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Classroom notes for: Radiation and Life 98.101.201 Professor: Thomas M. Regan Pinanski 207 ext 3283 Class 3: Units and Measures Derived Quantities – Oftentimes when numerically evaluating our observations to explain the natural world, it is necessary to perform mathematical operations on quantities to properly express their relationships. – Derived quantities result when mathematical operations have been performed on the fundamental (or other derived) quantities. Energy Energy is measured in N*m in SI units; or equivalently, it can be expressed in terms of the joule (J), also a shorthand notation. – Energy comes in many forms: light, heat, the kinetic energy of a moving object (kinetic energy), etc… – To put this unit of measure in perspective, consider another unit known as the calorie, which used in dietetics for stating the energy (heat) content of a food, i.e., the amount of heat energy that the food can yield as it passes through the body. One calorie = 4,185 joules in this context. – The heat of fusion for water is approximately 333 joules/gram. (http://www.infoplease.com/ce5/CE008611.html) – The unit is named for the English physicist James Prescott Joule (1818-1889). – (http://www.encarta.msn.com) Power Power is measured in J/s in SI units, or in watts (W). As an example, note that a 100-watt light bulb emanates 100 joules of infrared and light energy each second. The unit is named for the Scottish engineer and inventor James Watt (1736-1819). (http://www.encarta.msn.com) Flashlight Spectral Emission 4600 K Wien's displacement law & Stefan-Boltzmann law Frequency Frequency is measured in cycles per second (1/s), also known as the hertz (Hz). – A cycle can be a toss of the pen from my hand to the height of its travel and back; it can be a wave of water or sound, etc.. – When watching water waves in a pond, the number of wave crests that pass by each second is the frequency in Hz. – This unit is named in honor of Heinrich Hertz (18571894), a German physicist. (http://www.encarta.msn.com) Unit Prefixes If a quantity is very large, sometimes it easier to express it in shorthand notation. For example, suppose you measure a distance of 1000 meters. What is this called? – In radiation sciences unit prefixes are important because the numbers involved tend to be either very large or extraordinarily small. – Some common prefixes in the SI system are: – – – – – – – – Numbers larger than one: prefix multiple kilo (x1,000) mega (x1,000,000) giga (x1,000,000,000) tera (x1,000,000,000,000) peta (x1,000,000,000,000,000) exa (x1018) abbrev. k M G T P E To understand the relative scales of these values, consider: one kilogram = 1,000 grams (weighs about 2.205 lb on the earth’s surface); one megawatt of electricity would light 10,000 100-Watt light bulbs; ½ gigameter is about the distance between the earth and the moon (3.84 x108 m). Numbers smaller than one (fractions): prefix centi milli micro nano pico femto multiple (1/100) (1/1,000) (1/1,000,000) (1/1,000,000,000) (one trillionth) 10-15 abbrev. c m m n p Scientific Notation Scientific notation is simply another shorthand method for writing very large or very small numbers. – – – – – – – – – Numbers larger than one: 1 = 100 10 = 101 100 = 102 1,000 = 103 (kilo) 1,000,000 = 106 (mega) 1,000,000,000 = 109 (giga) 1,000,000,000,000 = 1012 (tera) The superscript is called an exponent. For numbers larger than one, the number is written as a “one” followed by a number of zeroes equal to the exponent. Numbers smaller than one: – 1 = 100 – 1/10 = 10-1 – 1/100 = 10-2 – 1/1,000 = 10-3 – 1/1,000,000 = 10-6 – 1/1,000,000,000 = 10-9 – 1/1,000,000,000,000 = 10-12 – 1/1,000,000,000,000,000 = 10-15 For numbers smaller than one (fractions), the number is written as a “one” divided by a “one” followed by a number of zeroes equal to the exponent. Notice that the exponent is negative for fractions of one. Historical Developments in Modern Physics “To understand a science it is necessary to know its history.” August Comte (1798-1857), the French positivist philosopher, was a founder of sociology. (http://www.encarta.msn.com) Circa 1800, we had a general understanding of the world around us. Newton’s three Laws of Motion were known. – An object at rest tends to stay at rest, an object in motion tends to stay in motion. – An object continues in its initial state of rest or motion with uniform velocity unless it is acted on by an unbalanced, or net external, force. (Physics 3rd Ed., Tipler, p. 77) – This may seem to be a counterintuitive thought. For example, push a book so that it slides freely along the surface of a table, and the book will eventually come to a stop. However, this is because of friction. If a book were thrown in the vacuum of space, it would continue to travel forever until it hit something. F = m*a – F is force in Newtons, – m is mass in kilograms, and – a is acceleration in m/s2. • Note that F and a are vector quantities. With this formula, it is demonstrated that exerting a net force on an object will accelerate it (speed it up or slow it down). Consider the example of throwing the book in a vacuum. Give it a single push and it will fly through the void at a constant speed. However, push it continuously and it will speed up. The book sliding on the desk can’t continue to move at a constant speed because the force of friction is causing it to slow down. For every action, there is an equal and opposite reaction. Forces always occur in pairs. If object A exerts a force on object B, an equal but opposite force is exerted by object B on object A. (Physics 3 Ed., Tipler, p. 78) rd Newton Continued For every action, there is an equal and opposite reaction. Forces always occur in pairs. If object A exerts a force on object B, an equal but opposite force is exerted by object B on object A. (Physics 3rd Ed., Tipler, p. 78) The classic example of this is a rocket. It pushes away its burning