AAA-Spring 2002 1 How do we know? The questions: archaeology, art, paleontology, The answers: carbon dating, trace analysis, Whats behind the knobs? AAA-Spring 2002 2 Atoms and Nuclei Posting of reading and lecture notes
How small is 10-15 meters? Scientific (powers of ten) notation Biological cells ~ 10-5 meters Atoms ~ 10-10 meters Any way to see atoms?STM Atomic structurenucleus + electrons Nuclei Nuclear masses Nuclear structureprotons + neutrons AAA-Spring 2002 3 How Big is an Atom?
Whats the limit to cutting a copper cube in half? Size scalespowers of ten; for more see powers of ten Betterpowers of thousand Familiarmeter AAA-Spring 2002 4 meter/1,000 millimetervisible
milli = 1/1,000 = 10-3 millimeter, millisecond, millivolt, etc. Physiological times ~ 10 milliseconds Cube volumebillion times less than meter cube! AAA-Spring 2002 5 millimeter/1,000 micrometer (micron) absurdly small micro = 1/1,000,000 = 10-6
microsecond, etc. Size of cell nucleus: what is length of contained DNA? A billion billion micron cubes in meter cube AAA-Spring 2002 6 micrometer/1,000 nanometer nano = 10-9 = 1/1,000,000,000 nanosecond = time light to go one foot DNA molecule
How many nanometer cubes in a meter cube? AAA-Spring 2002 7 Really???? Volume of DNA (spaghetti) = r2 L Volume of nucleus (pot) = (4/3) R3 If nucleus (pot) is full of DNA (spaghetti) these volumes are equal (since 4/3 = 1): L = (R2/r2) R = (3 x 103)2 R = 107 R AAA-Spring 2002
8 Another DNA AAA-Spring 2002 9 Scientific Notation H-atom: Radius = 0.000,000,000,0529 m AAA-Spring 2002 10
Scientific Notation H-atom: Radius = 0.000,000,000,0529 m = 0.0529 nm = 0.529 ngstrom AAA-Spring 2002 11 Scientific Notation H-atom: Radius = 0.000,000,000,0529 m = 0.0529 nm = 5.29 x 10-11 m = 0.529 x 10-10 m
= 52.9 x 10-12 m AAA-Spring 2002 12 *****Scientific Notation***** H-atom: radius = 5.29 x 10-11 m 10n = 1 with n zeroes
10-n = 1/(1 with n zeroes) 1.64 x 105 = 164,000 = 0.164 x 106 = 16.4 x 104 4.37 x 10-3 = 4.37/103 = 4.37/1,000 = 0.00437 (2 x 104) x (3 x 105) = 6 x 109
(2 x 104) x (3 x 10-5) = 6 x 10-1 = 0.06 (2 x 104) / (3 x 105) = 0.666 x 10-1 = 0.666 (2 x 10-4) / (3 x 105) = 0.666 x 10-9 AAA-Spring 2002 13
*****Orders of Magnitude***** Remember---Were interested only in very rough numbers. E.g., we dont care whether your heart rate is 50 beats per minute or 80. Its EASY to get USEFUL answers, even though theyre not accurate. How many times will your heart beat in your lifetime? (? beats per minute) x (? minutes per day) x (? days per year) x (? years per lifetime) = 3x106, 3x108, or 3x1010 (3x108) 2) How many revolutions does a car engine make in its lifetime? (At highway speed, typical engine speed is 3,000 revolutions per minute.) 3x108, 3x1010, or 3x1012? AAA-Spring 2002
(3x108) 14 1 nm Almost the Atomic Scale Copper surface Step heights a few nanometers Missing and extra atoms visible on surface Scanning Tunneling Microscopy (STM) AAA-Spring 2002 15
How to see atoms? AAA-Spring 2002 16 *****STM links***** animated description of operation of the STM history of the STM Nobel page, 1986 AAA-Spring 2002 17
And Move Them Around AAA-Spring 2002 18 And Do Other Physics AAA-Spring 2002 19 What Does the Copper Atom Look Like? 29 electrons
Negative charge (-e) Small mass (m) Atomic size ~ 1/10 nm 1 nucleus Positive charge (+29e) Large mass: thousands times m Nuclear size ~ 10-6 nm AAA-Spring 2002 20 Comparison with Solar System nucleus 3.3 miles
Gold Atom outermost electron Radius = 1 foot 1.6 miles Solar System 215 feet Sun outermost planet Pluto
Earth Gravity AAA-Spring 2002 Attraction of + and - charges 21 But a VERY Bad Picture Electron orbits NOT in a plane Electrons are not solid balls, but point particles Think of them as in a cloud, or in waves, not as points Language problem
AAA-Spring 2002 22 Links for atomic structure Modern view of atomic structure Atomic properties Atomic Structure make your own atom (or solar system) (from University of Colorado) AAA-Spring 2002 23 108 Other Kinds of Atoms?
Z = atomic number = number of electrons Charge on nucleus = Z e Add Z to chemical symbols as 1H, 6C, 7N, 8O, Set aside chemistry; interest now is in nucleus AAA-Spring 2002 24 What do we know about the nucleus? Charge = Z e
Masses, from Chemistry: From masses of reactants and products H-1.0, He-4.0, Li-6.9, Be-9.0, B-10.8, C-12.0, N-14.0, O-16.0, F-19.0, Ne-20.2, Na-23.0, Roughly 2 x Z Masses, from Physics: mass spectrometer AAA-Spring 2002 25 Boron Mystery Detector My Mass Spectrometer
Small mass Large mass Ion source Boron mass = 10.8 20% B----10.0 80% B----11.0 Magnetic field detector
current Small mass 10 AAA-Spring 2002 Large mass 11 position (mass) 26
Nuclear Model?? proton (= p) Positive charge, +e; Mass of 1 amu; Radius? neutron (= n) Neutral; Mass of 1 amu; Radius (dont ask) Nucleus: Z = atomic number = number of protons A = atomic weight = # protons + # neutrons
Number of neutrons = (A - Z) Nuclear radius: R = 1.2 x 10-15 m x A1/3 = 1.2 fermi x A1/3 neutron An element (Z) can have different ISOTOPES (different As) AAA-Spring 2002
proton 27 Radius of the proton???? The radius of a proton depends on how you mean radius. It turns out that a proton is not actually a ball. Latest experiments show that a proton is made of three smaller particles called quarks. Quarks have a size too small to measure. They may have no size at all. These three quarks spin around each other very quickly. In reality, a proton does not have a radius. As for radius of orbits, that involves an area of quantum mechanics that is still being explored. We do not yet know
enough about the force between quarks to determine a value for orbit sizes within a proton, or a neutron. (Sorry I asked) AAA-Spring 2002 28 Whats in a helium nucleus?3 Chemist says Z = 2 What about A? Tables give A = 3, 4, 5, 6, ??? 4
Isotopes He 2 Same Z (same chemistry) Different A (different mass) Notation AZX e.g., 146C Well often write C14
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Isotopes. The atomic number (or number of protons) defines the element. Elements have various isotopes which differ in their number of neutrons. Nuclide is another term used to define isotopes when speaking specifically about the nucleus
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