1. Chemistry 125: Lecture 2 Sept 4, 2009 Force Laws For copyright notice see final page of this file Silliman and Morse Lead! Stiles Trails. (race to complete their directory on the Wiki) (Note: the on-line audio recording for this lecture begins with Frame 12)

2. How to Succeed in Chem 125 Samuel Pepys as a Model Science Student

3. Samuel Pepys (1633-1703) July 9, 1662 Up by four o'clock, and at my multiplicacion-table hard, which is all the trouble I meet withal in my arithmetique. July 11, 1662 Up by four o'clock, and hard at my multiplicacion-table, which I am now almost master of… December 25, 1662 …so to my office, practising arithmetique alone and making an end of last night's book with great content till eleven at night, and so home to supper and to bed Motivated, Diligent

4. Samuel Pepys (1633-1703) December 6, 1663 [Sunday] …I below by myself looking over my arithmetique books and timber rule. So my wife rose anon, and she and I all the afternoon at arithmetique, and she is come to do Addition, Subtraction, and Multiplicacion very well, and so I purpose not to trouble her yet with Division... Worked with study partner

5. Isaac Newton (1643-1727)

6. Six years later Pepys encountered a “problem” with Dice.

7. Pepys’s Problem (11/22/1692) A - has 6 dice in a Box, wth wch he is to fling a 6. B - has in another Box 12 Dice, wth wch he is to fling 2 Sixes. C - has in another Box 18 Dice, wth wch he is to fling 3 Sixes. Q. whether B & C have not as easy a Taske as A, at even luck? If the Question be thus stated, it appears by an easy computation that the expectation of A is greater then that of B or C, that is, the task of A is the easiest. What is ye expectation or hope of A to throw every time one six at least wth six dyes? [etc.] Newton’s Reply (11/26/1692)

8. But yet I must not pretend to soe much Conversation wth Numbers, as presently to comprehend as I ought to doe, all ye force of that wch you are pleas'd to assigne for ye Reason of it, relating to their having or not having ye Benefit of all their Chances Pepys’s Reply (12/6/1692)...You give it in favour of ye Expectations of A, & this (as you say) by an easy Computation.. ; and therefore were it not for ye trouble it must have cost you; I could have wish'd for a sight of ye very Computation. Not ashamed to admit when he didn’t really understand Insisted on proof

9. 31031 46656 A 0.6651 = 1346704211 2176782336 B 0.6187 = 

10. Pepys “WHY?” "I cannot bear the Thought of being made Master of a Jewell I know not how to wear." “I never went to his office hours for help because I felt like he would make me feel stupid, because he is superior to me in chemistry.” (from an anonymous end-of-semester course evaluation - Jan 2007) Contrast with: Willing to swallow his pride in the search for solid understanding

11. Read Pepys & Newton and get together to do Problems for Monday.Pepys & Newton

12. Problems For Monday: Isotope problems (from Pepys & Newton )Pepys & Newton Two Coulomb Problems For Wednesday (Sept. 8): Compare Textbooks 1) Draw Lewis Structures for Functional GroupsFunctional Groups 2) Are Lewis/Resonance correct? 3) What do Lewis/Resonance Structures show? Collaborative Group Submissions form three groups of 3-5 students from each of the following sets of residential colleges: (BK,CC,JE) (BR,SM,SY) (DC,PC) (ES,TR) (MC,TD)

13. Isotope Ratio Mass Spectrometry

14. Are There Atoms & Molecules? What Force Holds Atoms Together?

15. What Holds Atoms Together? Hooks Hormones? The Hands of the Deity? Springs? Bolts? Friction? Clips?

16. What Holds Atoms Together? GravityQuarks Kinetic Energy Quantum Forces Strange Attractors Magnetic Forces Electrical ForcesThe Strong Force Shared Electron Pairs Exchange of Virtual Particles Exchange of Photons The Weak Force Let’s Vote 0 59 (unanimous) 10 5 20 58 0 7 12 3 5 5 Last Year

17. What Holds Atoms Together? GravityQuarks Kinetic Energy Quantum Forces Strange Attractors Magnetic Forces Electrical ForcesThe Strong Force Shared Electron Pairs Exchange of Virtual Particles Exchange of Photons The Weak Force 0 59 (unanimous) 10 5 20 58 0 7 12 3 5 5

18. Robert Boyle (1627-1691) P  V = const Air Pump built by his servant Robt. Hooke 1661

19. 1678

20. Hooke’s Law Hooke’s Force Law F = -k  x

21. Scale Potential Energy Force   x Hooke’s Law “Ut tensio sic vis”  x2 x2 extension force energy

22. Isaac Newton (1643-1727)

23. Force : Gravity Attraction at a Distance vs. Cartesian blocked repulsion Newton : Force  r -2 (How about mass?)

24. Isaac Newton (1643-1727)

25. Query 31 in Opticks (1717) Have not the small Particles of Bodies certain Powers, Virtues, or Forces by which they act at a distance, not only upon the Rays of Light for reflecting, refracting and inflecting them, but also upon one another for producing a great part of the Phaenomena of Nature? For it's well know that Bodies act one upon another by the Attractions of Gravity, Magnetism and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self.

