World Futures: Statistics (And Probability) – Part One

Los Alamos World
Futures Institute

In exploring the future of humanity and the world we must rely on the collection and analysis of statistical data and apply the inferences drawn to decision making, selecting what road we will take both collectively and individually.

In the previous series of columns about risks, rewards and responsibilities, we started with probability and concluded that often we cannot truly assess the probabilities in making personal decisions. Will he or she say yes or no when we ask her or him for a date? Yet in many fields of endeavor we are completely dependent of statistical data and subsequent probabilistic calculations.

The following paragraphs deal with nuclear reactors, fission reactions, and predicting them with a concept called a cross section. For simplicity, an atom can be thought of as a circular target with a small bullseye called the nucleus. The cross section is a statistic that permits scientific and engineering probabilistic calculations. If your head begins to hurt reading about it, that is okay. Mine felt the same way writing it. It all deals with very large and very small numbers and what degree of accuracy and precision is needed in design and decision making.

Chicago Pile-1, the first manmade nuclear reactor achieved criticality on December 2, 1942. Chicago Pile-1 was created by Enrico Fermi, the architect of the nuclear age, and was based on the fission of Uranium by induced neutrons, a subatomic particle with no net electrical charge and found in the nucleus of atoms. If a neutron hits the nucleus of an atom of U235 (an isotope of Uranium), U236 is formed and the atom has more energy because of the kinetic (moving) energy the neutron brings with it. The U236 atom becomes unstable (almost immediately) and fissions (breaks apart) into two smaller atoms, some additional high energy neutrons, some gamma rays (energetic photons) and other fragments. There is a net loss of mass and a release of energy.

One pound of  U235 (0.452592 kilograms)  has approximately 1.1624 septillion atoms. If you do a crude calculation of all the atoms fissioning simultaneously, about 10 million kilowatt hours of energy would be released. At Los Alamos residential rates the equates to about $1,152,000.00.

From another perspective, if all of the energy is released simultaneously from the pound of U235, it would be the same as about 9 metric tons of TNT (trinitrotoluene) exploding. If you want an explosion, that sounds pretty good. But if you want to harness the energy, convert it to electricity and distribute it, perhaps some control is needed. So how do you do it?

The neutron has to hit the nucleus of the atom, a small part of the complete atom with electrons moving in orbits around the nucleus. The radius of the atom itself (which includes the orbiting electrons) is more than 10,000 times the radius of the nucleus. So the neutron approaching the atom is like a bullet, dart or arrow approaching a target the size of a football field with a bullseye the size of an M&M. During the Manhattan Project, physicists at Purdue University had to come up with a unit to measure the cross section of a nucleus (the bullseye of the atom). The resulting unit was the barn, or an area equal to 100 square fm (fentometers or 0.0000000000000001 meters, also called a fermi). It represents the probability of interaction between small particles, with its name deriving from the American expression “can’t hit the broadside of a barn.”

Obviously, designing and building a nuclear reactor is not this simple. Cross sections may vary depending on the velocity of the neutrons. Neutrons can escape. Radioactive fission particles change the composition of the fissionable “material.” Energy must be removed or things are going to melt or explode. And the heat energy, when extracted, must be converted to electricity for distribution. But the cornerstone of the design rests on the cross section of the nucleus to the neutron – a probability measurement expressed in physical terms and obtained from experimentation and measurement. A statistic.

To put things in perspective, the number of atoms per pound of U235 is about 153 trillion times the population of the world. If an atom fails to fission, which is considered in the design calculations, who cares unless the design fizzles (as opposed to fissiles)? Plus, different designs can be tested to see which works best. But if the system is human or affects humans multiple testing is not allowed. The statistics from which response is predicted and decisions are made need to be accurate and well understood. We should care about accuracy both individually and collectively. It is a responsibility. So let us explore the implications of statistics and inferences drawn in our perception of “reality” and the choice of roads and road maintenance. While there is no statistical evidence that keeping the Cheshire Cat happy is essential, it is probably a good idea.

Till next time…

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