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ȭ - 5 ȭ (Isotope Geochemistry)
 
  5-1.
  5-2. ()
  5-3. 缺 Ҹ ̿
  5-4.
  5-5. к
 

5-3.缺 Ҹ ̿

    Ҵ ҾϿ رǾ ڿҸ . , ϼ () ڿҵ ԵǾ ִ. 츮 ݺ ̵ ҿ ڿ κ  ϼ ϴ 캸.

5-3-1. ر ݰ

1) ر

     P رϿ ڿD ٰ .

P -> D(R-5-3-1)

-> ǥõ  ȯ濡 ڿҰ D ٽ P ʴ Ÿ (̷ "񰡿 "̶ Ѵ), 츮 ִ ̴. (R-5-3-1) ӵ 翡 Ѵ. ,

-d[P]/dt [P](5-3-1)

Ŀ [P] P Ÿ ̸, տ - پ ̴. ϳ ʻ ̿Ͽ (5-3-1) Ʒ ٲ ִ.

-d[P]/dt = [P](5-3-2)

̶ (5-2) ʻ ر(decay constant) Ѵ. ر ־ ڿ- ¦ , µ з¿ ʴ´. (5-3-2) ϸ ´.

-d[P]/[P] = dt -->

ln([P]/[P]o) = -t

(5-3-3)

(5-3) ϸ Ʒ ر ´.

[P] = [P]oexp(-t)(5-4)

ر ڿ [D]* ϸ

[D]* = [P]o-[P](5-3-5)

̹Ƿ (5-3-4) ǥ ִ.

[D]* = [P]o(1-exp(-t))(5-3-6)

2) ݰ

    ݰ(half-life) ϴµ ɸ ð ǹѴ.

[P]=[P]o/2(5-3-7)

ҿð ǹϴ ̴. ݰ⸦ t1/2 ϸ, (5-3-3) (5-3-7)κ

t1/2 = ln(1/2)/ = 0.693/ (5-3-8)

Ʒ ǥ 5-3-1 ڿ ر ر ݰ⸦ ̴.

[ǥ 5-3-1] ڿ ر ر ݰ
() ر ر (a-1 ݰ() (%) ڿ
14C 1.21*10-4 5730 -- 14N
40K , EC 5.480*10-10 1.27*109 0.018 40Ca, 40Ar
50V , EC 1.16*10-16 6*1015 0.24 50Cr, 50Ti
87Rb 1.419*10-11 4.89*1010 27.85 87Sr
115In 1.39*10-15 5*1014 95.72 115Sn
123Te EC 5.78*10-14 1.2*1013 0.87 123Sb
138La EC, 6.3*10-12 1.1*1011 0.089 138Ba, 138Ce
142Ce ~1.4*10-17 ~5*1016 11.07 138Ba
144Nd 2.89*10-16 2.4*1015 23.85 140Ce
147Sm 6.54*10-12 1.06*1011 14.97 143Nd
152Gd 6.3*10-15 1.1*1014 0.2 148Sm
176Lu 1.98*10-11 3.5*1010 2.59 176Hf
174Hf 3.5*10-16 2*1015 0.18 170Yb
187Re 1.61*10-11 4.3*1010 62.5 187Os
190Pt 1*10-12 7*1011 0.013 186Os
232Th 4.990*10-11 1.39*1010 100 208Pb
234U 2.794*10-6 2.44*105 0.0055 206Pb
235U 9.8485*10-10 7.04*108 0.72 207Pb
238U 1.5512*10-10 4.47*109 99.28 206Pb

5-3-2.

1) ʱ ڿ 0 (Ǵ ׿ ϴ )

    , ̳ ϼ ÿ ڿҰ Ե ʾ Ǵ ڿҰ ر ̶, ̳ ϼ (5-3-6) ̿Ͽ ִ. (5-3-6) ٽ
[D]* = ([D]*+[P])(1-exp(-t))
(5-3-9)

(5-3-9) t ϸ,
t = ln(1+[D]*/[P])/
(5-3-10)

(5-3-10) Ǵ ð 뿬̴. ̷ ϴ δ 14C , K-Ar ִ.

