Give an example of a set which has exactly 10 elements and express it through a defining
property
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Answer:
Geologists have recently determined that the minerals goethite and hematite exist in abundance on Mars, sure signs of the presence of water (see Figure 1 for a picture). None of those geologists have been to Mars, of course, but the unmanned rovers Spirit and Opportunity have. These rovers are equipped with three mass spectrometers, each of which is capable of determining the chemical composition of a solid with a high degree of accuracy. With such a precise chemical analysis in hand, geologists on Earth had no problem identifying the minerals.
The small spheres in this picture were dubbed “berries” by geologists who first saw them.
The small spheres in this picture were dubbed “berries” by geologists who first saw them. They sit on the surface of Mars and were photographed by the Mars rover Opportunity. A mass spectrometer on the rover was able to determine the chemical content of the berries and geologists recognized the chemical formula for hematite (Fe2O3).
© NASA/JPL/Cornell
A mineral is defined in part by a specific chemical composition. In theory, therefore, it is always easy to identify a mineral, if you can determine the chemical composition with a mass spectrometer like the Mars rovers. In reality, however, even if you are looking at rocks on Earth, determining the exact chemical composition of a substance involves significant time preparing the sample and sophisticated laboratory equipment (and often significant money). Luckily, it is usually unnecessary to go to such lengths, because there are much easier ways that require little more than a magnifying lens and a penknife.
Identifying minerals by physical properties
The most common minerals in Earth's crust can often be identified in the field using basic physical properties such as color, shape, and hardness. The context of a mineral is important, too – some minerals can form under the same conditions, so you are likely to find them in the same rock, while others form under very different conditions and will never occur in the same rock. For this reason, context (the other surrounding minerals and type of rock) can often be used to rule out minerals that have similar color, for example. Although there are many thousands of named minerals, only a dozen or so are common in Earth's crust. Testing a few physical properties therefore means that you can identify about 90% of what you are likely to encounter in the field.
Because the physical properties of a mineral are determined by its chemical composition and internal atomic structure, they can be used diagnostically, the way a runny nose and sore throat can be used to diagnose a cold. There are many physical properties of minerals that are testable with varying degrees of ease, including color, crystal form (or shape), hardness, luster (or shine), density, and cleavage or fracture (how the mineral breaks). In addition, many minerals have unique properties, such as radioactivity, fluorescence under black light, or reaction to acid. In most cases, it is necessary to observe a few properties to identify a mineral; to extend the medical analogy even further, a runny nose is a symptom of a cold virus, allergies, or a sinus infection among other things, so we have to use other symptoms to diagnose the problem – a headache, fever, watery eyes, and so on.
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