exhaust gasses, and they in turn propel it forward. When I push on a desk or wall, it pushes back, but friction keeps me rooted to the spot. If I did this at an ice-skating rink, I would be pushed out into the rink. Newton’s theory for gravity was understood. Essentially, Newton described gravity as a force of attraction between any objects with mass, and was able to formulate this mathematically. Although Kepler’s laws were an important step in understanding the motion of the planets, they were still merely empirical rules obtained from the astronomical observations of Brahe. It remained for Newton to take the giant step forward and attribute the acceleration of a planet in its orbit to a force exerted by the sun on the planet that varied inversely with the square of the distance between the sun and the planet. Others besides Newton had proposed that such a force existed, but Newton was able to prove that a force that varied inversely with the square of the separation distance would result in the elliptical orbits observed by Kepler. Newton then made the bold assumption that such a force existed between any two objects in the universe (before Newton, it was not even generally accepted that the laws of physics observed on earth were applicable to the heavenly bodies). (Physics 3rd Ed., Tipler, p. 299) There seems to be no reason to doubt the basic truth of the story of Newton and the apple: that in 1666, having left Cambridge for a while on account of the Great Plague, he was moved by the fall of an apple to speculate if the Moon itself was falling toward the earth in a similar way. (Physics 3 Ed., rd Tipler, p. 299) Basic theories for electricity and magnetism were known. Electric charge can be either positive or negative. Two objects that carry the same type of charge –that is, two objects that are both positive or both negative– repel each other, and two objects that carry opposite charges attract each other.(Physics 3 Ed., rd Tipler, p. 599) – Electric current is defined as the rate of flow of electric charge through a cross-sectional area. (Physics 3 Ed., Tipler, p. 599) rd Basic theories for optics were understood. – Optics is the branch of physics dealing with the nature and properties of light and vision. (Webster’s New World Dictionary, Third College Edition) – Newton concluded that white light was composed of a mixture of a whole range of independent colors. (Optics, Hecht, p. 3) Light There was debate as to its exact nature; some viewed it as being made of particles, some viewed it as a wave. – Isaac Newton believed light to be particulate in nature. (Optics, Hecht, p. 3) – Christiaan (this is the correct spelling of the name) Huygens (1629-1695) advanced the wave theory of light. He was able to derive the laws of reflection (the angle-of-incidence equals the angle-of-reflection) and refraction. (Optics, Hecht, pp. 3, 97) The Law of Conservation of Mass The French chemist Antoine-Laurent Lavoisier (La-vwa-zee-ay) (1743-1794) had written a textbook in which he stated that in any closed system (one from which no mass was allowed to leave, and into which no mass was allowed to enter), the total amount of mass remained the same no matter what physical or chemical changes went on. (Asimov’s Chronology of Science and Discovery, Asimov, pp. 240, 266) Fouquier-Tinville’s notorious words during the Revolution sent the chemist Lavoisier to the guillotine: “The Republic does not need any scientists.” (wysiwyg://114/http://www.nobel.se/physics/articles/curie) Elements and Compounds Elements and compounds were known to exist. – An element can be informally defined as something with unique physical and chemical properties and something that cannot be broken down into any other substances. For example, gold, silver, and iron are elements. – A compound also is defined by its unique physical and chemical properties, but it can be broken down into simpler constituents (elements). For example, water can be broken down into hydrogen and oxygen, while table salt can be reduced to chlorine and sodium. – Subsequent investigations proved that the smallest unit of a chemical substance such as water is a molecule. Each molecule of water consists of a single atom of oxygen and two atoms of hydrogen joined. (http://www.encarta.msn.com) Subsequent investigations proved that the smallest unit of a chemical substance such as water is a molecule. Each molecule of water consists of a single atom of oxygen and two atoms of hydrogen joined. (http://www.encarta.msn.com) The discoveries of both John Dalton (1808) and Amedeo Avogadro (1811) were important in this area of investigation. – Essentially, Dalton returned to the Greek notions of Democritus that all matter was made up of tiny, indivisible particles. Dalton even used Democritus’ word atom for these particles. The Greeks thought that atoms differed among themselves in shape. Dalton, in whose time weight and measurements had grown important, maintained that the difference was one of weight, and he pioneered the concept of atomic weight. (Asimov’s Chronology of Science and Discovery, Asimov, p. 287) Avogadro The name "Avogadro's Number" is just an honorary name used to describe the calculated value of the number of atoms, and molecules in a gram mole of any chemical substance. It is 6.022 x 1023 atoms/mol. Avogadro’s Number 1820 – 1820- Several discoveries that year firmly established that moving charge (electric current in a wire, for example) produces a magnetic field. – As part of a classroom demonstration, Hans Christian Oersted (1777-1851) had brought a compass needle near a wire through which a current was passing. The compass needle twitched and pointed neither with the current nor against it but in a direction at right angles to it. When Oersted reversed the direction of the current, the needle pointed in the opposite direction but still at right angles to the flow. (Asimov’s Chronology of Science and Discovery, Asimov, pp. 308-309)