14C

14C ַ ߿ ּ(cosmic ray)κ ߼(neutron; n) Ұ Ͽ :

n + 14N -> 14C + p + e-(R-5-3-2)

Ŀ p 缺(proton) ǹѴ. ̷ 14C Ҿؼ Ʒó ӵ ٽ 14N ٽ رѴ:

14C -> 14N + + + Q-(R-5-3-3)

Ŀ ߼(neutrino), Q ر ̴. ־ ǿ (R-5-3-2) (R-5-3-3) ̷ 14C Է ϰ ϸ, ̿ ռ ϴ Ĺ ü ռ ӵǴ 14C ϰ ȴ. ̴ Ĺ Ͽ ư 鿡 ־ ̸, ̸ ȭϸ κ źҸ ޾ Ǵ ( , ź꿰, ) ־ 14C Է ȴ. ׷ٰ, ̵ ( Ѵٴ, Ÿȴٴ ϸ) ̵ 14C Է ر ( R-5-3-3) ð پ ȴ. ̵ 14C ( ̷ ) ʱ Է Է ˸ (5-3) ̿Ͽ ִ. (5-3-3) Ͽ ϸ

t = (1/) ln(Ao/A)(5-3-11)

A 缱 , Ao ʱ 缱 ʱ 14C ϴ ϸ ȴ. Ao ׸ ȯ濡 ٸ ־ Ѵ.

K-Ar

40K ȹر 40Ar ׸ ÿ ر 40Ca رȴ. ڿ ӵ (5-2) Ͽ ǥ ִ.

d[40Ar]/dt = Ar[40K] (5-3-12)

d[40Ca]/dt = Ca[40K] (5-3-13)

⼭, Ar=0.581*10-10/a̸ Ca=4.962*10-10/a̴. (5-3-12) (5-3-13)κ

d[40Ca]/dt = (Ca/Ar) d[40Ar]/dt (5-3-14)

ȭ

d[40K]/dt = -(d[40Ar]/dt + d[40Ca]/dt)(5-3-15)

(5-3-15) (5-3-14) ϰ ϸ

d[40Ar] = -Ard[40K]/(Ar+Ca) (5-3-16)

(5-3-16) ϸ

[40Ar]-[40Ar]o = -Ar/(Ar+Ca)([40K]-[40K]o) (5-3-17)

Ar ü̹Ƿ ʱ 0̴ (,[40Ar]o=0). Ŀ (5-3-4) Ͽ ϸ ִ:

[40Ar] = Ar[40K](exp(t)-1)/(5-3-18)

Ŀ = (Ar+Ca)̴.

2) ó ڿҰ ϴ

    츮 ϰ ϴ -ڿ ¦ ڿҰ ϼ ú ԵǾ ִٸ  ɱ? мǴ ڿ ѷ([D]t) ó ϴ ([D]o) ر ؼ ([D]*) ̹Ƿ, ʱ ˸ (5-3-10) ̿Ͽ ̴. , ܼ 꿡 ؼ ʱ ڿ ˱ . ̸ ˱ ؼ ر ˾ƾϰ, ر ˱ ؼ ٽ ʱ ڿ ˾ƾ ϴ ȯ ̴.

    ذ 缺 ̵ Ұ ȭ ߿ к(fractionation) ʴ´ٴ ִ. ̳ ϼ ó κп ҿ ڿ Է ٸ ̴. ð ر Ǹ鼭 Ұ κп ڿҰ κп ڿҰ . ϼ ڿ ܼ ϸ  ⼺ ã Ұϴ. , ر Ǵ ڿҿ ڿ ر ([D]n) ([D]t/[D]n) 캸 ϸ ̾߱ ޶. ռ ٿ , 缺 Ҵ к , ʱ⿡ ̴.

[D]t=[D]o+[D]* (5-3-4) (5-3-6)κ 踦 ִ:

[D]t=[D]o+[P](exp(t)-1)(5-3-19)

纯 [D]n ָ Ʒ ִ:

[D]t/[D]n=[D]o/[D]n+([P]/[D]n)(exp(t)-1)(5-3-20)

(5-3-20) [D]o/[D]n Ǯ ÿ ´. ̷ ([P]/[D]n) [D]t/[D]n xy ׷ ϸ, ð ̷ Ǹ, ð(isochron)̶ θ. ð y κ [D]o/[D]n (exp(t)-1)κ (t) ִ. Ʒ ׸ 5-3-1 87Rb-87Sr ر ¦ ̿  ϴ Ÿ ̴.

