Download Neutrons and Protons

From last time…
• Hydrogen atom
• Multi-electron atoms
This week’s honors lecture:
Prof. Brad Christian, “Positron Emission Tomography”
Course evaluations next week
Tues. Prof Montaruli
Thurs. Prof. Rzchowski
Thur. Dec 6, 2007
Phy208 Lecture 27
1
Atomic Quantum number summary
• Hydrogen atom states n, , m , ms 
– n: principle quantum number
• Determines energy
• (n=1, 2, 3…)

– ℓ: orbital quantum
number
• Magnitude of orbital angular momentum L 
• ℓ=0, 1, 2, … n-1

1
– mℓ: orbital magnetic quantum number
• Orientation of L Lz  m 

• mℓ = - ℓ, - ℓ + 1, … 0, … ℓ - 1, + ℓ
– ms: spin quantum number
• Orientation
  of S Sz  ms 
• ms=-1/2, +1/2
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Phy208 Lecture 27
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Elements in same
column have similar
chemical properties
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Na Optical spectrum
– Ne core = 1s2 2s2 2p6
(closed shell)
– 1 electron outside
closed shell
Na = [Ne]3s1
• Outside (11th) electron
easily excited to other
states.
Thur. Dec 6, 2007
Phy208 Lecture 27
589 nm, 3p -> 3s
• 11 electrons
Na
4
How do atomic transitions occur?
• How does electron in excited
state decide to make a
transition?
• One possibility: spontaneous
emission
• Electron ‘spontaneously’
drops from excited state
– Photon is emitted
‘lifetime’ characterizes average
time for emitting photon.
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Another possibility:
Stimulated emission
• Atom in excited state.
• Photon of energy hf=E ‘stimulates’ electron to drop.
Additional photon is emitted,
Same frequency,
in-phase with stimulating photon
One photon in,
two photons out:
hf=E
light has been amplified
E
Before
After
If excited state is ‘metastable’ (long lifetime for spontaneous
emission) stimulated emission dominates
Thur. Dec 6, 2007
Phy208 Lecture 27
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LASER :
Light Amplification by
Stimulated Emission of Radiation
Atoms ‘prepared’ in metastable excited states
…waiting for stimulated emission
Called ‘population inversion’
(atoms normally in ground state)
Excited states stimulated to emit photon from a spontaneous
emission.
Two photons out, these stimulate other atoms to emit.
Thur. Dec 6, 2007
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Ruby Laser
• Ruby crystal has the atoms which will emit photons
• Flashtube provides energy to put atoms in excited state.
• Spontaneous emission creates photon of correct frequency,
amplified by stimulated emission of excited atoms.
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Ruby laser operation
Relaxation to
metastable state
(no photon emission)
3 eV
2 eV
1 eV
Metastable state
PUMP
Transition by stimulated
emission of photon
Ground state
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Phy208 Lecture 27
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Good description of atom
• Hydrogen atom: single electron orbiting
around single positively-charged proton
• Hydrogen atom can be in different quantum
states, corresponding classically to different
orbits.
• Can also have more than one electron
orbiting around the nucleus.
• # of electrons determines the chemical
properties, and hence the element.
Thur. Dec 6, 2007
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Chap 42: Nuclear Physics
• Nucleus consists of protons and neutrons densely
combined in a small space (~10-14 m)
– Protons have a positive electrical charge
– Neutrons have zero electrical charge (are neutral)
– Neutrons & protons generically called ‘nucleons’
• Spacing between these nucleons is ~ 10-15 m
Neutron
• Size of electron orbit is 5x10-11 m
• Nucleus is 5,000 times smaller
than the atom!
Proton
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Neutrons and Protons
Neutron: zero charge (neutral)
Proton: positive charge
(equal and opposite to electron)
• Zero net charge ->
# protons in nucleus = # electrons orbiting.
• The number of electrons determines which element.
– 1 electron  Hydrogen
– 2 electrons  Helium
– 6 electrons  Carbon
• How many neutrons?
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Carbon
# protons
Total # nucleons
12
• Carbon has
6 protons, 6 electrons (Z=6):
this is what makes it carbon.
