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AAA-Spring 2002 2
How do we know?
• The questions: archaeology, art, paleontology, …
• The answers: carbon dating, trace analysis, …
• What’s behind the knobs?
AAA-Spring 2002 3
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
AAA-Spring 2002 4
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
AAA-Spring 2002 5
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!
AAA-Spring 2002 6
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 7
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 8
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
AAA-Spring 2002 11
Scientific Notation• H-atom:
– Radius = 0.000,000,000,0529 m
– = 0.0529 nm
– = 0.529 Ångstrom
AAA-Spring 2002 12
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 13
*****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 14
*****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)
AAA-Spring 2002 15
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 17
*****STM links*****•animated description of operation of the STM
•history of the STM
•Nobel page, 1986
AAA-Spring 2002 20
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 21
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
AAA-Spring 2002 22
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 23
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 24
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 25
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 26
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
AAA-Spring 2002 27
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
AAA-Spring 2002 28
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)