Isochron Dating


(̼ũ )

Copyright © 1994-1998 by Chris Stassen
[Last update, September 17, 1998]

(׳ ˱ ϴ ʿ ߽ϴ.)

Ϲ 缺

缱 ´ 4 ̷ Ŀ 3 ؼ 4° ˾Ƴ ̴. Ʒ ȴ.

P(now) = P(orig) * 2 ^ ( -age / halflife )

:

age ؼ Ǯ ų ִ.

age = halflife * log2( 1 + { D[now] / P[now] } )

Generic ߻

ܼϰ ϱ ؼ ϰ ִ. ǿ ִ. ̰ .

̷ ʴ´ٸ ܼ Ʋ ȴ. ׷ ̷ ͵ ܼ ǹϰ ʴ´. 쿡 ־ ŵ ( ġ, Ȥ ȭ ) ̰ Ѵٴ ٰŰ ȴ. ׷ ̷ ִ ų Ȥ ̰ Ȳ ٸ ſ ɽ ؾ Ѵ.

̼ũй ̷ ϱ ؼ .

̼ũ

̼ũ 4 ʿϴ. ̰ 缱 ر ٸ ϹǷ ̷ . ( ϱ ؼ P D Di 缱 ر ( Ҷ Ҵ ̹Ƿ) ǥϰڴ. ϳ ÷ᰡ ƴ϶ ȥչ ٸ ÷Ḧ Ѵ. ( ٸ ϴ ϼ ϴ.)

׷ ׷ ̷ ȴ. X P/ Di̸ Y D/ Di. ̴. Rb/Sr ̼ũ ׷.

P = 87Rb; D = 87Sr; Di = 86Sr.
Figure 1. Example isochron plot.

 

̰  ǹΰ?

׸ Ʒ 谡 ִ.

  1. P Ҽ X ప Ŀ.
  2. D Ҽ Y ప Ŀ.

Figure 2. Meaning of the plot axes.

 

׷ ̰ ̰ (+) ٸ 谡 ִ.

  1. ÷ P Ŀ
  2. ÷ῡ Ե D/Di Ŀ.

ð 鼭 D Եǰų ʾҴٸ ȴ.

̼ũ ڷ ̴°

ϸ ̰ ȴ. ϼ ó Ƽ ü ϴٰ ׷ ϳ ̰ ȴ.

 

Figure 3. Global composition of the melt.

 

ϼ 鼭 ׵ ȭ ؼ ϰ ȴ. (ϳ ϼ 鼭 ׵ ٸ ȴٴ ) D Di ̹Ƿ ȭ ȴ*. ̷ ٸ ǰ D/Di ׻ ϰ ȴ. Y ȴ.

* ̾߱ ణ ܼȭ Ų ̴. ణ ȭ ٸ ִ. Ұ ȭ ִ. ̷ isotope fractionation Ѵ. ̷ ȿ ſ ģ. ̰ Ƹ 0.2% ̸ ִ. (̰ Ͼ ̰ ſ ̰ Ͼٰ ص ̰ ſ ̴.)

ݴ P ٸ ̱ Ǹ鼭 ٸ . ׷Ƿ D/Di ؼ ׻ ٸ ִ. ׷ ÷ x ٸ ȴ.

ϼ ʱ ¿ X ٸ Y ̵ Ÿ.

 

Figure 4. Differential migration of elements as minerals form.

 

"0." ǹѴ.*

* ȮϰԴ 0 . κ 쿡 ݰ 1/1000 0 . ( ̴.) Rb/Sr ̼ũй õ 0 ̵ ʴ´. ڵ ϴ õ̴.

ð 귯鼭 缱 ر ϾǷ P پ D þ ȴ. P پ D ϹǷ ̵ϰ ȴ. P پ D ̴ -1 ⸦ δ.

ر ÷ῡ Ͼ. ( P 20% رǾٸ ÷ῡ 20% پ. ׷Ƿ P Ҵ ÷ᰡ ׷ ̵ϰ ȴ. ð 鼭 ϰ dz ϰ ȴ.

 

Figure 5. Movement of data points as decay occurs.

 

 ()D/(ִ)P. ̸ ̰ "Dnow/Pnow" .

 

 ǻ

ȮǼ

ܼ ϳ ¾Ҵ ƴ Ȯ ִ .