C
6
• Most common form of carbon has 6 neutrons
in the nucleus. Called 12C
Another form of carbon has
6 protons, 8 neutrons in the nucleus. This is
14C.
This is a different ‘isotope’ of carbon
Thur. Dec 6, 2007
Phy208 Lecture 27
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Question
Hydrogen is the element with one electron.
Which of the following is NOT the nucleus of
an isotope of hydrogen?
A. One proton
B. One proton and one neutron
C. Two protons and one neutron
Isotopes
of hydrogen
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Hydrogen
One proton
Phy208 Lecture 27
Deuterium
One proton
one neutron
Trituium
One proton
two neutrons
14
Isotopes
• Isotopes: Nuclei with
– same # protons, but
– different # neutrons
•
12C
and
14C
have same chemical properties.
– Both have 6 protons/6 electrons, same outer electron
configuration
– So both called carbon
• But have different number of neutrons.
–
12C
has 12-6 = 6 neutrons
–
14C
has 14-6 = 8 neutrons
Thur. Dec 6, 2007
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Heavy Water: deuterium oxide
D2O: two 2H, one 16O bonded together
How much heavier is D2O than H2O?
A. 5 %
$15 / cube!
B. 10%
C. 15%
D. 50%
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Nuclear Force
• So what holds the nucleus together?
• Coulomb force? Gravity?
• Coulomb force only acts on
charged particles
– Repulsive between protons,
and doesn’t affect neutrons at all.
• Gravitational force is much too weak.
Showed before that gravitational force is
much weaker than Coulomb force.
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The Strong Nuclear Force
• New attractive force.
• Dramatically stronger than Coulomb force at
short distances.
• Doesn’t depend on sign of charge.
• This is the ‘strong interaction’, one of the four
fundamental interactions:
electromagnetic interaction
strong interaction
weak interaction
gravitational interaction
Thur. Dec 6, 2007
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Estimating the strong force
The Coulomb attraction energy (~10 eV) binds the hydrogen
atom together.
Protons in nucleus are 50,000 times closer together than
electron and proton in hydrogen atom.
(Hint: Coulomb energy ~ 1/separation)
Attractive energy must be larger than the Coulomb repulsion,
so nuclear binding energies are at least
A. 5000 eV
B. 500,000 eV
C. 5,000,000 eV
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This is lower limit.
Experimental binding energy
~ 8 MeV/nucleon
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Nuclear masses
• Nuclear masses very accurately measured.
• New unit of measurement
Atomic Mass Unit: 1 u = 1.6605x10-27kg
– Defined so that mass of
12C
is exactly 1 u.
Proton mass
mp=(1.6726x10-27kg)(1u/1.6605x10-27kg)
mp =1.0073u
Neutron mass
mN=(1.6749x10-27kg) )(1u/1.6605x10-27kg
mN =1.0087u
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Nuclear masses
Isolated
protons & neutrons
1.0073 u
Protons & neutrons
bound in He nucleus
1.0073 u
1.0087 u
1.0087 u
4.0320 u
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4.0015 u
Phy208 Lecture 27
0.0305 u
difference!
23
Binding energy
• Only difference is interaction (strong force)
• Work required to separate the nucleons
E  mc 2
 0.0305 u1.6611027 kg/uc 2 
 0.0305 u931.494 MeV /u
 28.41 MeV  7.1 MeV /nucleon
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Binding energy
• Calculate binding energy from masses
E binding  Zmp  NmN  mnucleusc 2
Zme
Zme
E binding  ZmH  NmN  matom c 2


Mass of
Hydrogen atom
(1.0078 u)
Mass of atom with
Z protons, N neutrons

Atomic masses well-known-> easier to use
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Ebinding/nucleon ( MeV )
Binding energy/nucleon
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Fission and fusion
• Schematic view of
previous diagram
•
56Fe
is most stable
• Move toward lower
energies by fission or
fusion.
• Energy released
related to difference
in binding energy.
