1AAA-Spring 2002

2 How do we know? The questions: archaeology, art, paleontology, … The answers: carbon dating, trace analysis, … What’s behind the knobs?

3AAA-Spring 2002 Atoms and Nuclei Posting of reading and lecture notes How small is meters? –Scientific (powers of ten) notation –Biological cells ~ meters –Atoms ~ meters Any way to “see” atoms?—STM Atomic structure—nucleus + electrons Nuclei –Nuclear masses –Nuclear structure—protons + neutrons

4AAA-Spring 2002 How Big is an Atom? What’s the limit to cutting a copper cube in half? Size scales—powers of ten; for more see powers of tenpowers of ten Better—powers of thousand Familiar—meter

5AAA-Spring 2002 meter/1,000 millimeter—visible milli = 1/1,000 = millimeter, millisecond, millivolt, etc. Physiological times ~ 10 milliseconds Cube volume—billion times less than meter cube!

6AAA-Spring 2002 millimeter/1,000 micrometer (micron)— absurdly small micro = 1/1,000,000 = microsecond, etc. Size of cell nucleus: what is length of contained DNA? A billion billion micron cubes in meter cube

7AAA-Spring 2002 micrometer/1,000 nanometer nano = = 1/1,000,000,000 nanosecond = time light to go one foot DNA molecule How many nanometer cubes in a meter cube?

8AAA-Spring 2002 Really???? Volume of DNA (spaghetti) = π r 2 L Volume of nucleus (pot) = (4/3) π R 3 If nucleus (pot) is full of DNA (spaghetti) these volumes are equal (since 4/3 = 1): L = (R 2 /r 2 ) R = (3 x 10 3 ) 2 R = 10 7 R

9AAA-Spring 2002 Another DNA

10AAA-Spring 2002 Scientific Notation H-atom: –Radius = 0.000,000,000,0529 m

11AAA-Spring 2002 Scientific Notation H-atom: –Radius = 0.000,000,000,0529 m –= nm –= Å ngstrom

12AAA-Spring 2002 Scientific Notation H-atom: –Radius = 0.000,000,000,0529 m –= nm –= 5.29 x m –= x m –= 52.9 x m

13AAA-Spring 2002 *****Scientific Notation***** H-atom: radius = 5.29 x m 10 n = 1 with n zeroes 10 -n = 1/(1 with n zeroes) 1.64 x 10 5 = 164,000 = x 10 6 = 16.4 x x = 4.37/10 3 = 4.37/1,000 = (2 x 10 4 ) x (3 x 10 5 ) = 6 x 10 9 (2 x 10 4 ) x (3 x ) = 6 x = 0.06 (2 x 10 4 ) / (3 x 10 5 ) = 0.666… x = 0.666… (2 x ) / (3 x 10 5 ) = 0.666… x 10 -9

14AAA-Spring 2002 *****Orders of Magnitude***** Remember---We’re interested only in very rough numbers. E.g., we don’t care whether your heart rate is 50 beats per minute or 80. It’s EASY to get USEFUL answers, even though they’re 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) = 3x10 6, 3x10 8, or 3x10 10 (3x10 8 ) 2) How many revolutions does a car engine make in its lifetime? (At highway speed, typical engine speed is 3,000 revolutions per minute.) 3x10 8, 3x10 10, or 3x10 12 ? (3x10 8 )

15AAA-Spring nm Almost the Atomic Scale Copper surface Step heights a few nanometers Missing and extra atoms visible on surface Scanning Tunneling Microscopy (STM)

16AAA-Spring 2002 How to “see” atoms?

17AAA-Spring 2002 *****STM links***** animated description of operation of the STM history of the STM Nobel page, 1986

18AAA-Spring 2002 And Move Them Around

19AAA-Spring 2002 And Do Other Physics

20AAA-Spring 2002 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 ~ nm

21AAA-Spring 2002 Comparison with Solar System Gold Atom Solar System Radius = 1 foot outermost electron outermost planet 1.6 miles 3.3 miles nucleus Sun Pluto Earth 215 feet Gravity Attraction of + and - charges

22AAA-Spring 2002 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

23AAA-Spring 2002 Links for atomic structure Modern view of atomic structure Atomic properties Atomic Structure make your own atom (or solar system) (from University of Colorado)make your own atom (or solar system)

24AAA-Spring Other Kinds of Atoms? Z = atomic number = number of electrons Charge on nucleus = Z e Add Z to chemical symbols as 1 H, 6 C, 7 N, 8 O, … Set aside chemistry; interest now is in nucleus

25AAA-Spring 2002 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

26AAA-Spring 2002 Ion source Detector Magnetic field Large mass Small mass Boron Mystery detector current position (mass) Small mass Large mass Boron mass = % B % B My Mass Spectrometer

27AAA-Spring 2002 Nuclear Model?? proton (= p) –Positive charge, +e; Mass of 1 amu; Radius?Radius? neutron (= n) –Neutral; Mass of 1 amu; Radius (don’t ask) Nucleus: –Z = atomic number = number of protons –A = atomic weight = # protons + # neutrons –Number of neutrons = (A - Z) Nuclear radius: –R = 1.2 x m x A 1/3 = 1.2 fermi x A 1/3 An element (Z) can have different ISOTOPES (different As) neutron proton

28AAA-Spring 2002 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)

29AAA-Spring 2002 What’s in a helium nucleus? Chemist says Z = 2 What about A? –Tables give A = 3, 4, 5, 6, ??? Isotopes –Same Z (same chemistry) –Different A (different mass) –Notation A Z X e.g., 14 6 C –We’ll often write C He 4 2 He 5 2 He ……

30AAA-Spring 2002 NO MORE SLIDES!!!

31AAA-Spring 2002 UNUSED SLIDES

32AAA-Spring 2002 Sedimentation rates 500 feet in 10 7 years ––> 15 µm/year Lake is ~500 feet deep: will it fill up in 10 4, 10 7, or years

33AAA-Spring 2002 Sedimentation rates 500 feet in 10 7 years ––> 15 µm/year Lake is ~500 feet deep: will it fill up in 10 4, 10 7, or years 6 mile creek silt dam: foot/ year Area ratio = (1/20 x 1/5)/(4 x 40) = 6 x 10-5; maybe fed by ~10 creeks # years = 500 ft/6 x (ft/yr) = ~ 10 6 yr

34AAA-Spring 2002