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Slide1
Chemistry 125: Lecture 2Sept 4, 2009Force 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)Slide2
How to Succeed in Chem 125Samuel Pepysas a ModelScience StudentSlide3
Samuel Pepys (1633-1703) July 9, 1662Up by four o'clock, and at my multiplicacion-table hard, which is all the trouble I meet withal in my arithmetique. July 11, 1662Up 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,DiligentSlide4
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 partnerSlide5
Isaac Newton (1643-1727)Slide6
Six years later Pepys encountered a “problem” with Dice.Slide7
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)Slide8
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 ChancesPepys’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 whenhe didn’t really understand
Insisted on proofSlide9
31031
46656
A
0.6651
=
1346704211
2176782336
B
0.6187
=
Slide10
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 swallowhis pride in the search
for solid understandingSlide11
Read Pepys & Newton and get together to do Problems for Monday.Slide12
Problems For Monday: Isotope problems (from Pepys & Newton ) Two Coulomb Problems For Wednesday (Sept. 8): Compare Textbooks
1) Draw Lewis Structures for
Functional Groups2) 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) Slide13
Isotope Ratio Mass SpectrometrySlide14
Are There Atoms & Molecules?What Force HoldsAtomsTogether?Slide15
What Holds Atoms Together?HooksHormones?
The Handsof the Deity?
Springs?
Bolts?
Friction?
Clips?Slide16
What Holds Atoms Together?GravityQuarksKinetic EnergyQuantum Forces
Strange Attractors
Magnetic Forces
Electrical Forces
The Strong Force
Shared Electron PairsExchange 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 YearSlide17
What Holds Atoms Together?GravityQuarksKinetic EnergyQuantum Forces
Strange Attractors
Magnetic Forces
Electrical Forces
The Strong Force
Shared Electron PairsExchange of Virtual Particles
Exchange of Photons
The Weak Force
0
59
(unanimous)
10
5
20
58
0
7
12
3
5
5Slide18
Robert BoyleRobert Boyle
(1627-1691)
P
V = constAir Pump built by his servant Robt. Hooke
1661Slide19
1678Slide20
Hooke’s Law
Hooke’s Force Law
F = -k
xSlide21
ScalePotential EnergyForce x
Hooke’s Law
“Ut
tensio
sic vis”
x
2
extension
force
energySlide22
Isaac Newton (1643-1727)Slide23
Force
: GravityAttraction at a Distance
vs.
Cartesian blocked repulsion
Newton : Force r-2
(How about mass?)Slide24
Isaac Newton (1643-1727)Slide25
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. Slide26
Query 31How 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. Slide27
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
Fchymical
1/r>2
?Slide28
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. Slide29
Query 31There are therefore Agentsin 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 Philosophyto
find them out.Slide30
Felectrical =Fgravity =mass1 mass2
r
2
charge
1
charge2
r
2
Astronomy
Kepler, Newton
(
?
)Slide31
Initially wanted to be a mathematicianin charge of building Ft. Bourbon, Martinique, 1764-1772
Meyzi
ères 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
Acad
émie Royale des Sciences
1781-1793
electrical
torsion balance
1785
M
émoires 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
gilded pith ball
needle
deflection
scale
torsion pointer
with deg. scale
(0°)
Pointer Twist (°)
Net Deflection (°)
0 36
18
567 8.5
charge pinhead by rubbingSlide32
Pointer Twist (°)Net Deflection (°)
0 36
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.
Slide33
Binding Energies from Various SourcesMagnetic 12/r3
0
3
6
-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” BindingSlide34Slide35
DemonstrationwithMagnets
Valuable prize for balancing suspended
magnet
between sets of attracting ma gnt!
magnetsSlide36
End of Lecture 2Sept 3, 2009Copyright © 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).
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0