Читать книгу Modern Alchemy and the Philosopher's Stone - Wilfried B. Holzapfel - Страница 38

These exponents might remind you of the ‘exponentiation’ used by the alchemists. They are also often called orders of magnitude by the scientists of today.

Negative exponents refer to fractions with a one in the numerator and a power of ten in the denominator. For fractions of a meter we use the term millimeter (1 mm = 10^-3m) to describe one-thousandth of a meter. We also use micrometer (1 µm = 10^-6 m) for one millionth of meter, and nanometer (1 nm = 10^-9 m), for one billionth of a meter, one picometer (1 pm = 10^-12 m) for one trillionth of a meter, one femtometer (1 fm = 10^-15 m) for a thousandth of that and one attometer (1 am = 10^-18 m) for another thousandth of that.”

Helen and Marie spent a few moments discussing the figure with the professor. They were familiar with some of the small units, but they had not heard of the others.

Professor Wood continued his commentary. “Using these units, for example, you can say that simple molecules are a few nanometers in size, and that typical atoms measure a few 100 picometers in diameter. The diameters of the nuclei of the atoms are found to be in the range of some 10 fm, or about 10^-14 m. The electron is often considered to be smaller than a tenth of an attometer, or in the range of 10^-19 m. However, this ‘classical’ estimate is almost meaningless from the present point of view,” the professor cautioned.

“Of course you are familiar with the famous Bohr model for the atoms that dates from the early days of atomic physics. That model often shows tiny electrons orbiting around the atomic nucleus like the planets around the sun. It shows lots of space between the electrons. It is still possible to find this picture in scientific literature, but it conflicts with the evidence that physicists have obtained through experimentation later in the 20^th century.

“In contrast to the macroscopic view suggested by the typical drawing of the Bohr atom – not to mention baseballs and soccer balls and so on – the more modern microscopic view of an electron looks more like a misty cloud. Physicists today talk about uncertainty in the extent and location of the electronic charge associated with a single electron. They find that they get better mathematical agreement with some of the experimental observations if they model the electron as a cloud with a density described by some kind of a standing wave than they do if they think of the electron as an actual particle.”

Helen interrupted. “What is a standing wave,” she wanted to know.

“I can take that one,” Marie offered. “A standing wave is a wave that appears not to be moving, or ‘propagating,’ as it says in my physics book. Perhaps the most common example is a vibrating guitar string. It has stationary points at the ends of the string and it moves the greatest distance from its non-vibrating position at the middle of the string.”

“I’m not sure that I understand what you are trying to tell me,” Helen said.

“It is not really important for our discussion here today,” Professor Wood interjected. “It is only important to realize that these tiny electrons, with all their wave-particle uncertainty, determine the size of the atoms. The building blocks of the atomic nuclei, the protons and the neutrons are typically described as having smaller diameters that measure about 1 fm, or 10^-15 m. However, even these particles display an internal structure that we ascribe to even smaller particles called quarks. We estimate the diameter of a quark to be about 1 am, or 10^-18 m. Finally, there is a distance that physicist call the Planck Length. That is a distance of about 10^-35 meters. At that distance, due to the uncertainty in the so-called time-space continuum, it no longer makes any sense to talk about the length of something. That brings us to the bottom of this chart.”

Helen shook her head, “Unbelievable! I thought that this idea of quarks was just some kind of a fantasy,” she said.

Professor Wood pretended to be shocked by Helen’s remark. “Not at all,” he countered. “This is good physics! When the American physicist Murray Gell-Mann first postulated the existence of quarks in 1964, many people would have agreed with you. His idea that protons and neutrons consist of three quarks and many gluons that bind the quarks together like some kind of primordial glue was initially greeted with widespread skepticism within the scientific community. But Gell-Mann was also able to use his model to explain virtually all of the elementary particles that experimenters had discovered in the large “atom smashers” such as Brookhaven, Berkeley, and the Lawrence Berkely National Laboratories, as well as the Stanford Linear Accelerator, in the USA.⁹ He received the Noble Prize just five years later in 1969. Today, the existence of quarks is taken for granted by high-energy physicists.”

Professor Wood went back to his stack of illustrations. He extracted one that suggested that atoms are composed of “massive particles” like the protons, neutrons and electrons with which the students were familiar (Figure 16). It also showed that these particles interact through three kinds of force: the electromagnetic force; plus the “strong” and “weak” nuclear forces.