20) isotopes and radioactive decay

stable vs unstable isotopes, and applications

stable: don’t change over time, isotope thermometry, tracers

unstable: change into diff elemetn over time through radioactive decay, geochronology, tracer

elemental fractionation

controlled by size and charge
controlled by partitioning into diff minerals, meaning controlled by compatibility
compatibility is controlled by size and charge

isotopic fractionation

controlled by difference in mass

ionic radius is the same, same number of electrons, diff neutrons.

much smaller influence than elemental fractionation. during natural process, there is sometimes a slight preference for a material to incorporate a heavier isotope than a lighter one

relative mass difference between 16-17 and 16-18, twice difference
fractionates the isotopes by twice the amount
if we change 18/16 ratio by 2 units, the 17/16 ratio will change by 1 unit
slope is 0.5 = mass dependent fractionation line

relative mass difference of heavy elements is smaller, so isotopic fractionation will be smaller to (1/87 vs 1/86)

temperature influence of isotope fracitonation

increasing temperature means mass difference matter less due to flexibility of sites
at a certain temp they will have the same isotopic composition

low temp = larger fractionation

3 important points about isotope fractionation

mass dependent
effects are larger for bigger relative mass differences between isotopes
effects are stronger at lower temperatures

why does radioactive decay occur? extra info

unstable nuclides are in a higher energy state
band of stability is at the bottom of an energy valley
its an attempt of unstable nuclide to become more stable by getting rid of extra energy

radiogenic: generated by a radioactive isotope, daughter of parent isotope
decay rate is dependent on the energy state of the nuclide
independent of pressure, temp, and chem composition

types of radioactive decay

beta, positron, electron capture, alpha, nuclear fission

details on beta decay

neutron converted to a proton and beta- particle (negatron)
1 less neutron, 1 more proton
diagonally up-left

details on positron decay

proton converted to neutron and beta+ particle (positron)
1 less proton, 1 more neutron
diagonally down-right

details on electron capture decay

proton capturing an electron from orbital changes into neutron
1 less proton, 1 more neutron
diagonally down-right

details on alpha decay

alpha particle ejected from nucleus
mass number decreases by 4, number of protons decreases by 2
diagonally down-left skipping a box
Q is total alpha decay energy

details on nuclear fission

heavy nuclide breaking into smaller nuclides and energy

what’s important about K40

can decay to 2 different daughters
using positron decay (Ca40), or electron capture decay (Ar40)

know this a little bit

blue is beta+ or electron capture
red is beta–
yellow is alpha decay
green is spontaneous fission

details on gamma ray

gamma rays aren’t a radioactive decay mechanism, but they are released when decay occurs in any mechanism

what is a decay chain

when a parent decays to a stable daughter product through intermediate daughter nuclides that are also radioactive
U238 all the way to Pb206: first is alpha, then beta-, then again beta-, then a bunch of alpha decays to Po or Pb206

explain the basic radioactive decay eqtn

D: amount of daughter isotope you measure in a mineral today
D0: initial daughter, amount of daughter that was originally present in teh mineral or rock at the time of formation
N0: number of parent atoms (radioactive)
N((e^lam*t-1) daughter produced by radioactive decay, N: number of parent isotopes, lam: decay constant, T: time of formation of mineral/rock

reference isotope info

want one with reasonable abundance, semi-close to the one you are looking at
not too abundant

explain methods of radiometric dating using the equation

assume D0 is zero, assume no daughter isotope was taken in at formation
K40→40Ar Ar is noble gas, typically minerals don’t take it in, we can assume any Ar formed was from radiogenic decay

isochron method

explain isochron method

equation in linear form
take multiple samples that formed at the same time, take daughter isotope ratio as y and parent to daughter ratio as x
must form at same time
use this to find slope, then slope = e^lam*t-1, we know the time of formation
line is called isochron
extrapolating the line gives the y intercept, which is the original daughter to isotope ratio

explain isochron example

plag, kspar, biotite
when they crystallized from the magma, they have different parent to daughter ratio
biotite prefers to take Rb into its structure than Sr, so the Rb/Sr ratio is higher
Plag likes to take Sr into system more than Rb, so low Rb/Sr ratio

all minerals have same initial daughter isotope ratio
equal proportion of Sr ratios (mass diff between Sr isotopes is low)

over time, Rb/Sr ratio will decrease, because 86Rb will decay to Sr86
Sr87/Sr86 ratio will increase because Rb87 decays to Sr87
biotite had lots of Rb to start, so a larger change. plag had less Rb to start, so a lesser change
relationship will stay linear

over time the isochron gets steeper (slope increases)