̼ũй ٷ ȮǼ ٷ Ǿ ´ٴ ̴. ̰ ڷᰡ ̴ ȮǼ . ڷᰡ 󸶳 ̴° ȮѰ Ȯ ְ ȭ ֤. ̴ Ȯ ̴.

ؼ ϴ (ȸͺм) ˰ ʹٸ å ٶ.

(York) Gonick ξ ϴ. ̰ Gill's paper ٷ ȴ. Gonick ϱ 쳪 ʿ ٷ ʴ´. (1) ؼ X Y Ȯ ȭ (2) Ȯ Y Ȯ (3) ̼ũй ǹִ° Ȯϴ ׽Ʈ . ̷ ϱ ؼ ʿϴ.

 

Ϲ

ϱ ؼ Ȯ ϱ ؼ ʱ ¸ ˾ƾ ϰ Ѵ. ̼ũй ̷ ʾ Ÿ װ Ȯ ִٴ ̴. ܼ ̰ Ȯ ̼ũй ȮǼ Ȯ ִ.

 

Generic ϴ

⺻ κ ܼ ̼ũй ڴ.

ʱ Ұ

ʱ D "0" ʿ䰡 . D/Di Ŀ ö󰡱 ƹ Ű ʴ´.

P ٸ Y (ϼ ϳ ) ̰ ð ̴. ׷Ƿ Y D/Di Ÿ. ⸦ ʴ Y Ұ ̰ ð ʱ ̴.

ؼ Y ؼ ʱ D Ѵ ÷Ḷ ʱ ְ ܼ ̿ص ȴ. 翬 isochron ġϰ ȴ.

-

P ԰ ⿡ X ٲ ȴ.

 

effect of gain/loss of P on data points

Figure 6. Gain or loss of P.

 

⼭ ϰ ظ Ű ؼ data ʴ´. δ Ǵµ ͵̴. ߴµ ʴ´ٸ װ ÷ᰡ Ǿٴ ̴.

P Ѵٰ . P Di پ ٸ ̵ Ÿ ٸ ȴ.

 

effect of a loss of P in all samples

Figure 7. Loss of P in all samples

 

ҰԵȴ.

loss of P -

<non-colinear data">
Figure 8. Loss of P destroys the fit to a line.

 

ܼ 4 ְ 2 Ǿٰ ϴ Ʒ ȴ.

 

loss of P in two data points


Figure 9. Migration of parent in two data points.

 

2 DZ ؼ ʿ ŭ Ȯϰ ʴ´.

 

movement of other data points needed to restore colinearity


Figure 10. Specific loss of P required to yield a different colinear plot. The two samples must each change by the indicated amount -- no more and no less -- if the data are to remain colinear.

 

Note: Ⱑ 0 ſ Ưؼ Ұ ǵ 0׷ ̴. ٽ ؼ 0 쿡 ԰ ƹ Ű ʴ´. ڵ ϴ Ͼٰ ϴ 쿡 ƹ ʴ´ٴ ϰ ִ.

 

-

Rb/Sr ̼ũҹ 쿡 ϰ Ͼ ̵ 缺 ̴ (87Sr). Faure (1986, p. 123) ϱ:

κ, 缺 ر Ҵ Һ ٸ ̿ charge . Ư رǸ鼭 Ͽ ƴ̹ Ǹ ִ.

[...]
Ͽ ٸ 87Sr ̵ ־ٰ óص ȴ.

̷ ȭ ̵ϰ Ѵ.

 

effect of migration of D


Figure 11. Gain or loss of D.

 

P, ԰ ̰ ıѴ.

migration of radiogenic daughter usually destroys fit to a line


Figure 12. Gain/loss of D destroys fit to an isochron.

 

־ ̴ 찡 ִµ .

 

 

partial homogenization of daughter isotope


Figure 14. Partial homogenization of radiogenic daughter (in some exceptional cases) results in an apparently valid isochron of reduced age.

 

 

̷ Ͼٰ ؼ ڵ . (1) ̷ ſ Ͼ. (2) Ͼٰ ϴ 뺸 ȴ ̴.

׷ ̼ũй Ǽ °?

̼󿡴 . ̼ũй ʴ  찡 ִ. ̼ũй ߿伺 ʴ´ٴ ̴. ̼ũй ʴ 찡 ֱ ̰ ̼ũй ϴٰ ٰŰ Ǵ°? װ ƴϴ.

Ư ʸ

ʴ

̼ũй ϼ ÿ ϳ ȥչ Ѵ.