[׸ 5-3-1]. 87Rb-87Sr ر ð.
(ó: http://www.tulane.edu/~sanelson/eens211/radiometric_dating.php)

Rb-Sr

弮 ϴ ȭ ȴ. Ʒ :

87Sr /86Sr =(87Sr /86Sr)o + (87Rb/86Sr )(exp(t)-1)(5-3-21)

Sm-Nd, La-Ce, Lu-Hf

Ca dz (ķ긮Ʊ) ȭ ַ ̿Ǵ ̴. ̵ Ʒ :

143Nd/144Nd =(143Nd/144Nd)o + (143Sm/144Nd)(exp(t)-1)(5-3-22)
138Ce/140Ce =(138Ce/140Ce)o + (/)(138La/140Ce )(exp(t)-1)(5-3-23)
176Hf/177Hf =(176Hf/177Hf)o + (176Lu/177Hf)(exp(t)-1)(5-3-24)

Re-Os

, ʿ⼺ ּ(molybdenite) ϼ ȴ. ϼ Re-Os Է м ־ Ǵ ƴϴ. Ʒ :

187Os/186Os =(187Os/186Os)o + (187Re/186Os)(exp(t)-1)(5-3-25)

U, Th-Pb

U̳ Th ϴ Ͽ ˾Ƴ ִ:

206Pb/204Pb =(206Pb/204Pb)o + (238U/204Pb)(exp(1t)-1)(5-3-26)
207Pb/204Pb =(207Pb/204Pb)o + (235U/204Pb)(exp(2t)-1)(5-3-27)
208Pb/204Pb = (208Pb/204Pb)o + (232Th/204Pb)(exp(t)-1)(5-3-29)

ġ ִµ, ڿҰ Ϻ ǵǾ (Ǵ Ұ ȭ Ǿ ) ɼ ִ. ̷ 缱 տ Ͼ. ̷ , ٸ - (Lead-lead method) õ ִ.

(5-3-27) (5-3-26) ָ,

{(207Pb/204Pb)- (207Pb/204Pb)o}/ {(206Pb/204Pb)- (206Pb/204Pb)o}=
(235U/238U){(exp(2t)-1)/(exp(1t)-1)}
(5-3-30)

207Pb/204Pb y 206Pb/204Pb x Ͽ ϸ ־ 235U/238U ̷, (5-3-30) Ⱑ ȴ. , (5-3-30) ɿ Ǯ ʴ´.

ʱ 缺 (ڿ) 0 ִٸ, Pb ǿ ſ Ȯ ִ. (ZrSiO4), Ʈ, ȸ ǥ ̷ ε, Zr+4 U+4̳ Th+4 ġȯ Pb+2 Ͽ ũ ̰ ʹ ġȯ ʱ⿡ Pb Է 0 ȴ.

ʱ ڿ 0 , (5-3-26) (5-3-27) ȴ:

206Pb*/238U = (exp(1t)-1)(5-3-31)
207Pb*/235U = (exp(2t)-1)(5-3-32)

(5-3-31) (5-3-32) ,

(206Pb*/238U)/(207Pb*/235U) = (exp(1t)-1)/(exp(2t)-1)(5-3-33)

(5-3-33) 캯 ɿ ؼ , Pb ٸ 207Pb*/235U x 206Pb*/238U y ϴ ׷ 뿬 ȭ ϳ  ̷ ȴ.  concordia θ. Pb , ׷ 󿡼 ñ⿡ ܵ Pb ٸ Ǵµ, ϳ ̷ ȴ. discordia θ. discordia ̷ , discordia concordia concordia ȴ. Ʒ ׸ 5-3-2 concordia dicordia ִ ̴.


[׸ 5-3-2]. 207Pb*/235U - 206Pb*/238U concordia, discordia.

ð

ϼ , () ð 鼭 رϿ ڿҸ . Ǯ(pool)κ ϼ ʱ ڿ ٴ ̹ Ͽ. ̵ ϼ ܺο , ҿ ڿ ٸ, ҿ ڿ ð Ⱑ Ŀ ׸ (5-3-1) ̷ ȴ.

׷ , ϼ ܺο ۿ ޾ٸ ϼ ڿ  ұ? ϼ ü ȭ ٴ ̴. , ۿ뿡 ϼ ڿ Ǹ, ð 鼭 ٽ ڿ ϰ ȴ. ̷ ϼ ü ɰ иϿ ٸ ̴ 찡 ְ ȴ. ü , ð(reequilibrium time Ǵ reequilibrium age)̶ Ѵ. Ʒ ׸ (5-3-3) ϼ ü  ٸ ִ ִ ̴

[׸ 5-3-3]. ϼ ð . ti ϼ ̸, tm ð̴.

5-4.

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