AST 248 HW for Chapter 4
Ryan Richards
Review Questions
What do we mean by the geological record? Why is it important?
The geological record is the information about the Earth’s history through the study of rocks and
fossils. It is important because with this information, we can understand how the Earth has
developed over time.
Describe the technique of radiometric dating, and explain how we know it is reliable. Be
sure to explain what we mean by a radioactive isotope, parent and daughter isotopes, and a
half-life.
Radiometric dating allows us to measure the age of a rock or a fossil by measuring the object’s
proportions of atoms and isotopes. Considering an object with both atoms of type A and B, my
measuring the ratio of these atoms we can find the age. A radioactive isotope’s nucleus
undergoes spontaneous radioactive decay such as a proton turns into a neutron (This is known as
beta plus decay, where the proton decays into a neutron, positron and an electron neutrino. The
positron is the antiparticle of an electron and has positive like the proton). During the decay, A is
the parent isotope and B is the daughter isotope, i.e., the decay products. The number of atoms of
isotope A reduces in half in a certain amount of time known as the half-life. The following
formula for the age of the object is given here:
T = τ ln ((A +B)/A)/ln (2),
Where τ is the half-life and ln (2) comes from the definition. The value of ln (2) is 0.693, a
number worth noting. Radiometric dating is understood as we understand today the underlying
physics of nuclear processes. For our purposes we don’t need to know these mechanisms; to
understand them, one needs quantum mechanics and some basic quantum field theory.
To derive this we use the equation
A = (A+B) 2-t/τ.
Division gives
A/ (A+B) = 2-t/τ.
Taking the natural log i.e., ln = loge we get
-t/τ ln (2) = ln (A/ (A+B)),
Where we used the fact that ln (xy) = yln(x). Multiplying -τ on both sides gives the required
result. One should note that –ln(x/y) = ln(y/x).
What were the heavy bombardment and the late heavy bombardment, and what effect might
they have had on life?
The heavy bombardment period occurred in the first few hundred million years of the solar
system. During this period, asteroids and comets crashed into the Sun and planets which left
impact craters on the surfaces of planets and moons. The late heavy bombardment period
occurred about 4.1 billion years ago and ended 0.3 billion years later. Asteroids and comets as
well as other bodies crashed into the Sun and planets. These periods could have caused the orbits
of the planets to change.
The impacts could have affected life detrimentally. The impacts would have vaporized the
oceans and raised the temperature causing the crust to melt. However, the book mentions that
microscopic life living underground could have survived. It even mentions that these impacts
could have increased the habitability of the Earth.
Describe how plate tectonics shapes important geological features of Earth, including midocean ridges, continents, mountain ranges, rift valleys, and earthquakes. How did Hawaii
form?
Mid-ocean ridges occur when tectonic plates move apart. The region between the plates, molten
rock seeps into the ocean and eventually hardens thus causing mid-ocean ridges. Continents are
formed from thick slabs of continental crust. Mountain ridges are formed when two continental
plates collide causing them to be pushed upward. Rift valleys are thin patches of crust that result
from continental plates moving apart. Earthquakes occur when plates scrape against each other.
Hawaii was formed by plate tectonics moving the pacific plate over a hot spot. The lava erupted
from the hot spot gave rise to the islands.
What are ice ages, and what may cause them? What do we mean by snowball Earth
periods, and how does Earth recover from them?
Ice ages occur when the global average temperature drops a few degrees causing an increase in
snowfall. They possibly have been caused by small changes in the Earth’s rotation and orbit. The
Earth’s tilt varies with time and can affect the seasons making them less or more extreme.
Snowball Earth periods are long and cold ice ages where the Earth’s water freeze causing the
surface to be covered in ice. The Earth recovers from these periods through the CO2 cycle.
During these periods, the Earth’s interior remains hot leading to volcano buildups which add to
the atmospheric carbon dioxide. The building of carbon dioxide strengthens the greenhouse
effect which melts the snowball Earth.
Does It Make Sense
We can expect that if there are paleontologists a few million years from now, they will find
fossil remains of almost every human who ever lived.
This is unreasonable considering most organisms do not fossilize.
Nearly all the rocks I found in the lava fields of Hawaii are igneous.
This makes sense. Igneous rocks are made from molten rock.
The most common rock type in the strata of the Grand Canyon is sedimentary rock.
This makes sense. The answer is given to you on page 106 on the textbook.
Although the Earth contains its densest material in its core, it’s quite likely that terrestrial
planets in other star systems would contain their lowest density rock in their cores and the
highest density rock in their crusts.
This is unreasonable. We should expect to see the same due to gravity.
If you had a time machine that dropped you off on Earth during the Hadean eon, you’d be
quickly killed by a large impact.
Not necessarily since the large impacts didn’t occur continuously. If you happen to be
transported when an impact did occur then the situation would be different.
If there were no plate tectonics on earth, our planet would be far too hot to have liquid
oceans.
This doesn’t make sense since plate tectonics do not cool the Earth.
Without the greenhouse effect, there probably would be no life on Earth.
This makes sense. Without the greenhouse effect, the Earth would be too cold for liquid water as
evident in the discussion of ice ages (see discussion above).
If nitrogen were a greenhouse gas, our planet would be far hotter than it is.
This makes sense. Due to the large abundance of nitrogen, if it were a greenhouse gas the
temperature would increase. Greenhouse gases increase the temperature of the Earth.
We can learn a lot about the Earth’s early history by studying the Moon.
This makes sense since the Earth and the Moon are relatively close to one another. Due to this
proximity, they would have experienced the same effects.
Science can never be determined with confidence the times or sequence of events that
occurred millions or billions of years ago.
This does not make sense. Science for example has made huge progress in understanding the
beginning stages of our universe (e.g., cosmology).
Quick Quiz
Earth has retained a lot of internal heat primarily because of its (c) relatively large size
Earth has far less atmospheric carbon dioxide than Venus because (c) Earth’s carbon
dioxide is locked up in carbonate rocks
Quantitative Problems
The half-life of carbon-14 is about 5700 years.
a. You find a piece of cloth painted with organic dye. By analyzing the dye in the cloth,
you find that only 77% of the carbon-14 originally in the dye remains. When was
the cloth painted?
b. A well-preserved piece of wood found at an archaeological site has 6.2% of the
carbon-14 that it must have had when it was living. Estimate when the wood was
cut.
c. Suppose a fossil is 570,000 years old, which is 100 half-lives of carbon-14. What
fraction of its original carbon-14 would remain? Use your answer to explain
whycarbon-14 generally is not useful for dating fossils of this age.
To do this problem we need the equation given above
T = τ ln ((A +B)/A)/ln (2).
(A) We are given that τ = 5700 years. Recalling that A/A+B is the fraction of the remaining
atoms we deduce that A=.77 and A+B is 1 for part (a) of the problem. Therefore the ln
((A+B)/A) is simply ln (1/.77) or –ln (.77). One may be worried about the negative sign
but it doesn’t matter since .77 is less than 1 and the ln of anything less than 1 is also
negative. Of course we have to remember that the natural log cannot go to zero (for those
who have taken calculus know that ln (0) goes to negative infinity).
Plugging the numbers in we get T = 2,150 years for part (a).
(B) The only difference here is that the fraction now becomes –ln (0.062) or ln (1/0.062).
After plugging in we get T = 22,868
(C) In this part we know T, τ, and ln (2). So we have
2-T/τ = A/ (A+B)
2-100 = 7.9 x 10-31.
From the answer we can clearly see that after many lifetimes, it will be hard to measure
precisely this ratio. Carbon dating would only be helpful possibly after a few half-lives.