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IS 240: Discovering the Atom

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  1. IS 240: Discovering the Atom Dr. Dean Johnston Department of Chemistry and Biochemistry Dr. David Robertson Department of Physics and Astronomy

  2. Course Overview • Science as a “way of knowing” • Focus on the atomic structure of matter • How do we know about it? • What does it tell us? • Is there anything inside them? • A multi-disciplinary perspective – chemistry and physics • Includes laboratory exercises • Builds a foundation for later IS science courses

  3. Course Structure • Periodically split into two groups (A and B) for lab work in parallel tracks lasting two weeks • Each split session involves one chemistry and one physics lab • Each group spends one week at each, swapping in between • “Joint” sessions glue things together

  4. Course Materials • Text: The Last Sorcerers: The Path From Alchemy to the Periodic Table, by Richard Morris • Other readings provided as handouts or on line • Course web page: • Notices, lecture notes, the syllabus, online resources, grades, and more… • On reserve at the library: • The Blair Handbook • The Everyday Writer

  5. Modes of Inquiry • “Ways of knowing” – ways to ask (and answer) questions • Are there regularities in the natural world? If so, what are they? • What are the basic things that exist in the world? • Was there a creator? • What is the nature of good and evil? • Is there such a thing as beauty? • How can human societies best be organized? • Different modes may be more or less appropriate for different questions • Most people use all of them

  6. Philosophical • Study of the ultimate reality, causes, and principles underlying being and thinking • Esthetics, ethics, politics, metaphysics, logic, epistemology (nature and origin of knowledge) • A search for wisdom based on logic and principle • May be based in part on observation, though often speculative Philosophy is a hypothetical interpretation of the unknown, or of the inexactly known. It is the front trench in the siege of truth, while science is the captured territory. –Will Durant

  7. Theological • Knowledge is revealed, through • Scriptures • Personal revelations, prayer • Contemplation and interpretation of mystics • Modern religious interpretations focus mainly on ethical questions • How should you live your life? • What are right and wrong? • Historically, theology has not always considered science to be a valid way of knowing

  8. Scientific • Conclusions based on systematic observation and manipulation of the natural world • Only deals with the natural world! • Excludes the “supernatural” by definition • Systematized by Bacon, Descartes and Galileo in the 17th century • Aims to give conclusionsthat are independent of theindividual The task of science is both to extend the range of our experience and to reduce it to order. –Niels Bohr

  9. The Scientific “Method” The whole of science is nothing more than a refinement of everyday thinking. –Albert Einstein

  10. A Classical Example • Aristotle observes that during lunar eclipses the Earth’s shadow on the moon is curved

  11. A Lunar Eclipse

  12. A Classical Example, cont. • He assumes it will be curved for all eclipses • A hypothesis that explains this: the earth is round • A prediction of this hypothesis is that the location of the stars in the sky should be different for observers at different latitudes • This is confirmed by additional observations • E.g. Canopus is visible in Egypt but not further north

  13. N North Pole South Pole Local Sky Polaris • Depending on your location you see completely different stars!

  14. Solar Eclipse • Umbra – region of total shadow • Penumbra – region of partial shadow

  15. Observations • Scientific Fact (AAAS): An observation that has been repeatedly confirmed • Examples: • The sky is blue • Humans have 46 chromosomes in somatic cells under normal conditions • The sun rises in the east and sets in the west • Always subject to reconsideration (in principle) but in practice assumed to be true • Some are better established than others • At the “cutting edge” the facts may not be so clear (yet)

  16. Experimental vs. Historical Observations • Experimental • Tests/observations can be repeated with different conditions • Hypotheses can be refined after further testing • Physics, chemistry, molecular biology, etc. • Historical • Evidence that something happened in the past • Reconstruction of the past • Forensic science, geology, paleontology, cosmology, much of biology, etc. • Different sciences rely to different degrees on the two kinds of observations

  17. Scientific Theories • The word “theory” connotes “uncertainty” to non-scientists, but this is incorrect in the scientific context • AAAS Definition: “A well substantiated explanation of some aspect of the physical world” • The highest rank of scientific explanation! • Not “just” a theory • Substitute “body of knowledge known as...” for “theory of...” (e.g., “body of knowledge known as relativity” rather than “theory of relativity”) • Use “hypothesis” for an untested idea

  18. What is the aim of (experimental) science? • A search for order or patterns in nature • The “scientific method” sets out the rules for the search • In physics and chemistry these patterns are generally expressed mathematically • E.g. for falling bodies, d is proportional to t2 • Water is composed of hydrogen and oxygen in a mass ratio of 1:8 • (At least) two amazing facts: • That such patterns exist at all! • That so much can be explained by so few basic ideas (patterns) • Much of the history of science has involved the search for ever more general, all-encompassing patterns in nature

