴Nd = 0.1967, with λ(¹⁴⁷Sm) = 6.54 × 10⁻¹² yr⁻¹ and the exact form e^(λt). The value of ε(Nd) of the granite at 2,000 Ma, to the nearest whole number, is ____.
Numerical answer — type the value.
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Answer: 4
e^(λt) − 1 = e^(0.01308) − 1 = 0.013166. CHUR at 2,000 Ma = 0.512638 − 0.1967 × 0.013166 = 0.510048. ε(Nd) = (0.510252/0.510048 − 1) × 10⁴ = 0.000400 × 10⁴ ≈ +4.0, so 4. The comparison must be made with CHUR at the time of crystallisation, not with the present-day 0.512638, which would give a spurious large negative value.
A mantle source contains 0.50 ppm of an element whose bulk partition coefficient is D = 0.01. Using C(L)/C₀ = 1/[D + F(1 − D)] for batch melting with a melt fraction F = 0.10, the concentration in the melt, in ppm to one decimal place, is ____.
Numerical answer — type the value.
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Answer: 4.6
C(L)/C₀ = 1/[0.01 + 0.10 × (1 − 0.01)] = 1/(0.01 + 0.099) = 1/0.109 = 9.174. C(L) = 0.50 × 9.174 = 4.587, which rounds to 4.6 ppm. The shortcut 1/F = 10 (valid only for D = 0) would give 5.0.
A concordant zircon has a radiogenic ²⁰⁶Pb/²³⁸U atomic ratio of 0.30. Take λ(²³⁸U) = 1.55125 × 10⁻¹⁰ yr⁻¹ and the relation ²⁰⁶Pb/²³⁸U = e^(λt) − 1. Its age in Ma, to the nearest 10 Ma, is ____.
Numerical answer — type the value.
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Answer: 1690
t = ln(1 + 0.30)/λ = 0.262364/(1.55125 × 10⁻¹⁰) = 1.691 × 10⁹ yr = 1691 Ma, which is 1690 Ma to the nearest 10 Ma. Using 0.30/λ (about 1934 Ma) neglects the exponential and overestimates the age.
Field relations show that a granite crystallised at about 2,700 Ma, and its zircons lost lead in a single episode. They define a discordia with an upper intercept at 2,700 Ma and a lower intercept at 600 Ma on the concordia curve. What does the lower intercept date?
1. The crystallisation of the granite, since zircon begins to grow at the lower intercept
2. The present day, because lead loss is always a recent process
3. The single episode of lead loss, such as a metamorphic event, about 600 Ma ago
4. The age of the Earth, since every chord is extrapolated back to the origin of the curve
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Answer: C — The single episode of lead loss, such as a metamorphic event, about 600 Ma ago
For a single episode of lead loss from zircons of one age, the upper intercept gives the crystallisation age and the lower intercept dates the loss, here about 600 Ma ago. A lower intercept near zero would indicate recent or continuous loss, which is the tempting generalisation; the chord does not date the Earth, and zircon growth is dated by the upper intercept here.
Which conditions are required for a Rb-Sr whole-rock isochron to give the crystallisation age of a rock suite?
1. The samples are cogenetic and began with the same initial ⁸⁷Sr/⁸⁶Sr
2. The samples all have the same ⁸⁷Rb/⁸⁶Sr today, so that they plot as one tight cluster
3. The Rb-Sr system has stayed closed since crystallisation
4. The samples show a measurable spread in ⁸⁷Rb/⁸⁶Sr
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Answer: A — The samples are cogenetic and began with the same initial ⁸⁷Sr/⁸⁶Sr; C — The Rb-Sr system has stayed closed since crystallisation; D — The samples show a measurable spread in ⁸⁷Rb/⁸⁶Sr
A line needs points that are spread along it, from cogenetic samples with a common initial ratio that have behaved as closed systems. If all samples had the same ⁸⁷Rb/⁸⁶Sr they would plot as one cluster and no slope could be fitted, so identical ratios defeat the method rather than support it.