# PHYS 1470 Chapter Notes - Chapter 5: Infrared, Full Moon, Earth'S Rotation

Chapter 5 – The Earth Moon System 2/2/2013 4:53:00 PM

How The Earth Cooled

Buffon measured how long it took globes to cool

How time depended on the volume of the sphere

Buffon pondered the basic question "How old is our planet?" He

suspected that the Earth was a sphere of rock and metal, and he

wanted to determine its history

He produced a 36-volume encyclopedia called the Theory of Nature

Buffon addressed the question directly. He assumed that Earth had

formed in conjunction with the much hotter Sun, and that the Earth

had therefore started in a molten state

Buffon published his conclusion that the planet was 74,832 years

old

That the real age of the Earth is still greater

Early Estimates of the Earth’s Age

In the Middle Ages, scholars thought they could calculate Earth's

age by finding out how long humans had lived on Earth

Ussher deduced that the cosmos formed on Sunday, October 23, in

4004 B.C., and that humanity was created on Friday, October 28

the same year

This hypothesis suggested a simple question: how long would a

molten Earth take to cool to present-day temperatures?

First, they studied sedimentary layers exposed in canyons in many

parts of the world and realized that the total depth of sediments is

immense

Second, geologists found evidence that mountains had gone

through many cycles of erosion, subsidence, and uplift

Ages Using Radioactivity

The discovery of radioactivity happened by accident

A radioactive atom is an unstable atom that spontaneously changes

(usually into a more stable form) by emitting one or more particles

from its nucleus

The original atom thus becomes either a new element (change in

the number of protons in the nucleus) or a new form of the same

element, called an isotope (change in the number of neutrons in the

nucleus)

The original atom is called the parent isotope and the new atom is

called the daughter isotope

The time required for half of the atoms of any original radioactive

parent isotope to decay into daughter isotopes is called the half-life

of the radioactive element

rubidium-87 decays to strontium-87 with a half-life of 49 billion

years

uranium-238 decays (in a series of steps) to lead-206 with a half-

life of 4.5 billion years

potassium-40 decays to argon-40 with a half-life of 1.25 billion

years

carbon-14 decays to nitrogen-14 with a half-life of only 5570 years

This means that the exact time when an individual atom decays is

impossible to determine – random

Suppose we could determine the original number of parent and

daughter isotope atoms in a rock meaning at the time when the

rock first formed

This can be done by counting the relative numbers of different

isotopes in the minerals of the rock

Then, if we simply count the present numbers of parent and

daughter isotope atoms in the rock, we can tell how many parent

atoms have decayed into daughter atoms and hence tell how old

the rock is

For instance, if half the parent atoms have decayed, the age of the

rock equals one half-life of the radioactive parent element being

studied. This technique of dating rocks is called radioactive dating

Choose a parent isotope that is matched in half-life to the

approximate age of the phenomenon we want to measure

Radioactive Half-Life

Give the age of a rock sample in terms of the number of atoms that

have decayed

After 2 million years, half of that amount would be left. This would

be ½ × ½ = 1/4 of the original number. How many would be left

after 3 half-lives, or 3 million years? It would half that number

again, or ½ × ½ × ½ = 1/8

F = (1/2)N

log F = N log (1/2) = -0.301 N

A particular radioactive form of potassium decays with a half-life of

1.25 billion years (known to 3 significant digits), yielding a certain

form of argon atoms. Suppose we measure the argon and

potassium in the rock crystal, and we find that 58% of the

radioactive potassium has already decayed into argon, while 42%

of the original radioactive potassium atoms are left in the crystal.

How old is the rock? Our measurement has told us that F is 0.42,

and so our equation gives -0.376 = -0.301 N. Thus, N = 1.25 half-

lives. That would mean that the rock is 1.62 billion years old

Ages of the Earth and Moon

Using radioactive dating of rocks, we can measure the time since

the rock was last melted

By knowing the rate of decay processes, and measuring the ratio of

parent and daughter isotopes, it's possible to place constraints on

the age of a rock

The best estimate for the total age of the Earth is 4.6 billion years

Scientists add about 100 million years to this age for the time it

took the molten Moon to solidify

We've been around for less than a tenth of one percent of the

history of our planet!

Internal Heat and Geological Activity

Heat is the ultimate source of energy that drives geological activity

on the planet

Temperature is a measure of particles’ speed, so increased motion

results in a higher temperature

Radioactive material is therefore an energy source, and it heats the

interior of the planet in which it’s trapped

Planets produce heat according to their size

Radioactive atoms decay in the interior, and conduction and

convection transport this heat from the interior to the surface

Bigger planets have more gravity, and the pressure due to gravity

helps to create a molten interior that can drive geological activity

The bigger the planet, the longer it takes internal heat to reach the

surface