In what ways can we determine the age of the Earth? Or is the Earth infinitely old?


What would you look for to determine the Earth's age?


Are the lives of Earth and the Sun connected?

-Age of the Sun

Where does the Sun's energy come from?

First, we should address how much energy the Sun outputs every second. We measure 1400 Watts per square meter at the surface of the Earth. (Think of this as 14 100 Watt (Joule/Second) lightbulbs on a square meter of the ground). The Earth's surface is only a small part of the sphere defined by Earth's orbit, and the Sun shines in all directions!

So how many lightbulbs would it take to be equivalent to the Sun's energy output? The Earth is 150 million kilometers from the Sun. The surface area of a sphere this size would cover 2.8x10 to the power 23 square meters. Remember there are 14 100 Watt lightbulbs in each square meter... so the Sun's energy output is equal to 3.8x10 to the power 26 Watts!!


--Burning firewood/coal/? in the center?

Coal burning in our power plants provides about 29.6 million Joules per kilogram. The mass of the Sun has been calculated to be 1.989 x 10 to the power 30 kg. If the Sun were made of coal, it would output a total of 5.9x10 to the power 37 Joules over its lifetime. This means the Sun's lifetime would be 1.5 x 10 to the power 11 seconds... only 4900 years!!



--Gravitational Contraction?

If the Sun were originally much larger than it is today and has been radiating energy through collapse, it would output about 1.1 x 10 to the power 41 Joules.
This would lead to a lifetime of about 3x10 to the power 14 seconds... or about 10 million years.



--Nuclear Fusion

In the early 20th century, a new form of energy was discovered... nuclear fusion! From Solar spectra we know that the element Hydrogen is the main component of the Sun's mass, and Helium is the next most present element.

Nuclear fusion in the center of the Sun goes through a process of combining 4 Hydrogen nuclei to create a Helium nucleus. Each time this happens, 0.7% of the mass of the hydrogen atom is converted into energy. Using E=Mc^2, this means that 1 x 10 to the power -12 Joules of energy are released for every Hydrogen atom converted into Helium. Only the inner 10% of the Sun is hot enough for this reaction to take place, so 1.989 x 10 to the power 28 kg of Hydrogen is converted into Helium. When this 10% is completely converted, the Sun has released a total of 1.25 x 10 to the power 43 Joules! This gives the Sun a total lifetime of about 10 billion years.


Now that we have determined that the Earth could be billions of years old, we need to look for evidence from the Earth itself.

Does the surface of the Earth change? On what timescales?
-Mountains
-Grand Canyon
-Sedimentary deposits from ancient oceans, lakes

What else from the Earth do we have to show an ancient history??

-Hydrocarbon fuels
-dinosaur fossils

Evidence from nuclear chemistry:

Radioactive dating - Radioactive isotopes of particular elements decay into other elements over time, and these timescales are known.

Half-lives of important isotopes:

Carbon-14: 5730 years
Aluminum-26: 730,000 years
Potassium-40: 1.27 billion years

What challenges lie in dating materials from the Earth?
Erosion
Volcanism
Plate Tectonics

Lunar rocks and meteorites have been dated to over 4 billion years old!
Radioactive dating of Zircon crystals (which do not melt in temperatures reached in volcanoes, or even Earth's interior, so they haven't changed since the Earth formed!) have led to an age of 4.5 billion years.



To Review Some Atomic Physics Concepts from last time...


Spectra

Last time I explained that astronomers knew the Sun was mostly composed of Hydrogen and Helium because of a technique known as Spectroscopy. What is spectroscopy? How does it work?

To investigate this, we need to begin at the very basic level... atomic structure! Skipping over the evolution of thought of how an atom is structured... we can basically imagine it in the Bohr Model of the Atom:

There is a positively charged nucleus, and there are orbital levels outside of the nucleus where the negatively charged electrons are found. The levels closer to the nucleus take less energy to orbit in than the higher energy levels. Some energy must be given to the electron for it to jump to a higher orbital level, and energy must be lost from the electron when it moves to a lower orbital level.
Light carries energy in the form of E=hc/wavelength, so this is what causes absorption and emission lines:

Absorption Lines

When light of a certain wavelength (and therefore of a certain energy) interacts with an atom, it can be absorbed by an electron. The electron will move to a higher energy level, and that wavelength of light "disappears". If there is a bright (hot) source with a group of atoms (cooler) between you and the source, the atoms will cause certain wavelengths of the continuous spectrum (also known as the continuum spectrum), will be absorbed. These darkened sections of the spectrum are the "absorption lines".