̰ ´ ƴ Ȯϴ ϴ. ̼ũй ü ̰ ƴ϶ (  ǹǷ) ġ 踦 켭 ִ.

̷ 䱸 ʴ´ٰ ϴ ִ. ߿伺 ̰ ȭ DZ ƴ϶ ̰͵ pool  ȴ. ǹ̴ ִ. ̰ μ ϴ ǹ̰ ִ ƴϴ.

ϼ (Ⱑ 0 ƴ ̴ ) ٸ µ Ҵٰ . µ P/Di .

 

old isochron annotated with melting temperatures


Figure 15. An old rock, minerals annotated with melting temperatures

 

ϼ ׸ 帧 ǥ鿡 ð ٸٸ ʱ⿡ ̰ ̴.

ϵ ƴϴ. ̵ ǰ ȥչ ð и ƴϴ.

ؼ Ʒ ׸ ٰ .

 

isochron plot of different flows

Figure 16. The isotopic composition of the various lava flows

 

Ͽ ٽ 鼭 ȴٰ Ʒ ̴.

 

mineral isochrons


Figure 17. Mineral isochrons (red) of the various flows give several different young ages.

 

̷ 뺸 ſ 븦 Ÿ ִ. ̷ inherited age ſ Ȯϰ صǰ 忡 öϰ ٷ ִ. ̰ ÷Ḧ ϰ ν س ִ.

ȭ ȭ лŲ. ̷ ü ϼ ʴ´ٸ ſ лǾ ְ ȴ.

 

scatter in inherited isochron


Figure 18. Data points of individual mineral samples show scatter due to chemical differentiation at the last time of melting.

 

 

2 ҽ ȥ

ΰ ϼ ȥյǾ 쿡 ִ.

ٸ 2 ̵ ִٰ .


Source
material

P
(ppm)

D
(ppm)

Di
(ppm)

P
---
D
i

D
---
D
i


A

18

37

39

0.462

0.949

B

10

17

11

0.909

1.545


Table 1. Composition of two sources

̼ũ ̾Ʊ׷ ׷ ִ.

 

data points for source material


Figure 19. Position of source material on an isochron plot.

 

̷ 2 ҽ ȥ ǰ ϳ ϼ Ǹ, 2 ÷ᰡ ȭ ȭġ ʾƵ ٸ ȴ. ̰ Ʒ 찡 ִ.


Sample
source

P
(ppm)

D
(ppm)

Di
(ppm)

P
---
D
i

D
---
D
i


A

18

37

39

0.462

0.949

¾ A + ¼ B

16

32

32

0.500

1.000

½ A + ½ B

14

27

25

0.519

1.080

¼ A + ¾ B

12

22

18

0.667

1.222

B

10

17

11

0.909

1.545


Table 2. Samples of a mixture, with varying portions of A and B in each.

̷ ̼ũ ׸ ׷ A B Ѵ.

plot of sources and result of mixing


Figure 20. Isochron plot of two mixed sources

 

ȥ ſġ ̴. A B پϰ ġ ֱ  ̶ ִ.

̷ ȥ Ǹ Ⱑ 0 ̰ų Ѵ. ࿡ ̼ũ ׸׷ȴµ Ⱑ ٸ ̰ ȥյǾ ؾ Ѵ. ׸ ̷ ϰ ´ٸ ǹ ȥչ̶ ǽؾ Ѵ. ׷ ׷ 찡 .

Դٰ κ 쿡 ȥ ̷ Ȯϴ ִ. װ Y ϰ X 1/(D+Di) ׷ ׸ ̴.

ڷᰡ ִٰ

 


Sample
source

P
(ppm)

D
(ppm)

Di
(ppm)

1
------
(D+D
i)
(ppm
-1)

D
---
D
i


A

18

37

39

0.0132

0.949

¾ A + ¼ B

16

32

32

0.0156

1.000

½ A + ½ B

14

27

25

0.0192

1.080

¼ A + ¾ B

12

22

18

0.0250

1.222

B

10

17

11

0.0357

1.545


Table 3. Data for mixing plot

׸ Ÿ.

plot to test for mixing, mixing detected


Figure 21. Plot to detect mixing.

 

̰ ȴٸ ̼ũ Ƹ ȥչ ̰ ǹ̰ ̴.

δ ȥյ data ſ  ׸. Faure (1986, Equations 9.5 through 9.10 on p. 142) Ȯϰ ؼ ϸ ȥչ 쿡 ̰ ȴ.

