Exploration of the Solar System

Lecture 6

Radioisotopes and Ages of Rocks (Rocks of Ages?)

Now I will start talking about one of the most important concepts in solar system astronomy. How do we determine how long ago solar system objects came into existence? More generally, how do we put “time stamps” on events in the remote past? In most cases, this consists of determining the age of formation of rocks.

This material is on p144, Chapter 7of your textbook, but I will be putting a lot more info than is there.

The technique used is radioisotope dating, and the basic idea is used in archaeology as well as planetary science. Here goes.

Elements are determined by the number of protons in the nucleus, i.e. 6 for carbon, 7 for nitrogen, and 37 for Rubidium. It is this atomic number that determines its chemical characteristics.
In nature, elements have a number of isotopes, in which the atomic nuclei have the same number of protons, but different numbers of neutrons. Neutrons are subatomic particles which have the almost the same mass as a proton, but no electric charge. So the atomic weight of the isotopes differs.
Examples: Seawater on Earth consists of H₂O. The vast majority of the hydrogen atoms are plain old hydrogen, ¹H, but about 150 out of a million atoms is Deuterium, ²H or D, in which the nucleus has a proton and a neutron. Another famous example is carbon, in which the most common isotope is C¹², but C¹⁴ is present as well.

Some isotopes are stable, meaning that once formed, they will last forever. However, some of them are radioactive, meaning that they transform themselves to a different type of nucleus, and emit nuclear radiation in the process.

An example of a radioactive decay process is

₃₇Rb⁸⁷→ ₃₈Sr⁸⁷ + e + nu

Where e is an electron and “nu” means a kind of particle called a neutrino (see book for description).

>>>>>>> Demonstration with radioactive materials. See video clip accompanying Lecture 9 , or Lecture 9 Demo Clip on the CD sent to internet students)

For a given Rubidium atom, the decay process shown here is random. It could occur tomorrow or a billion years from now. However, statistically, a group of these atoms will decay at a rate such that after one half life, half of them have decayed and half remain.

After another half life, half of the ones left before will decay. After another half life, half of half of half will be left, and so on.

This statistical behavior is a consequence of the fact that atomic nuclei are governed by quantum mechanics, a branch of physics that has a distinctly probabilistic nature.

The crucial fact to emphasize is that every group of radioactive nuclei in the universe will have the same radioactive decay characteristics, with the same half life.

A plot showing the radioactive decay of the isotope of Nitrogen, N¹³, is shown in Figure 7.11 of your textbook.

This graph nicely defines the relationship between the half life of a radioisotope, and how many of the “parent nuclei” are left.

Say it with equations! Although we will not be carrying out calculations with the following equation in this course, there is a nice formula describing how a radioisotope decays with time. For those of you who remember a little of your high school algebra, here it is.

The equation describing radioactive decay is:

N(t) = N₀e^-0.693t/T

How Can We Use Radioisotopes as Clocks

A rock will form with atoms of various elements and isotopes. Once the rock forms, they are stuck there. The atoms which form the rock will include some radioisotopes. Once the rock has formed, the radioisotopes will begin to decay from the parent nucleus to the daughter nucleus. By comparing the number of daughter nuclei to parent nuclei, we can determine the time since the rock formed.

Example: Parent isotope A decays to daughter isotope B in 10 million years. When the rock forms, it has 100 atoms per cubic centimeter of isotope A, and none of isotope B. After 10 million years, there are 50 per cc left of A. The rest have changed to B, so we have 50 of each. After another 10 million years (another half life, 20 millions years after the rock has formed, only 25 of the 50 A atoms are left; the other 25 have gone on to an afterlife as B atoms, so we have A: 25 B: 75. After another half life (30 million years after the rock formation) we have 12 of A and 88 of B. Thus by counting the relative numbers of A and B we can tell how long it has been since the rock formed.

>>>>>>>> The sketch of this behavior is shown below

To use radioactivity for dating (or age determination) you need a radioisotope with a half life in the ballpark of the age of the objects you are interested in. For example, Carbon 14 dating uses the reaction

C¹⁴ → N¹⁴ + e + nu

This reaction has a half life of 5600 years, and is therefore useful for archaeological dating.

For geological and astronomical applications, we need radioactive decay schemes with much longer half lives. For example, the Rubidium-Strontium reaction has a half life of 48.8 billion years, and the Potassium-Argon, which has a half life of 1.31 billion years.

By the size of these numbers, you can conclude that the ages of rocks (on the Earth and elsewhere) are quite large.

Concluding Remarks.

(1) Question to think about: How can we assume that there is nothing (not a trace) of the daughter isotope when the rock forms? How will an initial presence throw off the basis of dating? How can we correct for the fact (for example, that Strontium 87 would already be present in the rock when it formed) and get a credible estimate for the age of the rock? Note: there is an answer to this.

.The Atmosphere of the Earth

In respect to the properties of its atmosphere, the Earth is unique in some important ways. This is discussed in Chapter 8 of the textbook. A view of the atmosphere, showing some of its aspect is seen in the following picture:

http://antwrp.gsfc.nasa.gov/apod/ap970527.html

>>>>>>> Look at Figure 8.23, showing profile of atmosphere. This figure shows how the temperature and pressure of the atmosphere change as you go up in altitude. One thing that always fascinates me is that at the altitude at which commercial airliners fly, the atmosphere is much, much thinner and colder than it is here at ground level. When you fly in a jet airplane, you are traveling a good part of the way to outer space!

· The composition of the Earth’s atmosphere is primarily N₂ and O₂. Next Argon, water vapor. Everything else is trace gases.

· Height: the lowest level of the atmosphere is the troposphere. Its scale height is 9.5 kilometers. At one scale height of altitude, the atmosphere pressure is down to 37% of what it is at sea level, so you are well on your way to outer space. Commercial airliners routinely fly at an altitude of one scale height or higher.

· The chemical composition of the Earth’s atmosphere is unusual by planetary standards. The other two terrestrial planets have atmospheres which are dominated by CO₂, with almost no oxygen. The presence of oxygen as a major gaseous constituent is a cosmic oddity. It is very significant, both for our understanding of how life came to be here on Earth, as well as the search for life elsewhere in the universe.

· The Earth’s atmosphere is the arena for some of the most important science policy issues of the present day. These are the phenomena of stratospheric ozone depletion and global warming , or the Greenhouse Effect.

The Ocean

Let’s take a look at the ocean:

http://antwrp.gsfc.nasa.gov/apod/ap030708.html

· Earth is the only solar system object where liquid water is stable on the surface. Earth has lots of it. About 70% of the surface is covered by water, up to a depth of several kilometers.

· How did the water get here? Oddly enough, this is something of a mystery in planetary astronomy. We can understand why it is that rocky, as opposed to gaseous planets, formed in the inner solar system. How a volatile material like water formed here is not so well understood. To understand this, we need to consider the remote prehistory of the Earth, and we come face-to-face with astronomical phenomena. This will be dealt with in future lectures.