Laboratory 7 - Nuclear Process in the Solar System

At this point, almost all astronomers agree that the primary source of energy to keep the sun burning and the center of the earth warm enough to produce volcanos, is nuclear energy. Until a new energy source is postulated and reasonably confirmed, the prudent person stays with what seems to work. As yet, no other source of energy, that we know about, is sufficient to provide the observed heat over so long a period. Further, components of atomic theory have been verified sufficiently well in laboratories around the world and in field trials (Hiroshima, Nagasaki, and Enowetok Atoll) that most scientists, and their financial backers, agree.

Atomic energy is released in three ways: Radioactive Decay, Fission and Fusion. Radioactive decay occurs when an element spontaneously disgorges one of the two radioactive particles and a gamma ray, and becomes a new element. Fission occurs when a nucleus is split by a slow neutron and (we think) rarely occurs in nature; however, it is the basis for nuclear power plants and the Atomic Bomb. Fusion occurs when two or more nuclei react to become a new element, isotope, or combination of nuclei.

All Radioactivity is potentially dangerous to living things; so we will not be doing any active measurements of radioactive materials in this lab. The danger from radioactivity occurs if the original atom becomes attached to or part of a cell. The radioactivity emitted when the atom decays will blast its way through the organic matter of the cell and could hit a vital part which could change the way the cell reproduces, especially the DNA, which makes up the "memory" of the cell. Most probably, the particle will simply kill the cell by breaking up the structure; however, if the cell begins to grow and reproduce out of control, we call that Cancer, or in people of prime reproductive age, birth defects are always possible.

For these reasons, we will use results of measurements which have been already taken under carefully controlled conditions. The data obtained and summarized in the Chart of the Nuclides, are the result of many person-years of careful study under sometimes hazardous conditions. Problems 1 and 2 of this lab use portions of the Chart of the Nuclides in Figures 1 and 2 which can be viewed, in its entirety, on the back wall of the LAB. Please print these figures but remember to use Landscape in Properties when you print one of them.

Reading the Chart of the Nuclides

The Horizontal axis gives the total number of neutrons. The vertical axis gives the total number of Protons.

The number of protons (plus charges) is the same as the number of electrons surrounding the neutral atom, and, remembering that the number of electrons controls the chemistry of the atoms, the chemical name (or symbol) can be substituted for the number of protons. In any given row, all boxes pertain to the same element. Each box, however, for the indicated element, contains a different number of neutrons from its neighbors. Thus, each row lists the isotopes of each of the elements. It is interesting to note that all of the elements have isotopes. Even the simplest element has three isotopes; normal hydrogen has one proton, but there are isotopes which have one or two neutrons.

Radioactive Decay

Radioactive decay is an important astronomical process which contributes to keeping the cores of planets warm. Originally, there seemed to be three types of radioactive rays, and they were named for the first three letters of the Greek alphabet; Alpha, Beta, and Gamma radiation. A nucleus of an atom undergoing alpha decay produces an alpha particle and energy. The alpha particle was found, by Rutherford, to be simply a helium nucleus; yet the velocity of the alpha particle makes it an effective bullet. The range of the bullet is small; a few centimeters of air are enough to slow it down to where it can grab electrons from other atoms and become the inert gas Helium.

A similar problem occurs with beta radiation, except that the particle emitted from the decaying nucleus is a high speed particle with the mass of an electron and may have either a negative (electron) or a positive (positron) charge. These particles can penetrate more air but generally have a range of no further than a few tens of centimeters in air.

Gamma radioactivity produces no particles; however, it is the most penetrating form of radioactivity and will pass through lead bricks. For years, it was felt that it was a separate form of radioactivity, but in the 1930's gamma rays were found to accompany alpha and beta radioactive decay. Gamma rays were found to be a form of electromagnetic radiation similar to x-rays. Because of the photoelectric effect (electromagnetic radiation can eject electrons from atoms), gamma rays can disrupt cellular chemicals, including DNA.

