Isotopes

1. Isotopes • Atom of an element that has the same number of protons but different number of neutrons, thus they have different atomic masses. • Isotope means “at the same place” (Greek isos topos). and it was first used by Margaret Todd • Two kinds: • Stable (e.g., O2 = 16O, 17O, 18O) • ~79% of nuclides on Earth are stable (out of 339 natural) • Unstable (e.g., radiogenic such as 26Al)

2. Isotopes - Stable • Three isotopes: 16O, 17O, 18O of which 16O is the most abundant at 99.762%. • They are typically expressed in , which are deviations in part per thousand (permil, ‰) in the 17O/ 16O and 18O/ 16O ratios of a measured composition referenced from a standard (typically SMOW, Standard Mean Ocean Water) with 17O/ 16O = 0.0003829 and 18O/ 16O = 0.0020052.

3. Isotopes - Stable • 17OSMOW = [(17O/ 16O )sample / (17O/ 16O)SMOW -1] x 1000 • 18OSMOW = [(18O/ 16O )sample / (18O/ 16O)SMOW -1] x 1000 • Or:17O = ([(17O/ 16O )sample - (17O/ 16O)SMOW]/ (18O/ 16O)SMOW) x 1000 • 18O = ([(18O/ 16O )sample - (18O/ 16O)SMOW]/ (18O/ 16O)SMOW) x 1000 • Thus, positive  values indicate enrichments of a sample in that isotope relative or compared to SMOW, whereas negative values imply depletion of those isotopes in a sample relative to SMOW.

4. Isotopes - Stable • Isotopes fractionate between sources: • Exchange reactions that redistribute isotopes of an element among different molecules containing that element. • Unidirectional reactions where rates of reactions depend on isotopic compositions of the reactants and products. • Physical processes that produce concentrations or temperature gradients in which mass differences com into play (e.g., evaporation, crystallization, diffusion, etc.).

5. Isotopes - Stable • They are commonly expressed graphically on an oxygen three-isotope (18O vs 17O) diagram. Material related to SMOW by mass fractionation fall on a nearly linear curve on this graph described by the equation: • 17OSMOW ~ 0.52 18OSMOW • Typically the equation is treated as an equality with mass fractionation shown as a straight line with a slope 0.52. • Terrestrial Fractionation Line (TFL or TF). • Isotopes fractionate based on their vapor pressure and kinetic effects that typically follow Rayleigh distillation: R/Ro = f(-1) where R is the a ratio (18O/16O ) of the remaining vapor, Ro is the ratio (18O/16O) of a vapor before condensation begins, f is the fraction of the vapor remaining, and  is the isotope factionation factor (which is an equilibrium approach).

6. Isotopes - Stable • Non-mass-dependant variations, which do not fall on the TF are described with the parameter 17O, which is essentially deviations from the TF but are parallel to the TF. These are defined by: 17O = 17OSMOW - 0.52  x 18OSMOW • Methods of analysis: Use of mass spectrometer. • Fluorination of bulk material • Laser fluorination (in situ) • Secondary ion mass spectrometry (in situ)

7. Isotopes - Stable • When a nuclei of an unstable atom undergoes spontaneous transformation that involves the emission of particles and radiation energy. • The Z and N of the original or parent atom or isotope is changed leading to its transformation to another isotope. • Alpha (), beta (), and/or gamma ().

8. Radiogenic Nuclei • Here we refer to decay and radioactive atoms. • Simply stated, a nuclei of an atom spontaneously transforms because it is not energetically stable through a process of the emission of particles and radiant energy. • A radioactive atom decays, which results in changes in Z (# of protons) and N (# of neutrons) of that parent atom to produce a daughter atom/element that is new. • Three different types of rays or decay mechanisms, alpha (particle with 2 protons and 2 neutrons), beta (electron emission), and gamma (electromagnetic energy-same element).

9. Radiogenic Nuclei • N = N0e-t (# of parent atom at time, t) • N = radioactive parent atoms, N0 = original number of atoms present at t = 0. • D* = N0(1- e-t) • Number of stable radiogenic daughter atoms (none lost or gained, none present at t = 0). The term  = decay constant. • T1/2 = (ln 2)/ = 0.693/l (half-life and decay constant).

10. Radiogenic Nuclei • Discussion of decay typically refers to the time required for one-half of a given number of radionuclide to dcay, which is termed half-life (T1/2): • T1/2 = (ln 2)/ = 0.693/  (half-life and decay constant). • Another means of discussing and quantifying decay is through the mean life of a radioactive species: •  = 1/  • The mean life is longer than the half-life by the factor 1/0.693.

11. Radiogenic Nuclei • For the method to produce ‘ages’ the following criteria must be understood: • The system must not have gained or lost either parent or daughter atoms, it must be a closed system. • We must determine a realistic value of Do. • The value of the decay constant must be known accurately. • The determination of D and N must be accurate and be representative of the sample to be dated. • In the case of Solar System materials the isotope in question is assumed to be heterogeneous within the rock-forming region of the disk.

12. Radiogenic Nuclei

13. Radiogenic Nuclei

14. Radiogenic Nuclei • Cosmogenic radionuclei: • These are produced from atoms that have been hit by a high-energy particle or a cosmic ray produced by the Sun or by galactic or extragalactic objects. • ~ 90% are protons • ~ 9% are helium nuclei (alpha particles) • Rest are electrons • Reactions occur in atmospheres, asteroids, etc. • 10Be, 14C, 26Al, 32Si, 36Cl, 39Al, 53Mn, 59Ni, 81Kr.