Math Is Fun Forum

Coin Quotes - I

1. All the perplexities, confusion and distress in America arise, not from defects in their Constitution or Confederation, not from want of honor or virtue, so much as from the downright ignorance of the nature of coin, credit and circulation. - John Adams

2. Peace and justice are two sides of the same coin. - Dwight D. Eisenhower

3. Leadership is the other side of the coin of loneliness, and he who is a leader must always act alone. And acting alone, accept everything alone. - Ferdinand Marcos

4. Silver and gold are not the only coin; virtue too passes current all over the world. - Euripides

5. If you call yourself a leader, then you have to be decisive. If you're decisive, then you have the chance to be a leader. These are two sides to the same coin. - Narendra Modi

6. German and European unification are two sides of the same coin. - Helmut Kohl

7. When the machine had been fastened with a wire to the track, so that it could not start until released by the operator, and the motor had been run to make sure that it was in condition, we tossed a coin to decide who should have the first trial. Wilbur won. - Orville Wright

8. I said, yet again, for Germany, Europe is not only indispensable, it is part and parcel of our identity. We've always said German unity, European unity and integration, that's two parts of one and the same coin. But we want, obviously, to boost our competitiveness. - Angela Merkel.

Isotope

Gist

An isotope is a form of a chemical element with the same number of protons but a different number of neutrons than other atoms of the same element. This difference in neutron count gives isotopes the same atomic number but different mass numbers, meaning they have identical chemical properties but different physical properties. For example, carbon-12 and carbon-14 are both isotopes of carbon; they both have six protons, but carbon-12 has six neutrons, while carbon-14 has eight.

An isotope is a version of a chemical element with the same number of protons but a different number of neutrons. This difference in neutrons gives isotopes the same atomic number but different mass numbers, leading to nearly identical chemical properties but different physical properties. For example, carbon-12, carbon-13, and carbon-14 are all isotopes of carbon, each with six protons but a different number of neutrons. 

Summary

Isotopes are distinct nuclear species (or nuclides) of the same chemical element. They have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), but different nucleon numbers (mass numbers) due to different numbers of neutrons in their nuclei. While all isotopes of a given element have virtually the same chemical properties, they have different atomic masses and physical properties.

The term isotope comes from the Greek roots isos ("equal") and topos ("place"), meaning "the same place": different isotopes of an element occupy the same place on the periodic table. It was coined by Scottish doctor and writer Margaret Todd in a 1913 suggestion to the British chemist Frederick Soddy, who popularized the term.

The number of protons within the atom's nucleus is called its atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons. The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number.

For example, carbon-12, carbon-13, and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13, and 14, respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons so that the neutron numbers of these isotopes are 6, 7, and 8 respectively.

Details

An isotope is one of two or more species of atoms of a chemical element with the same atomic number and position in the periodic table and nearly identical chemical behaviour but with different atomic masses and physical properties. Every chemical element has one or more isotopes.

An atom is first identified and labeled according to the number of protons in its nucleus. This atomic number is ordinarily given the symbol Z. The great importance of the atomic number derives from the observation that all atoms with the same atomic number have nearly, if not precisely, identical chemical properties. A large collection of atoms with the same atomic number constitutes a sample of an element. A bar of pure uranium, for instance, would consist entirely of atoms with atomic number 92. The periodic table of the elements assigns one place to every atomic number, and each of these places is labeled with the common name of the element, as, for example, calcium, radon, or uranium.

Not all the atoms of an element need have the same number of neutrons in their nuclei. In fact, it is precisely the variation in the number of neutrons in the nuclei of atoms that gives rise to isotopes. Hydrogen is a case in point. It has the atomic number 1. Three nuclei with one proton are known that contain 0, 1, and 2 neutrons, respectively. The three share the place in the periodic table assigned to atomic number 1 and hence are called isotopes (from the Greek isos, meaning “same,” and topos, signifying “place”) of hydrogen.

Many important properties of an isotope depend on its mass. The total number of neutrons and protons (symbol A), or mass number, of the nucleus gives approximately the mass measured on the so-called atomic-mass-unit (amu) scale. The numerical difference between the actual measured mass of an isotope and A is called either the mass excess or the mass defect.

The term nuclide is used to describe particular isotopes, notably in cases where the nuclear rather than the chemical properties of an atom are to be emphasized. The lexicon of isotopes includes three other frequently used terms: isotones for isotopes of different elements with the same number of neutrons, isobars for isotopes of different elements with the same mass number, and isomers for isotopes identical in all respects except for the total energy content of the nuclei.

