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Lecture 11 Stable Isotopes. Isotopes of Elements Chart of the Nuclides Delta Notation Isotope Fractionation Equilibrium Kinetic Raleigh. See E & H Chpt. 5. When the universe was formed 15 billion years ago (the “Big Bang”)

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Lecture 11 Stable Isotopes

Isotopes of Elements

Chart of the Nuclides

Delta Notation

Isotope Fractionation




See E & H Chpt. 5

When the universe was formed 15 billion years ago (the “Big Bang”)

light elements of H (99%), He (1%) and trace amounts of Li were formed.

Subsequent reactions during star formation created the remaining elements,


Isotopes of Elements

The chemical characteristic of an element is determined by the number of protons in its nucleus.

Atomic Number = # Protons = define the chemistry

Different elements can have different numbers of neutrons and thus atomic weights (the sum of protons plus neutrons).

Atomic Weight = protons + neutrons = referred to as isotopes

There are 92 naturally occurring elements

Some are stable; some are Radioactive


The chart of the nuclides (protons versus neutrons)

for elements 1 (Hydrogen) through 12 (Magnesium).

Valley of Stability

Most elements have more

than one stable isotope.

b decay

1:1 line



a decay

Number of neutrons tends

to be greater than the

number of protons


Examples for H, C, N and O:

AtomicProtons Neutrons% Abundance

Weight(Atomic Number) (approximate)

Hydrogen H 1P 0N 99.99

D 1P 1N 0.01

Carbon 12C 6P 6N 98.89

13C 6P 7N 1.11

14C 6P 8N 10-10

Nitrogen 14N 7P 7N 99.6

15N 7P 8N 0.4

Oxygen 16O 8P 8N 99.76

17O 8P 9N 0.024

18O 8P 10N 0.20

1/2 = 5730 yr

All Isotopes of a given element have the same chemical properties, yet there are small differences

due to the fact that heavier isotopes typically form stronger bonds and diffuse slightly slower

% Abundance is for the average Earth’s crust, ocean and atmosphere


Mass Spectrometer – Basic Schematics

1. Input as gases

2. Gases Ionized

3. Gases accelerated

4. Gases Bent by

magnetic field

5. Gases detected

Gases accelerated

Gases ionized

high vacuum

Magnetic field

deflects ion beam


Isotopes are measured as ratios of two isotopes by various kinds of detectors.

Standards are run frequently to correct for instrument stability



Report Stable Isotope Abundance as ratio to Most Abundant Isotope (e.g. 13C/12C)

-Why? The Ratio of Isotopes is What is Measured Using a Mass Spectrometer

The Ratio Can Be Measured Very Precisely.

The isotope ratio of a sample is reported relative to a standard using d(“del”) notation –

usually with units of ‰ because the differences are typically small.

Define H = heavy L = light

d (in ‰) = [(Rsample - Rstandard) / R standard ] x 1000


R / Rstd = if δ is in ‰



d13C (in %o) = [ (13C/12C)sample / (13C/12C) standard ] – 1 x 1000

Example: If (13C/12C) sample = 1.02 (13C/12C) std

d13C = 1.02 (13C/12C) std / (13C/12C) std - 1 x 1000

= 0.02 x 1000 = 20 %o


Isotopic Fractionation

The state of unequal stable isotope composition within different

materials linked by a reaction or process is called “isotope fractionation”

Fractionation Factor = a

aA-B = RA / RB where R = ratio of two isotopes in materials A or B


 = Rproducts / Rreactants


Two kinds of Isotope Fractionation Processes

  • Equilibrium Isotope effects
  • Equilibrium isotope fractionation is the partial separation of isotopes between two
  • or more substances in chemical equilibrium.
  • Usually applies to inorganic species. Usually not in organic compounds
  • Due to slightly different free energies for atoms of different atomic weight
  • Vibrational energy is the source of the fractionation. Equilibrium fractionation results from the reduction in vibrational energy when a more massive isotope is substituted for a less massive one. This leads to higher concentrations of the heavier isotope in substances where the vibrational energy is most sensitive to isotope fractionation (e.g., those with the highest bond force constants)
  • If molecules are able to spontaneous exchange isotopes they will exhibit slightly
  • different isotope abundances at thermodynamic equilibrium (their lowest energy state)

For example: exchange reactions between light = Al, Bl and heavy = Ah, Bh

aA1 + bBh ↔ aAh + bB1

The heavier isotope winds up in the compound in which it is bound more strongly.

Heavier isotopes form stronger bonds (e.g. think of like springs).

If α = 1 the isotopes are distributed evenly between the phases.

Example: equilibrium fractionation of oxygen isotopes in liquid water (l)

relative to water vapor (g).