׷ ׷ ʴ´ٸ

 


Figure 22. Mixing plot, detecting no mixing.

 

... ̼ũ ȥտ ƴϴ. ְ ȴ.

 

Zheng's

ֱٿ  Ϻ âڵ Zheng (1989), ִ. ġ ڵ ȽɽŰ ̼ũй Ȯϴٰ ϴ δ. Rb/Sr ̼ũй ̷ ߻ ˷ ʸ ٷ ִ.

忡 ʴ´.. Zheng ̼ڷ ߸ ɼ 4 ߴ.

  1. Protracted fractional crystallization
    ̰ õⰣ ľ 츦 Ѵ. ̰ ڵ鿡Դ Ұϴ. ̰Ϳ ̴ ſ . ̰ ʷ ִ (first entry in Table II on p. 14), (437 ± 10 Ma) μ (415 ± 10 Ma) ū ̰ .
  2. Inherited ( κи )
    ̹ ռ ߴ. ̷ ̱ ؼ ſ Ư Ȳ ƴϸ ȴ.
  3. Mixing isochron
    ̰͵ տ ٷ. ̰ κ mixing plot test Ȯ ִ.
  4. ۿ ̼ũ
    տ ٷ. ̰ ϼ ٽ ޾Ƽ ̼ũ ̰ Ǵ ̴. ̰ ڵ ޾Ƶ ̴.

̻ Ϻ ̼ũй ִ ̰͵ ڵ ݵǴ ̴.

̼ũй

̼ũй ߸ 븦 Ű  ִ. ѹ Ȯ ٸ 9 źְ ֱ Ȯ ִ.

  1. ߰ ڷ ׽Ʈ ( mixing test)
  2. ȭ ٸ Ҹ ̿
  3. ÷ᰡ

Brent Dalrymple ϱ:

κ ߸ safeguards standards ݺ ɷ ִ. Ϻδ ǥ ˾Ƴ ִ. ؼ 缺 ź ִ ׻ ׷ ƴϴ.

[...]
ɼ , ׸ 츮 ʾҴ ִ.
(1992, p. 1)

Gill

ֱٿ Gill (1996) creationist technical literature ߴµ ű⼭ ״ Rb-Sr ischron ages ߸ 踦 Ÿٰ ߴ. ʷ .

A mathematical answer is presented for the frequent occurrence of false of "fictious" Rb-Sr isochrons. The reason for these inconsistencies is that a simple linear regression procedure is mathematically invalid if two or more independent variables influence a single dependent variable. In many data sets for the "isochron" procedure, there are two independent variables involved. First, there is the desired radioactive relation between the amount of the rubidium parent and the strontium daughter. Second, since the atomic strontium concentration in the samples is a variable, then the isotopic Sr-87 content of the atom [sic] is also a variable. In such a situation, the "Isochron" regression is mathematically invalid, so both its slope and intercept are erroneous.

࿡ 1 Ӻ 2 شٸ 1 ȸͺм ǹ̰ ȴ. ̼ũ ־ ڷ 2 ϰ ִ. ù ° ǹ̰ . ҿ Ұ ° ÷ ƮƬ Է ̴. ׷ٸ Sr-87 ̴. ̷ Ȳ̶ ̼ũ ȿ ̰ ⳪ ̴. (ǹ̸ ϰ )

ִ о ٶ. ϴ Rb-Sr ٴ âڵ 忡 ũ 4 ִٰ Ѵ..

1. Ͱ ȭ :

̼ũ ڷ ε ִ ȭ ޴´. ̷ ó ͸ ٷ. ׷鼭 ȿ ȭ ͵ Ѵ. ׸ ȭ Ұ ġ ϸ鼭 ߸ п ̸ ȴ.

86Sr 87Sr 󵵰 ̶ Ѵ.

и divisor [86Sr] ̻  ܼ 赵 ʴ´. No such simple [...]
̿ؼ ȸͺм Ѵٸ ̸ Ұϰ ų ̴.

̰ ٽ Ǵ κ̴. Ȯ ʴٸ ġ Ʋ ȴ. ̹ տ Ҵ ϼ ( 쿡 ſ ª ð) õ ҵ Ӱ ̵ϰ Ǹ ϰ ȴ. ̷ ϰ ȴٸ ̻ 86Sr 87Sr ʰ ׷ .

