How Earth’s Age is InferredHow Earth’s Age is Inferred

Isotopic DatingIsotopic Dating

1. _______________ (Numerical) Age: Determination of the actual age of a rock unit in years.

a. ___________________ uses radioactive elements in earth

materials.

b. Previously called_________ dating by geochronologists.

AbsoluteAbsolute

Isotopic Dating

radiometric

2. Elements and Atomsa. _____________: A substance that cannot be

broken into simpler substances by ordinary chemical means.

Element

b. ______

• Smallest particles of an element that can enter a chemical reaction

• The smallest chemically indivisible particle of an element.

Atom

c. The Traditional Model of an Atom

i. Central nucleus containing __________ and ______________.

protonsneutrons

ii. Developed by Danish physicist Niels Bohrin 1913

• Referred to as the “Bohr Model” of the atom.

iii. Electrons are in ________i. Called shells

ii. Are specific distances from the nucleus.

orbits

d. The Modern Model of the Atom(__________________ Model)

i. Electrons are in a cloud-like region around the nucleusii The shells are referred to as _________.

(1) Three-dimensional regions around the nucleus. (2) Each can hold a different number of electrons and has a different shape. (3) Most stable if the outermost shell has _____ electrons.

Electron Cloud

orbitals

8

Nobel Gases• Have 8 electrons and are inert (unreactive)

e. The Size of the AtomThe Size of the Atom

i. An atom of iron is about 25 ten-millionths of a meter in diameter

- Most of its volume is empty space.

ii. Its nucleus has a diameter of about one-hundred-thousandths of the diameter of the space in which its electrons move.

Sizes of Most Common Ions in Minerals

• Sizes are in angstroms.– One angstrom = 1.0 x 10-8 cm

(one hundred millionth of a cm)

• Ions close in size are in the same row.

• Similar sized ions can replace one another in a crystal structure.

f. Subatomic Particles

i. ____________: Positively charged and equal to the unit charge of the electron. Protons are 1836 times heavier than electrons.

ii. ____________: Electrically neutral and equal in mass to the proton.

iii. _________________: The number protons contained in the nucleus and identifies the atom.

iv__________________: Sum of an atom’s protons and neutrons.

Protons

Neutrons

Atomic Number

Mass Number

Plotting Information around the chemical symbol

v. ____________: Atoms of the same element with the same number of protons but different numbers of neutrons.

Isotopes

Isotopes of Oxygen

The Mass of an AtomThe Mass of an Atom

• Measured using a mass spectrometer– An electron beam fragments gas atoms or molecules into

positively charged ions– Ions are

• Accelerated• Deflected by a magnet

– More massive particles are deflected by smaller amounts than the less massive particles

Standard MassStandard Mass

• Determined using a neutral atom of carbon-12• It is set at exactly 12 mass units (12 u)

– 1 atomic mass unit (amu) = 1/12 of this mass which is1.66 X 10-26 g.

– All atomic masses are set to this value• Only carbon-12 has a mass in amu that is exactly the same

as its mass number.• For other atoms, it is not precisely the same as the mass of

one proton and one neutron. For example . . .– 35Cl has a mass of 34.969 amu– 37Cl has a mass of 36.966 amu

vi. _____________: The average number of protons and neutrons in an atom

(1) Also called atomic ___________.(2) Given in ____________________(amu)(3) Also considers the ______________________ of each

isotope.Example using chlorine:

Of the two isotopes of Cl, 75% (75.53%) are the lighter isotope 35Cl25% (24.47%) are 37Cl

Finding the atomic mass(34.969 amu x .7553) + (36.966 amu x .2447) =

35.45 amu

Atomic Mass

fractional abundanceatomic mass units

weight

g. ____: A charged atom

i. Atoms that gain electrons are ____________charged.

ii. Atoms that lose electrons are ____________ charged.

Ion

negatively

positively

3. _________________________

a. Provides a “clock that starts when radioactive elements are sealed into newly crystallized minerals.

The_______ of decay is known.

Radioactive DecayRadioactive Decay

rate

b. ______________

i. Isotopes of some elements have ________ nuclei and spontaneously change or “_______” into new elements which are often unstable and decay into new ____________.

ii. _________and _________leave these atoms producing energy.

RadioactivityRadioactivity

unstabledecay

Protons neutrons

elements

Radioactive Decay

iii. There are three types of radioactive decay. The original isotope is referred to as the______ isotope and the new isotope formed is called the

_________ product.

parentdaughter

(1) _________ ( ) Emission

(a) Two protons and two neutrons (He atom) leave the nucleus.