  19. Key question: How are things happening? Major Works: Harmonices Mundi (1619) Rudolphian Tables (1612) Astronomia Nova Dioptrice Johannes Kepler (1571–1630)

  20. Astrologer and mystic Tried to find “music in the heavens” Attempted to explain distances to the five known planets by nested spheres resting on the five “Platonic” solids Pre-scientific Kepler’s Beginnings

  21. Manuscript: trying to disentangle The mystery of Mars’ orbit  Johannes Kepler

  22. Kepler’s First Law The orbits of the planets are ellipses, with the Sun at one “focus”

  23. Kepler’s Second Law An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal times

  24. Kepler’s Third Law The square of a planet’s orbital period is (in appropriate units) equal to the cube of its orbital semi-major axis: P2 = a3 Planet Orbital Semi-Major Axis Orbital Period P2/a3 (au) (Earth years) Mercury 0.387 0.241 1.002 Venus 0.723 0.615 1.001 Earth 1.000 1.000 1.000 Mars 1.524 1.881 1.000 Jupiter 5.203 11.86 0.999 Saturn 9.539 29.46 1.000 Uranus 19.19 84.01 0.999 Neptune 30.06 164.8 1.000 Pluto 39.53 248.6 1.001

  25. Isaac Newton (1642–1727) • Key question: Why are things happening? • Invented calculus and physics while on “vacation” from college • His three Laws of Motion, together with the Law of Universal Gravitation, explain the motion of planets and of objects on Earth (and more!) • Later in life he was Master of the Mint, dabbled in alchemy, and spent a great deal of effort trying to make his personal enemies miserable

  26. Newton’s Laws of Motion A general framework for describing any motion • Every body continues in a state of rest or in a state of uniform motion in a straight line unless it is compelled to change that state by forces acting on it (Law of Inertia) • The change of motion (acceleration) is proportional to the force applied (F = ma where m is the mass of the object) • For every action (force), there is an equal and opposite reaction

  27. Law of Universal Gravitation R MEarth Mman

  28. Orbital Motion

  29. Cannon “Thought Experiment”

  30. The Unity of Nature • Newton showed that the orbital motion of planets reflects the same pattern in nature as does motion on Earth (balls rolling down planes, cannonballs, falling apples, etc.) • Also explained the ocean tides • Due to gravitational attraction of the moon • Many apparently different phenomena are thus related! • Later, Einstein showed that Newton’s Laws are an approximation to an even deeper, more subtle pattern • That new pattern incorporates everything Newton does, plus more – including the structure of the universe itself!

  31. Scientific Theories • Must be falsifiable (Karl Popper) • There must be some way the theory could fail • Appeals to, e.g., supernatural influences are not allowed! • Should make predictions • The more, the better! • Theories that are very well tested and have the widest applicability are often known as “laws of nature” • Always subject to revision or modification, though • Occam’s Razor: simpler is usually better!

  32. Experiments • Experiments must be repeatable • Others must be able to duplicate your results! • Possible outcomes of an experiment: • The experiment may support the theory • We then continue to make predictions and test them • The experiment may falsify the theory • We need a new theory that describes both the original data and the results of the new experiment • Since we cannot do every possible experiment, a theory can never be proven true; it can only be proven false The aim of science is not to open the door to everlasting wisdom, but to set a limit on everlasting error. –Bertolt Brecht, in The Life of Galileo

  33. Other Characteristics • Science is cumulative and progressive • The new absorbs the old • Successful theories are never “merely” wrong, even when overthrown • They are usually seen to be approximations of the new, deeper principle • Science is self-correcting • Scientific work is open – scientists make their work available to others so that they may test it • Outright fraud is rare, and (usually) quickly detected • Mistakes are uncovered by independent checks

  34. Summary “Science is the systematic enterprise of gathering knowledge about the world and organizing and condensing that knowledge into testable laws and theories. [American Association of Physics Teachers, Am. J. Phys. 67 (8), p. 659 (1999)]

  35. “The success and credibility of science is anchored in the willingness of scientists to: • expose their ideas and results to independent testing and replication by other scientists; this requires the complete and open exchange of data, procedures and materials; • abandon or modify accepted conclusions when confronted with more complete or reliable experimental evidence. Adherence to these principles provides a mechanism for self-correction that is the foundation of the credibility of science.”