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Nuclear fusion
5.06x10-29 kg of mass released as energy when protons
& neutrons combined to form Helium nucleus.
This is the ‘binding’ energy of the nucleus.
E = mc2 = (5.06x10-29 kg)x(3x108 m/s)2 = 4.55x10-12 J
= 28 MeV = 28 million electron volts!
Binding energy/nucleon = 28 MeV / 4 = 7 MeV
Principle of nuclear fusion:
Energy released when ‘manufacturing’ light elements.
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What about different isotopes?
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Stability of nuclei
• Dots are naturally
occurring isotopes.
• Blue shaded region is
isotopes created in the
laboratory.
• Observed nuclei
have ~ N=Z
• Slightly fewer protons
because they cost
Coulomb repulsion
energy.
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Radioactive nuclei
~ equal #
neutrons and
protons
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Nuclear spin
• Since nucleus is made of protons and neutrons,
and each has spin, the nucleus also has a spin
(magnetic moment).
• Can be very large.
• Turns out to have a biological application.
• Water is ubiquitous in body,
and hydrogen is major element of water (H2O)
• Nucleus of hydrogen is a single proton.
– Proton has spin 1/2
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Magnetic resonance imaging
•
•
80% of the body's atoms are hydrogen atoms,
Once excited by the RF signal, the hydrogens will tend to return to their lower state in a process
called "relaxation" and will re-emit RF radiation at their Larmor frequency. This signal is detected
as a function of time, and then is converted to signal strength as a function of frequency by means
of a Fourier transformation.
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Magnetic resonance imaging
MRI detects photon resonance emission and
absorption by the proton spins.
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Radioactivity
• Most stable nuclei have about same number of
protons as neutrons.
• If the energy gets too high, nucleus will
spontaneously try to change to lower energy
configuration.
• Does this by changing nucleons inside the nucleus.
• These nuclear are unstable, and are said to decay.
• They are called radioactive nuclei.
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Particles in the nucleus
Can still, however,
get an approximate
description of nucleus
with protons and
neutrons.
• Proton
– Charge +e
– Mass
1.6726x10-27 kg
– Spin 1/2
• Neutron
– Charge 0
– Mass
1.6749x10-27 kg
– Spin 1/2
Both are spin 1/2 particles -> obey Pauli exclusion principle
One particle per quantum state
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Putting nucleons in the nucleus
• proton and neutron states in the nucleus are
quantized. Certain discrete energy levels
available (particle in box)
• Neutrons and protons are Fermions
– 2 protons cannot be in same quantum state
– 2 neutrons cannot be in same quantum state
• But neutron and proton are distinguishable, so
proton and neutron can be in same quantum
state.
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Proton and Neutron states
• Quantum states for nucleons in the nucleus
– Particles in a box
• Proton and neutron can be in the same state
neutrons
Nucleon quantum states
in the nucleus
Thur. Dec 6, 2007
Phy208 Lecture 27
protons
Schematic indicating
neutron & proton can
occupy same state
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Populating nucleon states
• Various quantum states for nucleons in the nucleus
• Similar to the hydrogen atom:
one electron in each quantum state.
• Two states at each energy (spin up & spin down)
neutrons
protons
Helium
This is 4He, with
2 neutrons and
2 protons
in the nucleus
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Other helium isotopes
Too few neutrons, ->
protons too close together.
High Coulomb repulsion energy
neutrons
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Too many neutrons, requires
higher energy states.
protons
neutrons
Phy208 Lecture 27
protons
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Radioactive decay
• Decay usually involves emitting some
particle from the nucleus.
• Generically refer to this as radiation.
• Not necessarily electromagnetic radiation,
but in some cases it can be.
• The radiation often has enough energy to
strip electrons from atoms, or to sometimes
break apart chemical bonds in living cells.
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Discovery of radioactivity
• Accidental discovery in 1896
• Henri Becquerel was trying to investigate
x-rays (discovered in 1895 by Roentgen).
• Exposed uranium compound to sunlight, then
placed it on photographic plates
• Believed uranium absorbed sun’s energy
and then emitted it as x-rays.
• On the 26th-27th February, experiment "failed"
because it was overcast in Paris.