Emission lines

Now, lets suppose there is a dark background, with a bunch of highly energetic atoms between you and it. The electrons in those atoms will, for some reason or another decide to jump to the lower energy levels. The lost energy from this transition becomes light. The transitions all occur at known energy levels, and so the light's wavelength is known. The light emitted from these atoms become the "emission lines".

The Sun is a bright object, and in its outer atmosphere, there are a lot of cooler atoms... aim a spectroscope to the sun, and voila, the Solar spectrum has a continuum from the hot, bright background, and absorption lines from the cooler atoms in the Sun's upper atmosphere. Since each transition in each element is unique, we can identify the elements in the Sun's upper atmosphere (and therefore, the Sun itself) by the different absorption lines!


Demonstrations: Prism and Ionization tubes


Radioactive Decay

Radioactivity was discovered through a series of accidents. In 1895, physicist William Roentgen was testing cathode rays, when he noticed a chemically coated screen nearby was glowing. He named the unseen rays that caused the flourescence "X-Rays". He found with further experimentation that the X-Rays could penetrate some materials but not others. He discovered that X-Rays can penetrate human flesh, but not bone. (He gave himself the very first X-Ray of a hand!)

A year later, Henry Becquerel left some photographic plates next to a rock which had been identified as Uranium ore. When he developed the plates a few days later, he noted some strange bright spots, and determined that Uranium gives off invisible rays.

Pierre and Marie Curie conducted experiments to show that radioactive decay of uranium produces X-Rays, and finally gave the name "Radioactivity" to this phenomenon. They also figured out that the result of decay was a daughter element. Other elements were also found to have other final isotopic daughter Products.

At the turn of the century, Ernest Rutherford was experimenting with radioactivity, and discovered that specific radioactive elements had constant decay rates. (So the total radioactivity decreases over time.)

Radioactive Parent : Stable Daughter : Half Life
Potassium 40 : Argon 40 : 1.25 Billion years
Rubidium 87 : Strontium 87 : 48.8 Billion years
Thorium 232 : Lead 208 : 14 billion years
Uranium 235 : Lead 207 : 704 million years
Uranium 238 : Lead 206 : 4.47 billion years
Carbon 14 : Nitrogen 14 : 5730 years


Now for a little explanation of what is happening, atomically, in the decay process, we need to look into the nuclei of atoms. There are two particles found in atomic nuclei, positively charged protons, and neutrally (no) charged neutrons. Remember from previous science classes that the number of protons defines the type of element, and the number of neutrons defines the isotope of an atom. In lower numbered elements, the number of neutrons is about equal to the number of protons in a stable nucleus. In higher numbered elements, more neutrons are needed to keep stability. No element with atomic mass greater than Uranium-238 has ever been found to be stable, and thats why all of them have to be made in a lab, and they are all radioactive.


There are three different forms of decay, named Alpha, Beta, and Gamma decay.

Alpha particles are essentially the same as Helium nuclei: Two protons and two neutrons. Alpha decay occurs when an alpha particle separates from the nucleus.

Beta particles are electrons. How does an electron come out of the nucleus?

Neutrons can be thought of as an electron and proton combined together. So, when a beta particle separates from the nucleus there is now one neutron which has become a proton. This is what happens in Carbon 14 decay.

Gamma decay occurs when there is an excited atom (that is to say, the electrons are in higher orbital levels) which loses its energy. The element is the same, only it occurs in a lower energy. Gamma particles are also called photons, the particle portion of the nature of light.


Radioactive decay is a spontaneous occurrence. The half-life is how long (on average) it will take half of the particles to spontaneously decay. A little bit of math and a good mass-spectrometer can tell you how much of a radioactive material was present at the beginning, and from the amount that's left, you can figure out how long it has been decaying! But, because these are spontaneous occurences, there are still statistical errors.

One half-life - 50% remains Two half-lives - 25% remains Three Half-lives - 12.5% remains Four Half-lives - 6.25% remains Five Half-lives - 3.125% remains etc.


Decay Demonstration -Pennies in a box