(b) Reduction in the atomic number results in a new element.

(c) U Th + He

αAlpha

238

92

234

90

4

2

New element (thorium)

Alpha particle isemitted

(2) ________ ( ) Emission

(a) Release of an electron from the nucleus.

(b) A neutron is actually a proton with an electron inside it making it electrically neutral.

βBeta

(b) ________ ( ) Emission

(c) When a neutron emits an electron, it becomes a proton which increases the atomic number by one.

(d) After the 238U undergoes alpha emission to become 234Th, the 234Th undergoes beta decay to become 234Pa (the atomic mass number is unchanged because the lost electron’s weight is negligible.

Th Pa + β Particle (electron)

βBeta

234

90

234

91

New element (protactinium) emitted

(3) _________ Capture

(a) A proton captures an orbiting electron and becomes a neutron.(b) The atomic number decreases by one, thereby changing it into another

element.

(c) The potassium-argon system is an example.

K + β Particle (electron) Ar

Electron

40

18 Emitted New Element

Uranium 238 Decay

c. ________

i. The time required for _____the amount of atoms of radioactive isotope to decay.

(1) The length of half-lives for different

isotopes of different elements can vary

from:

- less than 1/billionth of a second to

- 49 billion years

Half LifeHalf Life

half

(2) Radioactive decay is not linear

(a) Linear change has a constant rate– The same percentage

of the candle is burning away every minute

– The same amount of water drips into the glass every hour.

(b) Radioactive Decay is Geometric

(i) In radioactive decay, during each equal time unit the proportion of parent atoms decreases by ½

(ii) This produces a curved graph

ii. MethodMethod:

(1) Chemical analysis determines the amount of parent isotope and daughter isotope present in a rock using a mass spectrometer.

(2) Determine the parent/daughter __________.

(3 Age is calculated mathematically on the basis of it’s known half-life.

(4) Whenever possible, more than one isotope pair will be used.

ratio

ExampleExample

• Analysis of the biotite crystals in a granite determines that they contain– 25.0% potassium-40 (40K) atoms– 75.0% argon-40 (40Ar) atoms

• This is a 1:3 ratio.

• What is the age of the granite?

The potassium has gone through two half-lives

Lab Manual Figure 8.10 on page 183 (9th edition)

• 2 half-lives = 2.000 x T½

• The half life of 40K is 1.3 x billion years.• 2 x 1.3 billion years = 2.6 billion years.

iv. Reliability

1. _________________: When the rock or mineral was sealed off so that neither isotope could enter or leave the environment.

2. Must be able to infer no __________________were present at time of closure.

3. There must have been _________________for measurable result by a mass spectrometer.

4. Half-Life is not affected by:a. ______________b. ______________c. ______________

5. If a rock _______, it’s radioactive clock is _______and the age will be the time of solidification

Closed System

daughter products

sufficient time

heatchemical actionpressure

melts reset

• Crystallization of magma separates parent atoms – from previously formed daughters

• This resets the radiometric clock to zero.• Then the parents gradually decay.

Igneous Crystallization

Radioactive Isotopes Commonly Used

i. Uranium-Lead (Rocks must be at least 10 Ma (million years old).

ii. Potassium-Argon (Argon gas becomes trapped in different crystal structures)

iii. Carbon 14 (Radiocarbon)(1) Used for organic matter(2) Short half-life (5,730 years) (3) Useful only in dating objects accurately back to 40,000 years.

iii. Carbon 14 (Radiocarbon)

(1) Used for organic matter(2) Short half-life (5,730 years)(3) Useful only in dating objects

accurately back to 40,000 years.

(4) Fundamentally different from parent-daughter systems because 14C is continuously created in the atmosphere by bombardment of nitrogen by cosmic rays

(a) Cosmic radiation bombards nitrogen.

(b) A neutron strikes and is captured by a 14N atom.

(c) A proton is expelled from the nucleus and becomes 14C

Radiocarbon Dating(d) While 14C eventually reverts

to 14N because its nucleus is unstable, the rate of 14C production provides a balance so that the amount of 14C remains constant.

(e) Living matter incorporates 12C and 14C into its tissues. The ratio of 12C to 14C remains constant while it’s alive.

(f) Upon death, 14C decays and no further 14C replacement occurs.Age is estimated from the ratio of 14C to all other carbon in the sample