1.  A Few Definitions  Isotopes: ▪ iso (same) + tope (position) ▪ Elements having the same number of protons, but different neutrons ▪ Same elements with different mass ▪ 40 Ca, 42 Ca, 12 C, 13 C, 14 C, etc.  Isotones: ▪ Iso (same) + tone (pitch? pressure?) ▪ Elements having the same number of neutrons, but different protons ▪ 36 S, 37 Cl, 38 Ar  Isobars: ▪ Iso (same) + bar (weight or pressure) ▪ Elements having the same number of the sum of neutrons and protons ▪ Elements having the same mass ▪ 40 Ar, 40 K, 40 Ca

2.  Types of Isotopes  Stable isotopes: 12 C, 13 C  Unstable isotopes: 14 C, 235 U, 238 U  Radioactive isotopes: 14 C, 235 U, 238 U  Radiogenic isotopes: 206 Pb, 207 Pb, 208 U  Light isotopes: H, D, T, 12 C, 13 C  Heavy isotopes: 235 U, 238 U

3.  Radioactive Decay  Definition: tranforming nuclii from that of one to the other by decaying (transition) neutrons or protons in it.  Decay reaction is usually irreversible in nature  Is there any exception?  P (parent)  D (daughter)

4.  Mode of Radioactive Decay   (negatron): ▪ n  p + e ▪ Z  Z+1, N  N-1, A=no change ▪ 40 K --> 40 Ca + β -  Positron ▪ p  n + p (positron) ▪ Z  Z-1, N  N+1, A=no change ▪ 18 F --> 18 O + β +  Electron capture ▪ p + e  n ▪ Z  Z-1, N  N+1, A=no change ▪ 40 K --> 40 Ar + E.C.   ▪ Loss of 2p + 2n ( 4 He) ▪ Z  Z-2, N  N-2, A  A-4 ▪ 222 Rn --> 218 Po + α.

5.  Geological Application of Istopes  Radiogenic isotopes ▪ Age dating ▪ ellucidation of Geological history ▪ Identifying origin of materials ▪ Evaluation of epoch and provenance  Stable isotopes ▪ Tracing the sources ▪ Indication of the environment ▪ Geothermometry ▪ Hydrological application ▪ Evaluation of mixing processes

6.  Absolute Age Dating (Geochronology)  Decay equation ▪ For P  D ▪ -d[P]/dt = λ[P] ▪ [P] = [P] o exp(-λt) ▪ [D] * = [P] o -[P] ▪ [D] * = [P] o (1-exp(-λt))  Half life ▪ Time required to be [P]=[P] o /2 ▪ t 1/2 = ln(1/2)/λ = 0.693/λ

7. P Mode t1/2 Abund(%) D Decay constants and half lives of natural radioactive nuclides

8.  Age Dating ▪ When D o =0 ▪ [D] * = ([D] * +[P])(1-exp(-λt)) ▪ t = ln(1+[D] * /[P])/λ ▪ 14 C  n + 14 N -> 14 C + p + e -  14 C -> 14 N + β + ν+ Q -  t = (1/λ) ln(A o /A) ▪ K-Ar  d[ 40 Ar]/dt = λ Ar [ 40 K],  d[ 40 Ca]/dt = λ Ca [ 40 K]  d[ 40 Ca]/dt = (λ Ca /λ Ar ) d[ 40 Ar]/dt  d[ 40 K]/dt = -(d[ 40 Ar]/dt + d[ 40 Ca]/dt)  d[ 40 Ar] = -λ Ar d[ 40 K]/(λ Ar +λ Ca )  [ 40 Ar]-[ 40 Ar] o = -λ Ar /(λ Ar +λ Ca )([ 40 K]-[ 40 K] o )  [ 40 Ar] = λ Ar [ 40 K](exp(λt)-1)//(λ Ar +λ Ca )

9.  Age Dating ▪ When D o ≠0 ▪ [D] t /[D] n =[D] o /[D] n +([P]/[D] n )(exp(λt)-1) ▪ Rb-Sr ▪ Sm-Nd ▪ Os-Re ▪ U-Pb

10. ▪ Reequilibium age