Question

11. Use equations (9.15), (9.22) and (9.23) to construct a concordia diagram for 3500 Ma of Earth history. Begin with 1000 atoms each of ²³⁵U and ²³⁸U at an initial time of 0 years, and increment time in 200 Ma increments, calculating N (the number of atoms remaining) and D* (the number of daughter isotopes = N_o-N) for both decay schemes at each increment. Then plot ²⁰⁷Pb/²³⁵U vs. ²⁰⁶Pb/²³⁸U to construct a concordia diagram.

Once you have a diagram, add the following points as a discordia:You can add the points in Excel by copying them, selecting the chart, and using Paste-Special as a new series. Draw a best-fit line through the discordia points and estimate the initial crystallization age and the metamorphic age.

207Pb/235U	206Pb/238U
5	0.240
10	0.355
12	0.400
15	0.470
17	0.520
19	0.560

Answer 1

Equations:

λ1=1.55125x10-10 años¯¹ λ2=9.84850x10-10 años¯¹

You calculate for each period of time and show the result in the next table:

Tiempo(Ma)	N207Pb	N206Pb	D*N207Pb	D*N207Pb	207Pb/235U	206Pb/235U
0	1000,0000	1000,0000	0,0000	0,0000	0,000	0,000
200	999,9998	1000,0000	0,0002	0,0000	0,218	0,032
400	999,9996	999,9999	0,0004	0,0001	0,483	0,064
600	999,9994	999,9999	0,0006	0,0001	0,806	0,098
800	999,9992	999,9999	0,0008	0,0001	1,199	0,132
1000	999,9990	999,9998	0,0010	0,0002	1,677	0,168
1200	999,9988	999,9998	0,0012	0,0002	2,260	0,205
1400	999,9986	999,9998	0,0014	0,0002	2,970	0,243
1600	999,9984	999,9998	0,0016	0,0002	3,834	0,282
1800	999,9982	999,9997	0,0018	0,0003	4,887	0,322
2000	999,9980	999,9997	0,0020	0,0003	6,169	0,364
2200	999,9978	999,9997	0,0022	0,0003	7,729	0,407
2400	999,9976	999,9996	0,0024	0,0004	9,630	0,451
2600	999,9974	999,9996	0,0026	0,0004	11,944	0,497
2800	999,9972	999,9996	0,0028	0,0004	14,762	0,544
3000	999,9970	999,9995	0,0030	0,0005	18,193	0,593
3200	999,9968	999,9995	0,0032	0,0005	22,372	0,643
3400	999,9967	999,9995	0,0033	0,0005	27,460	0,695
3500	999,9966	999,9995	0,0034	0,0005	30,405	0,721

You construct your Concordia Diagram and estimate the initial crystallization age and the metamorphic age

Tiempo (Ma)

207Pb/235U

206Pb/235U

1000

1,677

0,168

3200

22,372

0,643

The initial crystallization age is approximately 1000 Ma

The initial metamorphic age is approximately 3200 Ma