26. Query 31 How these Attractions may be perform'd, I do not here con- sider. What I call Attraction may be perform'd by impulse, or by some other means unknown to me. I use that Word here to signify only in general any Force by which Bodies tend towards one another, whatsoever be the Cause. For we must learn from the Phaenomena of Nature what Bodies attract one another, and what are the Laws and Properties of the attraction, before we enquire the Cause by which the Attraction is perform'd, The Attractions of Gravity, Magne- tism and Electricity, react to very sensible distances, and so have been observed by vulgar Eyes, and there may be others which reach to so small distances as hitherto escape obser- vation; and perhaps electrical Attraction may react to such small distances, even without being excited by Friction.

27. Query 31 The Parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked Atoms, which is begging the Question; and others tell us that Bodies are glued together by rest, that is, by an occult Quality, or rather by nothing; and others that they stick together by conspiring Motions, that is, by relative rest amongst themselves. I had rather infer from their Cohesion, that their Particles attract one another by some Force, which in immediate Contact is exceeding strong, at small distances performs the chymical Operations above mention'd, and reaches not far from the Particles with any sensible Effect. Maybe F chymical  1/r >2 ?

28. Query 31 …the Attraction [between glass plates separated by a thin film of Oil of Oranges] may be proportionally greater, and continue to increase until the thickness do not exceed that of a single Particle of the Oil.

29. Query 31 There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. (This business will take us nearly five weeks) And it is the business of experimental Philosophy to find them out.

30. F electrical = F gravity = mass 1  mass 2 r2r2 charge 1  charge 2 r2r2 Astronomy Kepler, Newton (?)(?)

31. Initially wanted to be a mathematician in charge of building Ft. Bourbon, Martinique, 1764-1772 Meyzières Engineering School 1760-1761 National Maritime Museum, Greenwich ~1751 “Charles Augustin continued to deny his mother’s desire that he study medicine and was therefore temporarily disowned. Without funds, he was forced to join his father in Montpellier.” (Gillmour. 1971, p. 5) (1732-1799) Institut de France 1795-1806 Royal Corps of Engineers 1760-1790 Académie Royale des Sciences 1781-1793 electrical torsion balance 1785 Mémoires de l’Académie Royale des Sciences, pp. 569-577 Charles Augustin Coulomb (1736-1806) 1793 silver wire (~20  m thick ~1/4 of a hair) gilded pith ball needle deflection scale torsion pointer with deg. scale (0°) Pointer Twist (°) Net Deflection (°) 0 36 126 18 567 8.5 charge pinhead by rubbing

32. Pointer Twist (°) Net Deflection (°) 0 36 126 18 567 8.5 (1) Coulomb used these data to derive his law for repulsion of like charges: F  1/r 2 How certain could he be that the exponent for r is exactly 2, and not 2 +  ? That is, how large a  could be consistent with his data? (Modern experiments, relevant to the rest mass of the photon and to the dimensionality of space, show  < 10 -17 ) Hints: One approach would be to make a plot based on numbers derived from these data. You might want to consider experimental error and geometry. Detail on experiment and calculation is available in the translation of Coulomb’s paper on the course website. Two Problems (2) Two years later (1787) Coulomb extended this law for repulsion to include attraction between opposite charges. Explain why Coulomb would need to develop a new apparatus for this experiment. That is, why couldn’t he just use the same apparatus with different charges on the two gilded pith balls? Hint: Remember that the torsional force is approximately linear in the displacement. It might help to graph the Coulombic and torsional energies through a region that includes the point where they balance.

33. Binding Energies from Various Sources Magnetic   1  2 /r 3 036-3 Log (Potential Energy) kcal/mol Gravitational  m 1 m 2 /r Coulombic  q 1 q 2 /r Chemical Bond (similar to 1 e Coulombic) (What of Kinetic Energy?) (216 kcal/mol) : Proton-Electron at 1.54Å (0.0014 kcal/mol) : Electron Spins at 1.54Å (5 x 10 7 kcal/mol) : Proton-Neutron in Deuterium Nucleus (3 x 10 -32 kcal/mol) : C atoms at 1.54Å (90 kcal/mol) : C-C at 1.54Å “Strong” Binding

35. Demonstration with Magnets Valuable prize for balancing suspended magnet between sets of attracting ma gnt!

36. End of Lecture 2 Sept 3, 2009 Copyright © J. M. McBride 2009. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0