A suite of zircons from a metamorphic terrane

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth

Problem

A suite of zircons from a metamorphic terrane, disturbed once since crystallisation, gives three grains with

\bigl({}^{207}\mathrm{Pb}^*/{}^{235}\mathrm{U},\,{}^{206}\mathrm{Pb}^*/{}^{238}\mathrm{U}\bigr)

(10.22,\,0.4246)

(7.846,\,0.3407)

and

(4.282,\,0.2149)

. ((a)) Show that the three points lie on one straight line, and find its slope and intercept. ((b)) Using

X(t) = e^{\lambda_{235}t}-1

and

Y(t) = e^{\lambda_{238}t}-1

, find by bisection, to within

0.01\,\mathrm{Gyr}

, the two ages where this line meets concordia. ((c)) A field geologist reads only the middle grain's own

{}^{206}\mathrm{Pb}^*/{}^{238}\mathrm{U}

ratio as if it were a single closed-system date. Find the age this gives, and explain why it sits close to neither of the two real ages found in part (b).

Related theory

Nuclear Physics

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