Radioactivity Decay Reactions

Since chemists really did the most work in establishing the information on radioactivity, the equations for radioactive reactions look a lot like the equations you saw in Chemistry class. A sample reaction for the decay of Uranium (which has 92 protons and a total of 238 protons and neutrons) which decays producing an alpha particle (helium nucleus), thorium (the leftover nuclear material) and heat is

a) ₉₀Th²³³ --> Ra    +        +    Energy

b) ₈₆Rn²²² --> Po     +        +    Energy

₈O¹⁴ --> ₇N¹⁴ + ⁺ + Energy

Again, notice that the total number of nucleons is constant and the total number of positive charges is also constant. The ⁺ particle is sometimes written as ₁ and ^- is sometimes written as _-1.

Problem 2. Complete the following reactions involving beta decay:

a) ₆C¹⁰ --> + ⁺ + Energy

b) ₅B¹⁴ --> + ^- + Energy

c) ₈O²¹ --> + ^- + Energy

Both the changes in the composition of a material and the energy output are important to astronomical processes. Let's look at the energy release first. Each radioactive decay releases only a very little energy, but each little bit added to it's neighbor keeps the center of the earth molten, allowing the surface to be geologically active. The heat for volcanos and the driver for continental drift comes from many radioactive decays.

Probably the best place to start is with the decay of Uranium 235, a fairly prominent element in rocks. The rate of decay of an isotope is apparently dependent on the particular mix of the parts, or nucleons, of the isotope's nuclear structure. Each decay is apparently random, breaking up in "it's own sweet time", and, at the present state of knowledge, nothing we can do to it will affect the time when a particular atom will be "in the mood".

The time that half of the isotope has decayed, the "half life" of the isotope, is a useful concept which can give a way of stating the rate of decay of a large number of atoms of one kind. The easiest way to see how it works is to plot a graph of the amount of materials versus time. Assume we start at 9 AM with 10 Kg of an element which has a half life of one day. The next day when we come into the lab at 9 AM, we find we have only 5 Kg of the element and a little less than 5 Kg of the daughter element, a lot of helium, and it is somewhat warmer in the lab. (The mass of the daughter, the helium and the heat released should add up to 5 Kg.) The next day at 9 AM we find only half of the 5 Kg or 2.5 Kg of the element, a little less than 2.5 Kg more of the daughter element, some more helium and a little more added heat.

Problem 3. Graph the relationship for our hypothetical element for ten days. Plot time on the horizontal axis and element mass on the vertical. Would you expect to see all of the material disappear in a year? When would all of the material be gone?

Problem 4. Suppose that, today, the Earth contains 10⁸ Kg of Uranium 238 and that its half life is 4.5 x 10⁹ years. If the Earth were 5 billion years old, approximately how much Uranium 238 would there have been when the Earth formed?

Heat from Decay

If you add up the total mass of the left hand side and the right hand side, there is slightly less mass on the right hand side. The difference in the mass emerges as energy, in the form of gamma rays. The amount of energy can be determined using the famous equation E = mc², where m is the mass of the element which was converted to energy and c is the speed of light.

Problem 5. During each decay of an Uranium atom, 8.2 x 10^-36 kilograms of mass are missing. How much energy is released from this decay (units of Joules)?

Assume 1 calorie = 4.18 Joules, then convert to calories.

A calorie is the amount of heat needed to raise the temperature of a gram of water one degree Celsius.

Problem 6. How many reactions in an insulated container would have to occur before a gram of water were raised one degree? There are 6 x 10²³ atoms in 0.273 kilograms of Uranium. Is this a reasonable source of heat in the interior of the Earth?

The other types of nuclear reactions of importance are Fusion Reactions, which are apparently the main source of energy from the Sun, and controlled and uncontrolled nuclear fission, the stuff of nuclear generated electricity and Atom Bombs. Fusion will be discussed later when we deal with the text chapter; The Sun.