The discovery of isotopes

Evidence for the existence of isotopes emerged from two independent lines of research, the first being the study of radioactivity. By 1910 it had become clear that certain processes associated with radioactivity, discovered some years before by French physicist Henri Becquerel, could transform one element into another. In particular, ores of the radioactive elements uranium and thorium had been found to contain small quantities of several radioactive substances never before observed. These substances were thought to be elements and accordingly received special names. Uranium ores, for example, yielded ionium, and thorium ores gave mesothorium. Painstaking work completed soon afterward revealed, however, that ionium, once mixed with ordinary thorium, could no longer be retrieved by chemical means alone. Similarly, mesothorium was shown to be chemically indistinguishable from radium. As chemists used the criterion of chemical indistinguishability as part of the definition of an element, they were forced to conclude that ionium and mesothorium were not new elements after all, but rather new forms of old ones. Generalizing from these and other data, English chemist Frederick Soddy in 1910 observed that “elements of different atomic weights [now called atomic masses] may possess identical (chemical) properties” and so belong in the same place in the periodic table. With considerable prescience, he extended the scope of his conclusion to include not only radioactive species but stable elements as well. A few years later, Soddy published a comparison of the atomic masses of the stable element lead as measured in ores rich in uranium and thorium, respectively. He expected a difference because uranium and thorium decay into different isotopes of lead. The lead from the uranium-rich ore had an average atomic mass of 206.08 compared to 207.69 for the lead from the thorium-rich ore, thus verifying Soddy’s conclusion.

The unambiguous confirmation of isotopes in stable elements not associated directly with either uranium or thorium followed a few years later with the development of the mass spectrograph (see mass spectrometry) by Francis William Aston. His work grew out of the study of positive rays (sometimes called canal rays), discovered in 1886 by Eugen Goldstein and soon thereafter recognized as beams of positive ions. As a student in the laboratory of J.J. Thomson, Aston had learned that the gaseous element neon produced two positive rays. The ions in the heavier ray had masses about two units, or 10 percent, greater than the ions in the lighter ray. To prove that the lighter neon had a mass very close to 20 and that the heavier ray was indeed neon and not a spurious signal of some kind, Aston had to construct an instrument that was considerably more precise than any other of the time. By 1919 he had done so and convincingly argued for the existence of neon-20 and neon-22. Information from his and other laboratories accumulated rapidly in the ensuing years, and by 1935 the principal isotopes and their relative proportions were known for all but a handful of elements.

Additional Information

A family of people often consists of related but not identical individuals. Elements have families as well, known as isotopes. Isotopes are members of a family of an element that all have the same number of protons but different numbers of neutrons.

The number of protons in a nucleus determines the element’s atomic number on the Periodic Table. For example, carbon has six protons and is atomic number 6. Carbon occurs naturally in three isotopes: carbon 12, which has 6 neutrons (plus 6 protons equals 12), carbon 13, which has 7 neutrons, and carbon 14, which has 8 neutrons. Every element has its own number of isotopes.

The addition of even one neutron can dramatically change an isotope’s properties. Carbon-12 is stable, meaning it never undergoes radioactive decay. Carbon-14 is unstable and undergoes radioactive decay with a half-life of about 5,730 years (meaning that after 5,730 years half of the material will have decayed to the stable isotope nitrogen-14). This decay means the amount of carbon-14 in an object serves as a clock, showing the object’s age in a process called “carbon dating.”

Isotopes have unique properties, and these properties make them useful in diagnostics and treatment applications. They are important in nuclear medicine, oil and gas exploration, basic research, and national security.

Ultraviolet

Gist

Ultraviolet (UV) is a type of electromagnetic radiation from the sun and artificial sources, with a shorter wavelength than visible light but longer than X-rays. It is invisible to the human eye and includes three main types: UVA, UVB, and UVC. While beneficial for vitamin D production, excessive UV exposure can cause skin damage, premature aging, and increase the risk of skin cancer. 

Ultraviolet (UV) light has shorter wavelengths than visible light. Although UV waves are invisible to the human eye, some insects, such as bumblebees, can see them. This is similar to how a dog can hear the sound of a whistle just outside the hearing range of humans.

Summary

Ultraviolet radiation or UV is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of the total electromagnetic radiation output from the Sun. It is also produced by electric arcs, Cherenkov radiation, and specialized lights, such as mercury-vapor lamps, tanning lamps, and black lights.

The photons of ultraviolet have greater energy than those of visible light, from about 3.1 to 12 electron volts, around the minimum energy required to ionize atoms.  Although long-wavelength ultraviolet is not considered an ionizing radiation because its photons lack sufficient energy, it can induce chemical reactions and cause many substances to glow or fluoresce. Many practical applications, including chemical and biological effects, are derived from the way that UV radiation can interact with organic molecules. These interactions can involve exciting orbital electrons to higher energy states in molecules potentially breaking chemical bonds. In contrast, the main effect of longer wavelength radiation is to excite vibrational or rotational states of these molecules, increasing their temperature.  Short-wave ultraviolet light is ionizing radiation. Consequently, short-wave UV damages DNA and sterilizes surfaces with which it comes into contact.

