29:50 Modern Astronomy
Fall 1999
Lecture 35 ...November 19, 1999
The Moon- Part 2:
Watch the Moon over the next few nights. You will see it close to, but just
below the planets Jupiter and Saturn. This allows you to visualize the Moon's orbit
relative to the plane of the ecliptic.
THE MOON ...continued
Last time I introduced the basics of lunar geology, these were terms such as Maria, Terrae, Craters, Rilles, and Impact Basins. We also looked at pictures of these features. I also strongly encourage you to go up to the roof and look through the telescopes there.
To give a final sense of the nature of the lunar surface, I will show some Apollo and Ranger pictures from the time of the moon program.
Chapter 55 of Video Disk with Ranger Landing and Apollo 17, the
last Apollo mission.
The most valuable scientific information came from analysis of the rock samples returned from the Moon to the Earth. I recommend seeing these sometime if you are at the Smithsonian Museum of Natural History on the Mall in Washington.
Pictures of Lunar Rocks
Video disk, Chapter 16
Images of Moon Rocks
What I would now like to talk about is what we learned concerning the ages of
these Moon rocks. By age, I mean how long ago they formed. The method of determining
the age of a rock involves a technique called radioisotope dating. It is
an extremely important technique in archaeology and paleontology in addition to
astronomy, so I will go over it in some detail.
First what is a radioisotope, or a radioactive isotope?
What does it mean when I write a write a chemical symbol for Carbon which is
? How does this differ from 
? (No chemistry majors answer this)
The subscript is the atomic number. It gives the number of protons in the nucleus of the atom, which equals the number of electrons outside the nucleus. The superscript is the atomic weight, which gives the total number of protons plus neutrons in the nucleus.
The chemistry of and is the same; both are carbon. However,
the nuclear physics can be vastly different. Nuclei with the same number of
protons (and thus the same chemistry) but different numbers of neutrons in their
nuclei are called isotopes of the element.
So what? It turns out that some isotopes are stable and will hang
together forever, and others are unstable and literally fall apart, or better yet
blow up. This
falling apart process is called radioactive decay. This is described fairly
nicely on p138 and 139 of the textbook. Let's see some examples of radioactive
decay.
This is a reaction in which a Carbon nucleus changes itself into Nitrogen nucleus.
It is called Beta decay because an electron (the old fashion term was ``Beta Rays"")
is emitted.
Another example of a Beta decay is:
or
We can detect these decays with an instrument called a Geiger counter,
or other similar instruments. A Geiger counter is a gas-filled cylinder with an
insulated metal wire running up the middle. A high electrical voltage is applied
between the metal case and the wire. If a particle like an electron or a gamma ray
goes through the gas, it ionizes the gas, and a spark is produced. We can
have electrical circuitry which picks up this spark and make a sound or register
an electronic count. Demonstration with Geiger counter.
Every time you hear a click, a radioisotope is biting the dust, and a daughter nucleus is produced in its place. You don't want to be around this stuff in great intensity because the gamma rays and electrons can mess up the molecular bonds in your body.
All of this is interesting, but you still might wonder what it has to
do with determining the age of rocks, or papyrus, or anything like that. The answer,
is that the number of nuclei which decay per unit time is proportional to the
number present. This means that a graph of the number of radioisotopes as a function
of time looks like Figure 7-11 of your textbook.
Figure 7-11 of textbook.
If we start out with 4000 
nuclei, then after 10 minutes there are
half of them left. After 10 more minutes, half of those are left (now 1000 nuclei) ,
and so on.
There are two remarkable facts about radioactivity. The first is that every
sample of ever studied had the same Half-Life. The other
remarkable fact is that the value of half lives for different isotopes varies so
greatly. For 
it is ten minutes. For 
it is 
seconds! For 
it is 5730 years, and for 
it is 47 Billion
years! ( 
).
This means that if you knew the initial number of 
and
atoms in a rock counting them at a later time would tell you the age
of the rock. This is illustrated in the following simplified diagram.
Figure: Relative number of Rb and Sr atoms and the age of a rock
Let's pretend, for the sake of making things simple, that the half life of
was 2 billion years. Let's imagine that a rock was formed with
1000 atoms of Rb and none of Sr. The Rb forms in the mineral of the rock and
time goes on. After 2 billion years, half of the Rb atoms have decayed, so we
have 500 left. At the same time, the number of Sr atoms has increased from 0 to
500. After another 2 billion years, i.e. 4 billion years after the rock formed,
the number of Rb atoms has declined to 250, and the number of Sr has increased to
750.
So by measuring the relative abundance of Rb and Sr atoms in a
substance, one can determine the time since the rock formed. An astute
audience member might wonder how you would know for sure that there had been no
in the rock when it formed. The answer is that you don't. How then
do you correct for the Sr already in the rock? The answer is that there is another
abundant isotope of Strontium, 
which is not the decay product
of a nuclear reaction. The chemistry of and is the same so a rock
doesn't care which atom it picks up. When the rock formed, the abundance of
to 
reflected the relative abundance of the two isotopes in
the early solar system. In simplified form, we can look at minerals which
contain very little Rb by nature, and look at the to ratio.
If no Rb was ever there, the Sr ratio should give you the same value as it originally
was. A large number of rocks, meteorites, etc give a remarkably constant value for
this number.
You can then take a rock which does contain Rb, and look at the abundance
of to tell how much would have been there when the rock formed.
The excess is the number of nuclei that have formed by radioactive decay,
and thus can be used to determine the age of the rock as described above.
An interesting aside worth describing is dating. The most
abundant isotope of carbon is . This is what most of the carbon in
hydrocarbons in life forms is. However, cosmic rays produce a very small
amount of a radioactive isotope . As long as a thing is alive, it is
breathing and ingesting along with 
and there is a constant
ratio of the two. However, as soon as a thing dies, it is not acquiring new ,
and that which is present begins to decay. The net result is that the 
ratio declines with age, and its precise ratio tells how long it is since the material
died. This technique is used extensively in archaeology, and has been used to date
the shroud of Turin, among other things.
What are the results when you make these measurements with the Moon rocks?
Table with ages of lunar rocks.
From this table of ages we can deduce three things.