Geochronology - The Solid Earth - page 248

in order to understand their history. This concordia/discordia method provides a
wayofdating altered rocks.

6.4.2 Isochrons: U-Pb and Pb-Pb
Lead isotopes 204, 206, 207 and 208 all occur naturally, but only 204 Pb is non-
radiogenic. Equations (6.31)-(6.34) assume that all the lead present is a decay
product of uranium. However, we can normalize the equations and correct for an
initial, unknown amount of lead, in the same manner as for initial strontium in
the rubidium-strontium method:
206 Pb
204 Pb

206 Pb
204 Pb

0 +

238 U
204 Pb

now =

(e λ 238 t

− 1)

now

207 Pb
204 Pb

207 Pb
204 Pb

0 +

235 U
204 Pb

(6.36)

(e λ 235 t

now =

− 1)

now

Thus, uranium-lead isochrons can be plotted in exactly the same manner as for
rubidium-strontium. This method can fail because extensive losses of uranium
can occur in certain geochemical settings (Fig. 6.4(b)).
Taking the ratio of Eqs. (6.36)gives
207 Pb /

204 Pb now − 207 Pb / 204 Pb 0

235 U
238 U

e λ 235 t

− 1

204 Pb] 0 =

[ 206 Pb /

204 Pb] now −

[ 206 Pb / e λ 238 t − 1

now

e λ 235 t 1

137 . 88

− 1

= (6.37)

e λ 238 t − 1

This is the equation of a straight line that passes through the points
206 Pb
204 Pb

207 Pb
204 Pb

and

0 0

and has a slope of

1
137 . 88

e λ 235 t − 1

e λ 238 t − 1

Thus, plotting [ 207 Pb

204 Pb] now gives a straight line, a
lead-lead isochron (Fig. 6.4(c)). A lead-lead isochron yields a reliable value for
t provided that all the samples have the same initial isotope ratios and were closed
to uranium and lead at least until recent time. Lead-lead methods are commonly
used for dating granulites and limestones.

204 Pb] now against [ 206 Pb

/ /

6.5 Thorium-lead
Applying Eq. (6.11)tothe thorium-lead decay ( 232 Th- 208 Pb) gives
[ 208 Pb] now = [ 232 Th] now (e λ t

− 1)

(6.38)