ATOMIC RADIUS - BASIC INFORMATION AND TUTORIALS



Unfortunately, atomic radius is hard to define. The probability of finding an electron decreases with increasing distance from the nucleus, but nowhere does the probability fall to zero, so there is no precise outer boundary to an atom.

We might describe an effective atomic radius as, say, the distance from the nucleus within which 95% of all the electron charge density is found, but in fact, all that we can measure is the distance between the nuclei of adjacent atoms (internuclear distance).

Even though it varies, depending on whether atoms are chemically bonded or merely in contact without forming a bond, we define atomic radius in terms of internuclear distance.

Because we are primarily interested in bonded atoms, we will emphasize an atomic radius based on the distance between the nuclei of two atoms joined by a chemical bond. The covalent radius is one-half the distance between the nuclei of two identical atoms joined by a single covalent bond.

The ionic radius is based on the distance between the nuclei of ions joined by an ionic bond. Because the ions are not identical in size, this distance must be properly apportioned between the cation and anion. One way to apportion the electron density between the ions is to define the radius of one ion and then infer the
radius of the other ion.

The convention we have chosen to use is to assign an ionic radius of 140 pm. An alternative apportioning scheme is to use as the reference ionic radius.

When using ionic radii data, one should carefully note which convention is used and not mix radii from the different conventions. Starting with a radius of 140 pm for the radius of Mg2+ can be obtained from the internuclear distance in MgO, the radius of from the internuclear distance in and the radius of from the internuclear distance in NaCl.

For metals, we define a metallic radius as one-half the distance between the nuclei of two atoms in contact in the crystalline solid metal. Similarly in a solid sample of a noble gas the distance between the centers of neighboring atoms is called the van der Waals radius.

There is much debate about the values of the atomic radii of noble gases because the experimental determination of the van der Waals radii is difficult; consequently, the atomic radii of noble gases are left out of the discussion of trends in atomic radii.

THE SCIENTIFIC METHOD USE IN CHEMISTRY BASICS


Science differs from other fields of study in the method that scientists use to acquire knowledge and the special significance of this knowledge. Scientific knowledge can be used to explain natural phenomena and, at times, to predict future events.

The ancient Greeks developed some powerful methods of acquiring knowledge, particularly in mathematics. The Greek approach was to start with certain basic assumptions, or premises. Then, by the method known as deduction, certain conclusions must logically follow.

For example, if and then Deduction alone is not enough for obtaining scientific knowledge, however. The Greek philosopher Aristotle assumed four fundamental substances: air, earth, water, and fire. All other materials, he believed, were formed by combinations of these four elements.

Chemists of several centuries ago (more commonly referred to as alchemists) tried, in vain, to apply the four-element idea to turn lead into gold. They failed for many reasons, one being that the four-element assumption is false.

The scientific method originated in the seventeenth century with such people as Galileo, Francis Bacon, Robert Boyle, and Isaac Newton. The key to the method is to make no initial assumptions, but rather to make careful observations of natural phenomena.

When enough observations have been made so that a pattern begins to emerge, a generalization or natural law can be formulated describing the phenomenon. Natural laws are concise statements, often in mathematical form, about natural phenomena.

The form of reasoning in which a general statement or natural law is inferred from a set of observations is called induction. For example, early in the sixteenth century, the Polish astronomer Nicolas Copernicus (1473 1543), through careful study of astronomical observations, concluded that Earth revolves around the sun in a circular orbit, although the general teaching of the time, not based on scientific study, was that the sun and other heavenly bodies revolved around Earth.

We can think of Copernicus s statement as a natural law. Another example of a natural law is the radioactive decay law, which dictates how long it takes for a radioactive substance to lose its radioactivity.

The success of a natural law depends on its ability to explain, or account for, observations and to predict new phenomena. Copernicus s work was a great success because he was able to predict future positions of the planets more accurately than his contemporaries.

We should not think of a natural law as an absolute truth, however. Future experiments may require us to modify the law. For example, Copernicus s ideas were refined a half-century later by Johannes Kepler, who showed that planets travel in elliptical, not circular, orbits. To verify a natural law, a scientist designs experiments that show whether the conclusions deduced from the natural law are supported by experimental results.

A hypothesis is a tentative explanation of a natural law. If a hypothesis survives testing by experiments, it is often referred to as a theory. In a broader sense, a theory is a model or way of looking at nature that can be used to explain natural laws and make further predictions about natural phenomena.

When differing or conflicting theories are proposed, the one that is most successful in its predictions is generally chosen. Also, the theory that involves the smallest number of assumptions the simplest theory is preferred. Over time, as new evidence accumulates, most scientific theories undergo modification,
and some are discarded.

The scientific method is the combination of observation, experimentation, and the formulation of laws, hypotheses, and theories. Scientists may develop a pattern of thinking about their field, known as a paradigm.

Some paradigms may be successful at first but then become less so. When that happens, a new paradigm may be needed or, as is sometimes said, a paradigm shift occurs. In a way, the method of inquiry that we call the scientific method is itself a paradigm, and some people feel that it, too, is in need of change.

In any case, merely following a set of procedures, rather like using a cookbook, will not guarantee scientific success. Another factor in scientific discovery is chance, or serendipity. Many discoveries have been made by accident.

For example, in 1839, the American inventor Charles Goodyear was searching for a treatment for natural rubber that would make it less brittle when cold and less tacky when warm. In the course of this work, he accidentally spilled a rubber sulfur mixture on a hot stove and found that the resulting product had exactly the properties he was seeking.

Other chance discoveries include X-rays, radioactivity, and penicillin. So scientists and inventors always need to be alert to unexpected observations. Perhaps no one was more aware of this than Louis Pasteur, who wrote, Chance favors the prepared mind.