2. Ǵ Rb-Sr :

ſ Rb-Sr ̼ũ 밡 ߸ ַ ̶ Ѵ.

ǽɽ Rb-Sr ̼ũ 볪 Ȥ Ұ 븦 ư ִ. Woodmorappe (1979, pp. 125-129) ؼ 65 ư , Fause (1977, pp. 97-105) 7 "fictitious" ̼ũп ؼ ϰ ִ. Zheng (1989, pp. 15-16) 42 οϰ ִ..

Ʋ ̴. ߸ ̼ũй Ϲ Ͼ ȥ ̴(ٿ ϸ Faure 7 ̷ ̴.) ׷ ȥ ϸ 󿡼 ŵ ִ. ִ Ϳ û ڷ 츮 ϴ Ϲ帧 ſ ġϰ ¾ ȴ.

Rb/Sr ̼ũ Ǿ, 츮 Ϻ ߸ ڷḦ . ߸ ڷ ſ ̸, װ ̿ ǥϴ ̴. ϴ ڷ ȥ Ͼ ̰ ʹ  ɰϰ ʿ䰡 .

츮 Rb-Sr ̼ũ 󸶳 ߸ ˾ƺ ؼ (1) mixing ׽Ʈ (2) data 4 ̻ (3) پ 踦 ̴ ľؾ Ѵ. ̰ Rb-Sr ̼ũп ؼ ǽϴ Ϻ ڷῡ ؼ ִ.

Brent Dalrymple (1991, Chapters 5 and 6)  ؼ Rb-Sr ̼ũ 븦 ߴ. ̰ ſ ׽Ʈ ڷ̴. ֳϸ (1) ſ ܼ 縦 ͵̸ ؼ ϰ (2) ÷ ƴϱ ̸, âڵ ϴ ʴ ڷ ̴.

3. Gill's ʵ ̴

ϳ ʸ ٷ. ̰ ſ ̴. ״ 4 2 ϰ ְ 2 ʿ ִ ٷ.

̰ Ģ 2 ׷ ڷ̴. ׸ 2׷ ڷ  ǹ̿ Ѵ. 󿡼 ϴ. ڷ鿡 ־ ó 2 ʰ ó data 4 ų Ȥ ٸ ⸦ ϱ ξ δ.

 

4. Gill ϰ ִ ̼ũ 򰡱 Ѵ.

ܼ ȸͺм ̼ũй ϴ ƴϴ. ϴ ؼ ſ ȮѴ. ̱⿣ ̶ ϴ ̰ ̼ũ ȿϴٰ .

ʴ װ ̶ ϱ . ֳϸ ƴ϶ ׳ ̱ ̴. 0.993 ſ δ. ̰ͺ ͵ (0.997-8) ִ.

 

talk.origins

Ʒ ̼ũп ִ ִ. ̸ ʾұ ʾҴ.

  1.  缺  ر Ͱ ִ 87Sr ִ°??

    Rb/Sr ̼ũй ־ 87Sr 86Sr ʿ䰡 ϴ. ̰ ̼ũ Y μ ֽϴ. ڷ ̷ ִٸ ˾Ƴ Դϴ.

  2. ̼ũ ? ΰ? ΰ? ƴϸ ׷ΰ?

    ̼ũ ѽð Ÿ ִ data (set) մϴ. (̼Ҵ ٴ ǹ̰ ũ ð̶ ǹԴϴ. ũ̶ ̷ ϴ ϰ ֽϴ. ̼ũ̶ θ⵵ մϴ. ̼ũ Ÿ ׷ plot ̼ũ ̾Ʊ׷ Ȥ ̼ũ plot̶ մϴ.

    ̷ plot ̿ϴ ̼ũ ̶ ϰ ̱ۿ ̼ũ ̶ ̼ũ ϴ ϰ ֽϴ.

    ̼ũ ҿ ֽϴ:


    P

    D

    Di

    half-life (*109 yr)


    87Rb

    87Sr

    86Sr

    48.8

    40K *

    40Ar

    36Ar

    1.25

    147Sm

    143Nd

    144Nd

    106

    176Lu

    176Hf

    177Hf

    35.9

    187Re

    187Os

    186Os

    43

    232Th *

    208Pb

    204Pb

    14

    238U *

    206Pb

    204Pb

    4.47


    * Most dating with these isotopes is not performed via the exact isochron methodology described here.

