Geochemistry & Isotope Geology

Geochemistry & Radiometric Dating

Goldschmidt's element classification and radioactive-decay dating — how chemistry and isotopes read the age and source of rocks.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Goldschmidt's classification groups elements by affinity: lithophile (silicate-loving), siderophile (iron-loving, e.g. Ni, Co, Au), chalcophile (sulphide-loving) and atmophile (gaseous). Radiometric dating exploits the constant decay of unstable isotopes: the parent decays exponentially

N = N_{0} e^{- λ t}

, with half-life

T_{1/2} = ln 2/ λ

. Measuring the daughter/parent ratio yields the age

t = \frac{1}{λ} ln (1 + D / P)

. Different clocks suit different ages:

^{14}

C (5730 yr) for the late Quaternary; U–Pb, Rb–Sr and K–Ar for deep time.

The Core Formula Matrix

Decay:

N = N_{0} e^{- λ t}

λ = ln 2/ T_{1/2}

.

Remaining fraction:

N / N_{0} = (1/2)^{t / T_{1/2}}

.

Isochron age:

t = \frac{1}{λ} ln (1 + \frac{D}{P})

.

Partition coefficient:

C_{so l i d} = K_{D} C_{m e l t}

The ‘IIT Traps’

⚠
Decay constant vs half-life. $λ = ln 2/ T_{1/2}$ — they are not equal.
⚠
** $^{14}$ C is short-lived.** It dates ≤ ~50 ka, not millions of years.
⚠
Low initial Sr = mantle. High initial $^{87}$ Sr/ $^{86}$ Sr signals crustal contamination.

📚 Standard references

Geochemistry — William M. White
Using Geochemical Data — Hugh R. Rollinson

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

In Goldschmidt's classification, iron-loving elements (Ni, Co, Au) are termed

Q2MEDIUM2 Marks · NAT

A system with half-life

1250

Myr decays for

2500

Myr. The fraction of parent remaining is _____.

Q3HARD2 Marks · NAT

A mineral has daughter/parent ratio

D / P = 1

for a system of half-life

1250

Myr. Its age is _____ Myr.

Myr