Lithosphere: solid Earth

Geologic time: dating2 types

1. Relative Dating = sequential age- based on positions of rocks relative to

each other

- e.g., rock layer B is older than A and younger than C

2. Absolute Dating = actual age- based on radiometric dating

- e.g., rock layer B is 50 million years old

Radiometric dating= dating based on the steady decay of

unstable isotopes

Atoms = nucleus of protons & neutrons orbited by electrons

Isotopes = different forms of element w/ different numbers of neutrons

unstable (Mother or Parent) isotopes

stable (Daughter) isotopes

decay

Radiometric Dating

Half-life = time required for ½ of the unstable isotopes in a sample to decay into stable isotopes

Decay is a perfectly random process; every atom has a 50/50 chance of decaying in a given time period (i.e., the half-life)

time (My)

Pro

port

ion

of u

nsta

ble

isot

opes

1.0

0.5

0.25

0.125

Half-life = 1 My

Radiometric Dating

1 2 3 400

0.0625

5

Radiometric Dating

P = P0e-kt

P = # unstable isotopes (parent) at time tP0 = # unstable isotopes (parent) at time 0

(the initial # of isotopes)e = 2.718…k = decay constant = 0.693/H

(to be precise, -k = ln(½)/H = -0.693/H)H = half-lifet = time

Radiometric Dating

P = P0e-kt

To find the age of a rock, solve this eq. for t:

But we don’t know how many parent isotopes we started with!!

ln∙t =1k

P0

P

Radiometric Dating

P = P0e-kt

To find the age of a rock, solve this eq. for t:

+ 1ln∙t =1k

P0- P P

ln∙t =1k

P0

Pln∙t =

1k

P0 - P + P P

P0 - P = # stable (daughter) isotopes at time t!

Let’s call this D.

Radiometric Dating

P = P0e-kt

To find the age of a rock, solve this eq. for t:

This is the equations we’ll use.

ln∙t =1k

P0

P

+ 1ln∙t =1k

DP

How old are the oldest rocks on Earth?Given: Sample from Acasta Gneiss in Canada

It has crystals of zircon that

contain 238U.238U is unstable.

It decays into 206Pb.

The half-life (H) of decay

of 238U into 206Pb = 4.47 billion years

We can measure how much 206Pb (D) and 238U (P) is in the rock and report it as a ratio…

How old are the oldest rocks on Earth?Given: Sample from Acasta Gneiss in Canada

H of 238U into 206Pb

= 4.47 billion years

D/P = 0.85

where t = ageD = amount of daughter (stable) isotopeP = amount of mother (unstable) isotopek = 0.693/HH = half-life

+ 1ln∙t =1k

DP

How old are the oldest rocks on Earth?

+ 1ln∙t =1k

DP

+ 1ln∙t = H 0.693

DP

0.85 + 1ln∙t =4.47 Ga 0.693

t = 6.45 Ga · ln(1.85)

t = 6.45 Ga · 0.615

G = giga = billiona = annum = years

t = 3.96 Ga

+ 1ln∙t =1k

DP

How old are the oldest rocks on Earth?

How old is the Earth?

• oldest rocks = 3.96 billion years old

• difficult to find older rocks because early crust destroyed

• most meteorites = 4.5 - 4.6 Ga

we presume that the

age of the Earth

≈ 4.6 billion years

Radiometric dating

= dating based on the steady decay of unstable isotopes

This is where we get the numbers on the following geologic time scale

Geologic Time

Earth ≈ 4.6 billion years old

Geological Time Scale

• calendar of Earth history

• divided into eons, eras, and periods

Mill

ion

s o

f ye

ars

This is just for your own edification; I don't expect you to memorize this!!

Geologic Time

Earth ≈ 4.6 billion years old

Geological Time Scale

• calendar of Earth history

• divided into eons, eras, and periods

Mill

ion

s o

f ye

ars

Geologic Time

Mill

ion

s o

f ye

ars

End of the last ‘Ice Age’: ~12,000 yrs ago

End of the dinosaurs: ~65 million yrs ago

If the Earth were the age of the USA…

• Let’s condense the ~4.6 billion years of the Earth down to the ~230 years of the Republic

• How long ago (in Republic time) did the dinosaurs die out?

• How long ago did the last ice age end?

Scaling problem

• Revisiting the concept of scale…

• 99% of our atmosphere: 50 km thick

If you shrunk the Earth down to the size of a basketball, how thick would the atmosphere be?

≡

Scaling problemGiven

• Earth’s radius = 6400 km

• Thickness of the atmosphere = 50 km

Need to figure out

• Basketball radius?

• How thick the atmosphere would be if the Earth was the size of a basketball

Scaling problem calculation

1.

Thickness of mini atm = Radius of mini Earth

Thickness of atm Radius of Earth

2. X cm = 10 cm50 km 6400 km

3. (6400 km)(X cm) = (50 km)(10 cm)

Scaling problem calculation

4. X cm = (10 cm)(50 km) 6400 km

5. X = 0.078 cm

Unit conversion?

Significant figures?

If the Earth were the age of the USA…

• Let’s condense the ~4.6 billion years of the Earth down to the ~230 years of the Republic.

• How long ago (in Republic time) did the dinosaurs die out (65 Ma)?

• How long ago did the • last ice age end (12 ka)?

If the Earth were the age of…

• Pick some familiar time interval– Possibilities: a day, a week, your life, your

time at W&M, etc.

• Scale down Earth’s age to that time interval. How long is recorded history on your new time scale?

• The Sumerians developed cuneiform writing in ~4000 B.C. (~6000 years ago)

• Earth is ~4.6 billion years old