  36. The Domain of Science • Science deals with natural phenomena, and only allows natural explanations • Remember, theories must be falsifiable! • Some questions are not answerable in this way • Is there life after death? • Do we have souls? • Is abortion wrong? • Should capital punishment be allowed? • What is the best form of government? • … • However, science may provide input for these questions, e.g. by predicting consequences

  37. Science and Religion • Often seen as being in conflict • Copernicus vs Ptolemey; Galileo • Evolution • Whether or not there is a conflict, and if so what it entails, is a philosophical judgment that each person must make • Many scientists are religious • Many churches accept scientific findings • The converses are true also!

  38. “Same World” Model • Science and Religion deal in principle with the same subjects • Conflicts are hard to resolve since science cannot accept evidence on faith and religion need not accept scientific explanations • Example: What is the age of the Earth? • Usually results in a claim that one is right and the other wrong • Fundamentalists • Some scientists who see religion as unnecessary and regressive

  39. “Separate World” Model • Science and Religion deal in principle with different subjects • Therefore no overlap or conflict; can co-exist peacefully • Science deals with the natural world • Religion deals with the spiritual world, ethics • There may be conflict in a few areas, which vary from person to person • The position of many churches and scientists

  40. Measurements: The Metric System • Units of length: • The meter (m)  3 ft. 4 in. • The kilometer (km) = 1000 m or about 0.6 mi. • Units of mass: • The kilogram(kg). 1 kg weighs about 2.2 lbs. (The lb. is a unit of weight) • Units of time: • The second, same as in the English system

  41. Scientific Notation • 108 means multiply by 10 eight times • 108 is 1 followed by 8 zeroes • Example: 1.5  108 km = 1.5  100,000,000 = 150,000,000 km • 100 is a 1 followed by no zeroes, i.e. just 1 • A negative exponent means divide instead of multiply: • 10–6 means divide by 10 six times • Example: 2  10–6 m = 2/1,000,000 = 0.000002 m • To multiply numbers, add exponents: • Example: 104 1023 = 104 + 23 = 1027 • To divide, subtract exponents: • Example: 104 / 1023 = 104 – 23 = 10–19 • Note: 1 / 104 = 100 / 104 = 10–4

  42. Exercises • Evaluate the following: • 102 1017 • 100 10–4 • 102/108 • (1.5  103)  (2  1023) = 1019 = 10–4 = 10–6 = 3  1026

  43. “Fermi Problems” • (Very!) rough estimation • Looking basically for the right power of 10 in the answer • Is the answer more like 10 or 100 or 1000…? • Round off, drop fractions, estimate needed information to the nearest power of 10 • No single “right” answer; only more or less reasonable ones • The Classic: How many piano tuners are there in Chicago?

  44. Example • How long would it take a person to run from New York to LA? (A week? A year? Several years?) • Assume good runner: maybe 6 mph for 5 hours a day • Hence about 30 miles per day • Probably too optimistic, but in the right ballpark • Distance from NY to LA about 3000 miles, so T = (3000 mi)/(30 mi/day) or about 100 days • If another person arrived at 123.45 days, that’s fine – it has the same “order of magnitude” (power of 10) • Need to know some basic quantitative facts about the world

  45. Problems • About how many pizzas are consumed in the US each day? • Say 300 million people in the US (3  108) • Maybe 2/3 of these eat pizza regularly (2  108) • Say these people eat half a pizza every three weeks • Likely more for students , less for some others • So every three weeks about 1  108 pizzas are eaten • About 1  108 /20 = 1  108  5  10–2 = 5  106 per day

  46. Problems • Estimate the total amount of human blood in the world. If Lake Erie were emptied of water and filled with this blood, about how deep would it be? • Say 6 billion people in the world (6  109) • Say each has about 5 pints of blood on average (30  109 pints total) • A pint is half a quart, or about 30 cubic inches • Assume Lake Erie a rectangle about 200 mi by 80 mi • Surface area about 6  1013 square inches • Depth = (volume of blood)/(area) would be about (30  109 30)/ 6  1013 = 30  5 10–4 = 1.5  10–2 inches

  47. The probability that a woman of age 40 has breast cancer is about 1%. If she has breast cancer, the probability that she tests positive on a screening mammogram is 90%. If she does not have breast cancer, the probability that she nevertheless tests positive is 9%. What are the chances that a woman who tests positive actually has breast cancer?

  48. Powers of Ten – From Man to Universe – 100 meters =1 meter The Human Scale

  49. Powers of Ten – From Man to Universe – 101 meters =10 meters Pond with lilly pads

  50. Powers of Ten – From Man to Universe – 102 meters =100 meters Japanese Tea Garden