## LECTURE 14: EARTH: AGE, COMPOSITION AND STRUCTURE

Key Questions:
• How do we estimate the age of the Earth? What is it?
• What does the density of the Earth tell us about its composition?
• What is the structure of the Earth? How do we infer it from seismology and from the Earth's magnetic field?
• What keeps the center of the Earth hot?

### EARTH: BASIC NUMBERS

Orbital Properties:

• Semi-major axis: 1.000 Astronomical Units (AU) = 150 million km
• Period: 1 year
• Eccentricity: 0.017
Physical Properties:
• Diameter: 12,800 km
• Mass: 6 x 1024 kg
• Rotation period: 1 day

Isotopes:

• Consider two atomic nuclei with same number of protons, different number of neutrons.
• Same chemical properties, but different mass.
• Called isotopes.
• Example: carbon-12 (6 protons + 6 neutrons), carbon-13 (6 protons + 7 neutrons), carbon-14 (6 protons + 8 neutrons).
• Isotopes with too many neutrons are unstable, and "decay," emitting particles and changing into other kinds of atoms.
• Two common processes:
• Neutron emits an electron and converts to a proton. Proton number goes up by one.
• Nucleus emits an "alpha-particle", 2 neutrons + 2 protons. Proton number goes down by two.
• Decaying nuclei often emit gamma-rays and other particles called neutrinos, in addition to electrons and alpha-particles.
• These particles carry energy and can heat their surroundings.
• Gamma-rays are responsible for the most damaging physical effects of radioactivity.

• Radioactive decay is a random process.
• Characterize speed by half-life, t1/2, average time for half the atoms to decay.
• After t1/2, 1/2 of original atoms are left, other 1/2 have decayed into new kind of atom.
• After 2 t1/2, 1/4 of original atoms are left. After 3 t1/2, 1/8 are left.
• The more unstable the nucleus, the shorter the half-life.
• Examples:
• hydrogen-3 to helium-3: half-life 12.26 years
• carbon-14 to nitrogen-14: half-life 5730 years
• For dating rocks on Earth, usually want isotopes with half-lives of billions of years.

• Uranium-238 has 92 protons, 146 neutrons.
• Unstable, decays to Lead-206 (via several intermediate products).
• Half-life of 4.5 billion years, measured in laboratory.
• Suppose we find a rock that we know had no Lead-206 when it formed.
• Today we find equal numbers of Uranium-238 and Lead-206 atoms in the rock.
• When did the rock form?
Difficulty of this method:
• Assumption that rock started with no Lead-206 is wrong.
• Can correct for this using other isotopes of uranium and lead.
• Details complicated.

Potassium-Argon method:

• Potassium-40 decays into Argon-40, half-life of 1.3 billion years.
• Argon is inert (chemically inactive) gas, doesn't form molecules.
• When "free" Potassium-40 decays, Argon-40 just leaves.
• Measure Argon-40 trapped in rocks.
• It must have come from decay of Potassium-40.
• Compare amounts of Argon-40 and Potassium-40, infer age of rock.
• With sophisticated analysis, can get accuracy of 0.1%.

Several other radioactivity methods also used to date old rocks.

### AGE OF THE EARTH AND THE SOLAR SYSTEM

• Rocks have wide range of ages.
• Oldest are 4.2 Gyr (4.2 billion years).
• Conclusion: Earth older than 4.2 Gyr.
• Moon rocks as old as 4.3 to 4.5 Gyr.
• Meteorites measured to be 4.5 to 4.6 Gyr.
• Accepted as age of solar system, age of Earth.
• Took 0.3 Gyr for Earth to cool enough to form first surviving solid rocks.
• Moon cooled faster, slightly older rocks.

Can estimate age of Sun from its structure and luminosity.
Completely independent method, different assumptions.
Get consistent answer, 4.5 Gyr, uncertainty of 0.1 Gyr.

### DENSITY AND ITS IMPLICATIONS

• Density = mass / volume.
• Measure radius Rearth from improved version of Eratosthenes experiment.
• Volume = (4 \pi / 3) x Rearth3
• Measure mass Mearth from gravitational acceleration,
g = G Mearth / Rearth2
• Divide mass by volume to get average density: 5500 kg/m3 = 5.5 g/cm3.
• Density of water: 1000 kg/m3.
• Typical density of rock: 3000 kg/m3.
Implication?
• Much of Earth's interior is something denser than water or rock.
• A good candidate: iron.
• Relatively abundant in universe, and fairly dense.
• At atmospheric pressure, 7000-8000 kg/m3.

### STRUCTURE OF THE EARTH

Established view of Earth's structure, from outside in:

• Crust: light rock, 0 - 100 km
• Mantle: denser rock, 100 - 2900 km
• Outer core: liquid iron (and some nickel), 2900 - 5100 km
• Inner core: solid iron (and some nickel), 5100 km - center (6400 km)
• How do we know?
• Makes reasonable sense if early Earth was very hot, molten.
• Heaviest elements sink to bottom.
• Lightest elements float to top.
• Core hotter than surface, keeps iron liquid.
• Very high pressure makes central iron solid.
• What keeps the core of the Earth hot?

### SEISMOLOGY AND THE EARTH'S STRUCTURE

Earthquakes and pressure waves:

• Earthquakes produced by slippage of plates on Earth's crust.
• Create pressure waves ("sound" waves) that travel through Earth.
• Two kinds:
• Compression waves (P waves), like sound waves in air.
• Transverse (bending) waves (S waves), only possible in solids.
• Wave speed depends mainly on density of medium, also pressure and composition.
• Waves bent (refracted) by Earth's different sound speeds.
• Same phenomenon as bending light by glass.
• Study of earthquakes and their transmission through Earth called seismology.

Decoding the Earth's structure:

• Wait for earthquakes (small ones will do).
• Measure quake arrival times at points on Earth's surface.
• Reconstruct sound speed at every point inside the Earth.
• Infer density profile, changes in material.
• Transverse waves do not make it to other side of the Earth.
• Implies central part of Earth is liquid.
• Gives good determination of mantle-core boundary.
• Solid inner core inferred from deflection of compression waves.

### EARTH'S MAGNETIC FIELD

• Earth has magnetic field, sort of like giant bar magnet.
• Magnetic fields are produced by circulating electric currents.
• Studies of magnetized rock show Earth's magnetic field flips, changing direction every million years or so.
• Understandable if field arises from currents flowing in liquid iron.
• Not understandable if entire core is solid.
• Flipping magnetic field is independent evidence for liquid core.

### WHAT KEEPS THE CENTER OF THE EARTH HOT?

• Volcanos show mantle is hot.
• Liquid iron must be hotter still.
• Earth would have been hot when formed, from collisions of material, sinking of heavy stuff to center.
• But 4.5 Gyr is lots of time to cool.
• Calculations show: need an energy source to keep core as hot as it is.
• The energy source is radioactive decay, of uranium, thorium, potassium, and other elements.