For humans, suntan and sunburn are familiar effects of exposure of the skin to UV, along with an increased risk of skin cancer. The amount of UV radiation produced by the Sun means that the Earth would not be able to sustain life on dry land if most of that light were not filtered out by the atmosphere. More energetic, shorter-wavelength "extreme" UV below 121 nm ionizes air so strongly that it is absorbed before it reaches the ground. However, UV (specifically, UVB) is also responsible for the formation of vitamin D in most land vertebrates, including humans. The UV spectrum, thus, has effects both beneficial and detrimental to life.

The lower wavelength limit of the visible spectrum is conventionally taken as 400 nm. Although ultraviolet rays are not generally visible to humans, 400 nm is not a sharp cutoff, with shorter and shorter wavelengths becoming less and less visible in this range. Insects, birds, and some mammals can see near-UV (NUV), i.e., somewhat shorter wavelengths than what humans can see.

Details

Ultraviolet (UV) light has shorter wavelengths than visible light. Although UV waves are invisible to the human eye, some insects, such as bumblebees, can see them. This is similar to how a dog can hear the sound of a whistle just outside the hearing range of humans.

The Sun is a source of the full spectrum of ultraviolet radiation, which is commonly subdivided into UV-A, UV-B, and UV-C. These are the classifications most often used in Earth sciences. UV-C rays are the most harmful and are almost completely absorbed by our atmosphere. UV-B rays are the harmful rays that cause sunburn. Exposure to UV-B rays increases the risk of DNA and other cellular damage in living organisms. Fortunately, about 95 percent UV-B rays are absorbed by ozone in the Earth's atmosphere.

Scientists studying astronomical objects commonly refer to different subdivisions of ultraviolet radiation: near ultraviolet (NUV), middle ultraviolet (MUV), far ultraviolet (FUV), and extreme ultraviolet (EUV). NASA's SDO spacecraft captured the image below in multiple wavelengths of extreme ultraviolet (EUV) radiation. The false-color composite reveals different gas temperatures. Reds are relatively cool (about 60,000 Celsius) while blues and greens are hotter (greater than one million Celsius).

In 1801, Johann Ritter conducted an experiment to investigate the existence of energy beyond the violet end of the visible spectrum. Knowing that photographic paper would turn black more rapidly in blue light than in red light, he exposed the paper to light beyond violet. Sure enough, the paper turned black, proving the existence of ultraviolet light.

Since the Earth's atmosphere absorbs much of the high-energy ultraviolet radiation, scientists use data from satellites positioned above the atmosphere, in orbit around the Earth, to sense UV radiation coming from our Sun and other astronomical objects. Scientists can study the formation of stars in ultraviolet since young stars shine most of their light at these wavelengths. This image from NASA's Galaxy Evolution Explorer (GALEX) spacecraft reveals new young stars in the spiral arms of galaxy M81.

Chemical processes in the upper atmosphere can affect the amount of atmospheric ozone that shields life at the surface from most of the Sun's harmful UV radiation. Each year, a "hole" of thinning atmospheric ozone expands over Antarctica, sometimes extending over populated areas of South America and exposing them to increased levels of harmful UV rays. The Dutch Ozone Monitoring Instrument (OMI) onboard NASA's Aura satellite measures amounts of trace gases important to ozone chemistry and air quality. The image above shows the amount of atmospheric ozone in Dobson Units—the common unit for measuring ozone concentration. These data enable scientists to estimate the amount of UV radiation reaching the Earth's surface and forecast high-UV-index days for public health awareness.

Aurorae are caused by high-energy waves that travel along a planet's magnetic poles, where they excite atmospheric gases and cause them to glow. Photons in this high-energy radiation bump into atoms of gases in the atmosphere causing electrons in the atoms to excite, or move to the atom's upper shells. When the electrons move back down to a lower shell, the energy is released as light, and the atom returns to a relaxed state. The color of this light can reveal what type of atom was excited. Green light indicates oxygen at lower altitudes. Red light can be from oxygen molecules at a higher altitude or from nitrogen. On Earth, aurorae around the north pole are called the Northern Lights.

The Hubble Space Telescope captured this image of Jupiter's aurora in ultraviolet wrapping around Jupiter's north pole like a lasso.

Additional Information

Ultraviolet (UV) radiation covers the wavelength range of 100–400 nm, which is a higher frequency and lower wavelength than visible light. UV radiation comes naturally from the sun, but it can also be created by artificial sources used in industry, commerce and recreation.

The UV region covers the wavelength range 100-400 nm and is divided into three bands:

* UVA (315-400 nm)
* UVB (280-315 nm)
*UVC (100-280 nm).

