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Chapter 5

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


Department
Physics and Astronomy
Course Code
PHYS 1470
Professor
Paul Delaney
Chapter
5

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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)

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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

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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
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