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How do we know?

• The questions: archaeology, art, paleontology, …

• The answers: carbon dating, trace analysis, …

• What’s behind the knobs?

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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 structure—nucleus + electrons

• Nuclei– Nuclear masses– Nuclear structure—protons +

neutrons

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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 ten

• Better—powers of thousand

• Familiar—meter

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meter/1,000

• millimeter—visible

• milli = 1/1,000 = 10-3

• millimeter, millisecond, millivolt, etc.

• Physiological times ~ 10 milliseconds

• Cube volume—billion times less than meter cube!

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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

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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?

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Really????

• Volume of DNA (spaghetti) = π r2 L

• Volume of nucleus (pot) = (4/3) π 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

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Another DNA

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Scientific Notation• H-atom:

– Radius = 0.000,000,000,0529 m

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Scientific Notation• H-atom:

– Radius = 0.000,000,000,0529 m

– = 0.0529 nm

– = 0.529 Ångstrom

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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

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*****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

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*****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) = 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? (3x108)

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1 nm Almost the Atomic Scale

• Copper surface• Step heights a few

nanometers• Missing and extra

atoms visible on surface

• Scanning Tunneling Microscopy (STM)

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How to “see” atoms?

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*****STM links*****•animated description of operation of the STM

•history of the STM

•Nobel page, 1986

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And Move Them Around

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And Do Other Physics

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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

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Comparison with Solar System

Gold Atom

Solar System

Radius = 1 foot

outermost electron

outermost planet1.6 miles

3.3 miles

nucleus

SunPluto

Earth

215 feet

Gravity Attraction of + and - charges

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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

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Links for atomic structure

• Modern view of atomic structure

• Atomic properties

• Atomic Structure

• make your own atom (or solar system) (from University of Colorado)

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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

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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

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Ion source

Detector

Magnetic field

Large mass

Small mass

Boron Mystery

detectorcurrent

position (mass)

Small mass

Large mass

10 11

Boron mass = 10.820% B----10.080% B----11.0

My Mass Spectrometer

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Nuclear Model??• proton (= p)

– Positive charge, +e; Mass of 1 amu; 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 10-15 m x A1/3 = 1.2 fermi x A1/3

• An element (Z) can have different ISOTOPES (different As)

neutron

proton

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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)

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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

ZX e.g., 146C

– We’ll often write C14

32He

42He

52He

……