As sunlight passes through the atmosphere, all UVC and approximately 90% of UVB radiation is absorbed by ozone, water vapour, oxygen and carbon dioxide. UVA radiation is less affected by the atmosphere. Therefore, the UV radiation reaching the Earth’s surface is largely composed of UVA with a small UVB component.

The amount of UV radiation from the sun that hits the Earth’s surface depends on several factors, including the sun’s height in the sky, latitude, cloud cover, altitude, the thickness of the ozone layer and ground reflection. Reductions in the ozone layer due to human-created pollution increase the amount of UVA and UVB that reaches the surface. This can impact human health, animals, marine organisms and plant life. In humans, increased UV exposure can cause skin cancers, cataracts and immune system damage.

Ultraviolet radiation is that portion of the electromagnetic spectrum extending from the violet, or short-wavelength, end of the visible light range to the X-ray region. Ultraviolet (UV) radiation is undetectable by the human eye, although, when it falls on certain materials, it may cause them to fluoresce—i.e., emit electromagnetic radiation of lower energy, such as visible light. Many insects, however, are able to see ultraviolet radiation.

Ultraviolet radiation lies between wavelengths of about 400 nanometres (1 nanometre [nm] is {10}{-9} metre) on the visible-light side and about 10 nm on the X-ray side, though some authorities extend the short-wavelength limit to 4 nm. In physics, ultraviolet radiation is traditionally divided into four regions: near (400–300 nm), middle (300–200 nm), far (200–100 nm), and extreme (below 100 nm). Based on the interaction of wavelengths of ultraviolet radiation with biological materials, three divisions have been designated: UVA (400–315 nm), also called black light; UVB (315–280 nm), responsible for the radiation’s best-known effects on organisms; and UVC (280–100 nm), which does not reach Earth’s surface.

Ultraviolet radiation is produced by high-temperature surfaces, such as the Sun, in a continuous spectrum and by atomic excitation in a gaseous discharge tube as a discrete spectrum of wavelengths. Most of the ultraviolet radiation in sunlight is absorbed by oxygen in Earth’s atmosphere, which forms the ozone layer of the lower stratosphere. Of the ultraviolet that does reach Earth’s surface, almost 99 percent is UVA radiation.

When the ozone layer becomes thin, however, more UVB radiation reaches Earth’s surface and may have hazardous effects on organisms. For example, studies have shown that UVB radiation penetrates the ocean’s surface and may be lethal to marine plankton to a depth of 30 metres (about 100 feet) in clear water. In addition, marine scientists have suggested that a rise in UVB levels in the Southern Ocean between 1970 and 2003 was strongly linked to a simultaneous decline in fish, krill, and other marine life.

Unlike X-rays, ultraviolet radiation has a low power of penetration; hence, its direct effects on the human body are limited to the surface skin. The direct effects include reddening of the skin (sunburn), pigmentation development (suntan), aging, and carcinogenic changes. Ultraviolet sunburns can be mild, causing only redness and tenderness, or they can be so severe as to produce blisters, swelling, seepage of fluid, and sloughing of the outer skin. The blood capillaries (minute vessels) in the skin dilate with aggregations of red and white blood cells to produce the red coloration. Tanning is a natural body defense relying on melanin to help protect the skin from further injury. Melanin is a chemical pigment in the skin that absorbs ultraviolet radiation and limits its penetration into tissues. A suntan occurs when melanin pigments in cells in the deeper tissue portion of the skin are activated by ultraviolet radiation, and the cells migrate to the surface of the skin. When these cells die, the pigmentation disappears. Persons of light complexion have less melanin pigment and so experience the harmful effects of ultraviolet radiation to a greater degree. The application of sunscreen to the skin can help to block absorption of ultraviolet radiation in such persons.

Constant exposure to the Sun’s ultraviolet radiation induces most of the skin changes commonly associated with aging, such as wrinkling, thickening, and changes in pigmentation. There is also a much higher frequency of skin cancer, particularly in persons with fair skin. The three basic skin cancers, basal- and squamous-cell carcinoma and melanoma, have been linked to long-term exposure to ultraviolet radiation and probably result from changes generated in the DNA of skin cells by ultraviolet rays.

Ultraviolet radiation also has positive effects on the human body, however. It stimulates the production of vitamin D in the skin and can be used as a therapeutic agent for such diseases as psoriasis. Because of its bactericidal capabilities at wavelengths of 260–280 nm, ultraviolet radiation is useful as both a research tool and a sterilizing technique. Fluorescent lamps exploit the ability of ultraviolet radiation to interact with materials known as phosphors that emit visible light; compared with incandescent lamps, fluorescent lamps are a more energy-efficient form of artificial lighting.