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How do we know?
• The questions: archaeology, art,
paleontology, …
• The answers: carbon dating,
trace analysis, …
• What’s behind the knobs?
AAA-Spring 2002
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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 m
-11
• 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?
AAA-Spring 2002
(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
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
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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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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
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Large
mass
11
position (mass)
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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)
neutron
• 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)
AAA-Spring 2002
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?3
2He
• Chemist says Z = 2
• What about A?
– Tables give A = 3, 4, 5, 6, ???
4
• Isotopes
–
–
–
–
Same Z (same chemistry)
Different A (different mass)
Notation AZX e.g., 146C
We’ll often write C14
2He
5
2He
……
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