Istpes Istpes Same Z, different A (variable # f neutrns) General ntatin fr a nuclide: 4 6C Reading: Winter, Chapter 9, pp. 67-80 Istpes Have the same Z but different A (variable # f neutrns) General ntatin fr a nuclide: 4 6C Superscript (n) specifies the different istpes f an element 2 C 3 C 4 C Stable Istpes Stable means they last nearly frever Chemical fractinatin is impssible Mass fractinatin is the nly istpic discriminatin pssible Oxygen Istpes 8 O and 6 O are the cmmnly used istpes and their rati is expressed as δ: 6 O 99.756% f natural xygen 7 O 0.039% 8 O 0.205% Cncentratins expressed by reference t a standard The internatinal standard fr O istpes is: standard mean cean water δ ( 8 O/ 6 O) = sample the result is expressed in per mille ( ) What is δ f? x000
What is δ fr meteric water? Evapratin seawater prduces water vapr Light istpes are enriched in vapr > liquid This is efficient since mass = /8 ttal mass δ = vapr x000 therefre ( 8 O/ 6 O) < Vapr thus δ cluds is (-) Relatinship between d( 8 O/ 6 O) and mean annual temperature fr meteric precipitatin, after Dansgaard (964). Tellus, 6, 436-468. Stable istpes are useful in assessing relative cntributin f varius reservirs, each with a distinctive istpic signature! O and H istpes Juvenile vs. meteric vs. brine water! δ 8 O fr mantle rcks surface-rewrked sediments Evaluate cntaminatin f mantle-derived magmas by crustal sediments Radiactive Istpes Unstable istpes decay t ther nuclides The rate f decay is cnstant, and nt affected by P, T, X Parent nuclide is the radiactive nuclide that decays Daughter nuclide(s) are the radigenic atmic prducts Istpic variatins between rcks, etc. due t:. Mass fractinatin (as fr stable istpes) 2. Daughters prduced in varying prprtins resulting frm previus event f chemical fractinatin K Ar by radiactive decay Basalt rhylite by FX (a chemical fractinatin prcess) Rhylite has mre K than basalt K mre Ar ver time in rhylite than in basalt Istpic variatins between rcks, etc. due t:. Mass fractinatin (as fr stable istpes) 2. Daughters prduced in varying prprtins resulting frm previus event f chemical fractinatin 3. Time The lnger K Ar decay takes place, the greater the difference between the basalt and rhylite will be Ar/ 39 Ar rati will be different in each 2
Radiactive Decay The Law f Radiactive Decay # parent atms dn N r dt dn dt = λn ½ ¼ D = Ne λt -N= N(e λt -) T calculate the age f a sample (t) if we knw: D the amunt f the daughter nuclide prduced N the amunt f the riginal parent nuclide remaining λ the decay cnstant fr the system in questin time The K-Ar System K decays t either Ca r Ar Ca is cmmn. Cannt distinguish radigenic Ca frm nn-radigenic Ca The apprpriate decay equatin is: eq 9-6 Ar = λe Ar + K(e -λt -) λ Where λ e = 0.58 x 0-0 a - (prtn capture) and λ = 5.543 x 0-0 a - (whle prcess) Ar is an inert gas which can be trapped in many slid phases as it frms in them Blcking temperatures fr varius minerals differ Ar- 39 Ar technique grew frm this discvery The - System On the rubidium side f the equatin: + a beta particle (λ =.42 x 0 - a - ) behaves like K, it cncentrates in micas and alkali feldspar 3
behaves like Ca Strntium Side It cncentrates in plagiclase and apatite (but nt in clinpyrxene) 88 : : : 84 Average sample yields 0 : 0.7 : : 0.07 is a stable istpe It is nt created by breakdwn f any ther parent Ischrn Technique Requires 3 r mre cgenetic samples with a range f / cncentratins 3 cgenetic rcks may be derived frm a single surce by partial melting, FX, etc. r 3 cexisting minerals with different K/Ca ratis in a single rck Recast age equatin by dividing thrugh by stable Begin with 3 rcks pltting at a b c at time t / = ( / ) + ( / )(e λt -) λ =.4 x 0 - a - Fr values f λt less than 0.: e λt - λt Thus eq. 9-5 fr t < 70 Ga (!!) reduces t: / = ( / ) + ( / )λt y = b + x m =This is the equatin fr a line in a / vs. / plt After sme time increment (t 0 t ) each sample lses sme and gains an equivalent amunt f At time t 2 each rck system has evlved new line Again still linear and steeper line t 2 c t a b c 2 t b 2 c a 2 b a 4
Ischrn technique prduces 2 valuable things:. The age f the rcks (frm the slpe = λt) 2. ( / ) = the initial value f / Figure 9-9. - ischrn fr the Eagle Peak Plutn, central Sierra Nevada Bathlith, Califrnia, USA. Filled circles are whle-rck analyses, pen circles are hrnblende separates. The regressin equatin fr the data is als given. After Hill et al. (988). Amer. J. Sci., 288-A, 23-24. Figure 9-3. Estimated and istpic evlutin f the Earth s upper mantle, assuming a large-scale melting event prducing granitic-type cntinental rcks at 3.0 Ga b.p After Wilsn (989). Igneus Petrgenesis. Unwin Hyman/Kluwer. 5