H216O(l) + H218O(g) ↔ H218O(l) + H216O(g)

At 20ºC, the equilibrium fractionation factor for this reaction is:

α = (18O/16O)l / 18O/16O)g = 1.0098



The carbonate buffer system involving gaseous CO2(g), aqueous CO2 (aq),

aqueous bicarbonate HCO3- and carbonate CO32-.

An important system that can exhibit equilibrium isotope effects for both

carbon and oxygen isotopes

13CO2(g) + H12CO3-↔ 12CO2(g) + H13CO3-

The heavier isotope (13C) is preferentially concentrated in the chemical

compound with the strongest bonds. In this case 13C will be concentrated

in HCO3- as opposed to CO2(g).

For this reaction  has the form:

H/L = (H/L)product / (H/L)reactants = (H13CO3- / H12CO3-) / (13CO2 / 12CO2)

H/L = 1.0092 at 0ºC and 1.0068 at 30ºC


Example: Estimation of temperature in ancient ocean environments

CaCO3(s) + H218O  CaC18OO2 + H2O

The exchange of 18O between CaCO3 and H2O

The distribution is Temperature dependent




last glacial

d18O of planktonic and benthic foraminifera

from piston core V28-238 (160ºE 1ºN)

Planktonic and Benthic differ due to differences

in water temperature where they grow.


1. Organism ppted CaCO3 in isotopic equilibrium

with dissolved CO32-

2. The δ18O of the original water is known

3. The δ18O of the shell has remained unchanged

Planktonic forams measure sea surface T

Benthic forams measure benthic T


d18O in CaCO3 varies with Temperature

from lab experiments

E & H Fig 5.3


Complication: Changes in ice volume also influence d18O

More ice, thus higher salinity – more d18O left in the ocean

d18O increases with salinity


2. Kinetic Fractionation

Non-equilibrium – during irreversible reactions like photosynthesis

Occurs when the rate of chemical reaction is sensitive to atomic mass

Results from either differential rates of bond breaking or diffusion rates

Compounds move at different rates due to unequal masses.

Light are always faster.

For kinetic fractionation, the breaking of the chemical bonds is the

rate limiting step. Essentially all isotopic effects involved with formation /

destruction of organic matter are kinetic

There is always a preferential enrichment for the lighter isotope in the products.

12CO2 mw = 44 These must have the same kinetic energy (Ek = 1/2mv2)

13CO2 mw = 45 so 12CO2 travels 12% faster than 13CO2.

All isotope effects involving organic matter are kinetic


12CO2 + H2O = 12CH2O + O2 faster

13CO2 + H2O = 13CH2O + O2 slower

Thus organic matter gets enriched in 12C during photosynthesis (d13C becomes negative)



Carbon has only two stable isotopes with the following

natural abundances:

12C 98.89%o

13C 1.11%o

Below are some typical d13C values on the PDB scale in %o.

Standard (CaCO3; PDB) 0

Atmospheric CO2 -8 (was -6‰, getting lighter due to new CO2)

Ocean SCO2 +2 (surface)

0 (deep)

Plankton CaCO3 +0 (same as seawater)

Plankton organic carbon -20

Trees -26

Atmospheric CH4 -47

Coal and Oil -26


Raleigh Fractionation -

A combination of both equilibrium and kinetic isotope effects

Kinetic when water molecules evaporate from sea surface

Equilibrium effect when water molecules condense from

vapor to liquid form

Any isotope reaction carried out so that products

are isolated immediately from the reactants will show

a characteristic trend in isotopic composition.

Example:Evaporation – Condensation Processes

d18O in cloud vapor and condensate (rain)

plotted versus the fraction of remaining vapor

for a Raleigh process. The isotopic composition

of the residual vapor is a function of the

fractionation factor between vapor and water

droplets. The drops are rich in 18O. The vapor

is progressively depleted.

Where Rvapor / R liquid = f (a-1)

where f = fraction of residual vapor

a = Rl/Rv

Fractionation increases with

decreasing temperature


Distillation of meteoric water – large kinetic fractionation occurs between

ocean and vapor. Then rain forming in clouds is in equilibrium with vapor

and is heavier that the vapor. Vapor becomes progressively lighter.

dD and d18O get lower with distance from source.

Water evaporation is a kinetic effect.

Vapor is lighter than liquid. At 20ºC the difference is 9‰ (see Raleigh plot).

The BP of H218O is higher than for H216O

Air masses transported to

higher latitudes where it is cooler.

water lost due to rain

raindrops are rich in 18O relative

to cloud.

Cloud gets lighter


d18O variation with time in Camp Century

ice core.

d18O was lower in Greenland snow

during last ice age

Effect of temperature

Effect of ocean salinity

15,000 years ago d18O = -40‰

10,000 to present d18O = -29‰


1. d18O of precipitation

2. History of airmass – cumulative depletion of d18O


Influence of carbon source and kinetic fractionation on the average

isotopic composition of marine and terrestrial plants.


Meteoric Water Line

linear correlation between

dD and d18O in waters of

meteoric origin