assumptions / conditions in age dating

the number of parent and daughter atoms have changes only by decay of parent to daughter (isotopic system is closed)
no daughter isotope was present in the system to start with
decay constant is known accurately
analytical data are accurate (from mass spectrometry)

choosing an appropriate decay scheme for geochronology

isotopic decay must be active to determine absolute time
clock has to be running
if all parent has decayed to daughter, no way of knowing time

which type of disturbance is most likely

loss of daughter

parent is something the mineral usually likes to take into the structure, but if the daughter is something the mineral reall doesn’t like to have in its strucutre, the system is strained, and daughter will leave
weathering can cause parent to leave, mineral structure likes parent, causing it to gain

isotopic disturbance is a funciton of what

closure temperature
temp below which a mineral/rock becomes closed to diffusional exchange of isotopes with the surroundings

explain this

if you use A for dating, you get the time at which it became closed to diffusion
A mineral with a lower closure temp will give you a younger age

what is the effect of cooling rate on closure temp

a fast cooling rock will have less difference in age using different minerals for dating (steeper slope)
a slow cooling rock will have much more difference in age using diff minerals for dating

what is the effect of metamorphism on closure temp

using A, you’d get the original T1 crystalizing temp because closure T of A is higher than the meta temp
using B, you’d get the age of meta if all the daughter that was accumulated between T1 and T2 leaks out

meta resets the time, you start at time zero
if only some daughter is lost, you get an age between original and meta (but that’s not significant)
partial metamorphism has no geological significance, gives you a date where nothing happened

details on summary

losing daughter is as if decay hasn’t occured as much, you get a younger age, same as if you gain parent. daughter/parent ratio decreases

losing parent or gain of daughter results in apparent older age. daughter/parent ratio increases

discordance

if the dates disagree from multiple methods

causes of discordance: isotopic system did not remain closed
commonly loss of Pb or intermediate daughter products

secular equilibrium

established if parent isotope has significantly longer half-llife compared to intermediate daughters
once all bowls are full, one drop from top bowl will correspond to a drop out of the last bowl, no overall change

details on zircon

common accessory mineral in igneous and meta rocks
harder than quartz, doesn’t get destroyed easily, survives multiple sedimentation cycles
when it forms, takes in uranium
Zr4+ cation and U4+ is a simple substition
Pb2+ is not easily substituted, so zircon has neglible initial daughter levels
high closure tmep for Pb diffusion, need high grade meta to reset the clock

explain U-Pb concordia method

for minerals with no common Pb, it’s a function of time
concordia curve: points in time showing isotopic evolution of Pb with time in a closed system

each number is millions of years
if it plots on the curve, it tells you that 2 methods are giving the same age (concordant)

a sample with lead loss will plot below the concordia
a sampel with uranium loss will plot above the concordia (reversely discordant)

advantages of the U-PB concordia methad

two different isotopic decay systems offer as a check to each other
meaningful geocrhonological info can be dervied even if teh system behaved as an open system

why are isotopes fractionated

difference in bond strength between a molecule with heavy isotopes and one with light isotopes

differences in vibrational energy and bond strength affect the way different isotopes respond to certain physical processes

lighter atoms bonded together will vibrate more than the heavier isotope
potential energy of H-H bond is higher than the D-D bond

details on eqlm isotopic fractionation

reaction at eqlm
due to differences in bond strenght of different isotopes within these phases
heavier isotope forms a stronger bond, so it preferentially partitions into the material with a stronger bonded structure

ex: condensation of water vapour: 18O is preferentially transferred to the precipitation
D is preferentially transfered into the precipitation

liquid has stronger bodning than vapour
liquid will be enriched in heavier isotopes
D/H ratio in rain would be higher than in vapour

what are isotopologues

compoudns that differ only in teh isotope makeup of the elements they contain
H2O, HS16O, Hs18O, D216O, D218O, DH17O

details on kinetic isotopic fracitonation

when one isotope reacts more rapidly than another in an irreversible reaction
kinetically controlled stable isotope fractionation reflects the readiness of a particular isotope to react
lighter isotopes diffuse faster than heavier isotopes in many situation
lighter isotopes react more readily and get preferentially incorporated at noneqlm

Ex: evaporation of water
H2 and 16O molecules escape into vapour preferentially compared to D2 and 18O. water vapour is enriche in 16O and 1H
D/H in water is larger than D/H in vapour

reporting stable isotope compositions

measure heavy/light ratio
ligihter isotope is usually most abudnant one by a lot, so number ends up being very small
why we use delta notation
delta = heavy/light sample - heavy/light standard
/ heavy light standard *1000
in parts per mille %.

positive means sampel is enriched in 18O relatie to standard
negative measn the sample is depleted in 18O relative to standard