    Table 4. Isotopes used for isochron dating

  3.  ݰ⸦ մϱ ?  Ҵ 600 Ǿ ر Ǵµ. ر  ð Ȯϰ ֽϱ?

    ݰ⸦ ϴ ð ϴ ƴմϴ. Davis et al. (1977) 87Rb (48.9 ± 0.4 billion years) ر 19Ⱓ ȿ ߽ϴ.

    ȮǼ ϰ Ǵµ ð̶ ð ſ ª ð̶ ݰ⸦ ݰ 1/1015 ̰ и׷ Ұ 1018 ڸ ٴ ð ƴմϴ..

    ſ ݰ⸦ Ҷ ر Ͼ ſ մϴ. ÷Ḧ Ȯϰ ִٸ ر Ͼ ſ ϰ ֱ ݰ ſ Ȯϰ մϴ.

     

  4. 츮 ÷ ̴ ҿ ׻ ٴ ݴϴ. [...]
    ׷ ϼ Ǹ ҿ Ұ Ǹ鼭 ̰͵ 񱸷 ϰ ȴٸ 츮 ̼ũ ϰ ( X ϳ)̰ ÷ ̸

    ̼ũй (P) r (D) ؼ ׸ٸ ½ϴ. ׷ P/Dv D/Di ؼ ׸ϴ. Di ٸ P D ؼ ׸ Ÿ ʴ ̼ũ Ÿ Դϴ.

     ٸ P/Di ޶ ½ ذ ˴ϴ. P Di ٸ ȭ ǹǷ  P ְ ݴ밡 ֽϴ. ̰ ٷ ÷Ḷ ٸ X ִ մϴ.

    ׷ ϼ  D/Di ٸ ִ ذ ʽϴ. ̰ ٷ ̼ũй ߰ߵ ε, ⸦ ٸ ⿣ (1) D (2) P ̿ 谡 ֽϴ. ̰ D P ؼ Ǿ Դϴ. ̷ 谡ٷ ÷ ̸ ˷ְ ÷ᰡ Ǿ° ݴϴ.

     

  5. ࿡ κ ϰ ̰ ÷ᰡ θ Ǿ ִٸ ...õ ر ٸ, ̼ũ ϰ Ÿ ƴѰ?

    Ÿ Ȳ 븦 Ÿ մϴ. P (D Di) ȭ и Ͼ ʴ´ٸ Ѱ ǰ δ ϴ.

  6. ࿡ ڵ ÷ᰡ Ǿٰ Ǹ  ϳ?

    ̸ ϴ ƴϸ ϰ װ ǥϴ 鸮µ ׷ ʽϴ.

Further Reading

An excellent semi-technical introduction to isotope dating methods (with an emphasis on isochron and Pb isotope dating) is available in Dalrymple (1991). I highly recommend this text. It is accessible to those who haven't studied the field, and has even received reasonably positive review in creationist literature. Isochron methods are introduced in a section titled "Age-Diagnostic Diagrams" (pp. 102-124).

For those who don't mind wading through a college-level textbook on isotope dating, I also highly recommend Faure (1986). It is the standard text on the entire field, and includes a large number of references to the primary literature. And, like Dalrymple's book, it has also received reasonably positive review in creationist literature. Isochron methods are first introduced in Chapter 6 (specifically pp. 72-74). More detailed treatment is given in Chapter 8, and Chapter 9 is an extended treatment on mixing.

References

Dalrymple, G. Brent, 1991. The Age of the Earth. California: Stanford University Press, ISBN 0-8047-1569-6.
Back to the reference to this work

Dalrymple, G. Brent, 1992. Some Comments and Observations on Steven Austin's "Grand Canyon Dating Project". Unpublished.
Back to the reference to this work

Davis, D.W., J. Gray, G.L. Cumming, and H. Baadsgard, 1977. "Determination of the 87Rb decay constant" in Geochim. Cosmochim. Acta 41, pp. 1745-1749.
Back to the reference to this work

Faure, Gunter, 1986. Principles of Isotope Geology (Second Edition). New York: John Wiley and Sons, ISBN 0-471-86412-9.
Back to
contamination, questions, or further reading

Gill, G.H., 1996. "A Sufficient Reason for False Rb-Sr Isochrons" in Creation Research Society Quarterly 33, pp. 105-108.
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Gonick, Larry, 1993. The Cartoon Guide to Statistics. New York: HarperPerennial, ISBN 0-06-273102-5.
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