• Becquerel developed plates anyway,
finding strong images,
• Proved uranium emitted radiation without an
external source of energy.
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Detecting radiation
• A Geiger counter
• Radiation ionizes (removes electrons) atoms
in the counter
Leaves negative
electrons and
positive ions.
Ions attracted to
anode/cathode,
current flow is
measured
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Radioactive tracers
Worked on radioactivity
as student with Ernest Rutherford.
Lodged in nearby boarding home.
Suspected his landlady was serving meals later in the
week ‘recycled’ from the Sunday meat pie. His
landlady denied this!
deHevesy described his first foray
into nuclear medicine:
“The coming Sunday in an unguarded moment I
added some radioactive deposit [lead-212] to the
freshly prepared pie and on the following Wednesday,
with the aid of an electroscope, I demonstrated to the
landlady the presence of the active deposit in the soufflé.”
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Phy208 Lecture 27
George de Hevesy
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Energy of nucleus
• Nucleons attracted by nuclear force,
so more nucleons give more attractive force.
– This lowers the energy.
• But more nucleons mean occupying higher
quantum states, so higher energy required.
• Tradeoff gives observed nuclear
configurations
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Stable and Unstable Isotopes
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Question
• The nucleus of a helium atom consists of two
protons and two neutrons.
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Different nuclear configurations
Lower energy
Higher energy
Tendency toward
equal #
protons & neutrons
Nucleus with only protons:
high energy states
must be occupied.
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Nucleus with protons and neutrons:
don’t need to occupy higher
energy states
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Comparing the ‘old’ and ‘new’
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What is this nuclear force?
• Modern view is that all forces arise from an
exchange of particles.
• Coulomb force is the
exchange of photons that have zero mass
• Strong nuclear force is the
exchange of a particle with mass.
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EM force and Strong Force
Electromagnetic force
Thur. Dec 6, 2007
Strong nuclear force
(approximate view)
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Nucleons are not fundamental
• We now know that
protons and neutrons
are not fundamental
particles.
• They are composed
of quarks, which
interact by
exchanging gluons.
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The ‘new’ nuclear force
• Strong force is actually between
quarks in the nucleons.
• Quarks exchange gluons.
• Most of the strong force glues
quarks into protons and neutrons.
• But a fraction of this force leaks
out, binding protons and neutrons
into atomic nuclei
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What makes a nucleus stable?
• A nucleus with lower energy is more stable.
• This is a general physical principle,
that systems tend to their lowest energy
configurations
– e.g. water flows downhill
– Ball drops to the ground
– Hydrogen atom will be in its ground state
• Same is true of nucleus
• Observed internal configuration
is that with the lowest energy.
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Radioactivity
• Stable nuclei have about the same
number of protons and neutrons.
Neutrons are somewhat favored
because of the electric repulsion
between protons.
• If the ratio of protons to neutrons
gets too far off-balance, a nucleus
will spontaneously transform itself
into another nucleus with a better
balanced ratio by emitting , , 
particles (2p2n, electrons, photons).
Marie Curie,
Nobel prizes in
physics, chemistry
Stability of nuclei
• Dots are naturally occurring
isotopes.
• Blue shaded region is isotopes
created in the laboratory.
• Observed nuclei
have ~ N=Z
• Slightly fewer protons because
they cost Coulomb repulsion
energy.
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Stable and Unstable Isotopes
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Binding energy of different nuclei
Fusion vs. fission 1)
• Schematic view of
previous diagram
•
56Fe
is most stable
• Move toward lower
energies by fission or
fusion.
Visualizing
a nucleus
A nucleon made up of
interacting quarks.
Thur. Dec 6, 2007
A nucleus of several nucleons,
with their interacting quarks
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Four fundamental forces
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Nucleus bound very tightly
• To change properties of nucleus, need much
larger energies than to change electronic states.
• Properties of nucleus that might change are
– Exciting nucleus to higher internal energy state
– Breaking nuclei apart
– Fusing nuclei together.
• Required high energies
provided by impact of high-energy…
…protons, electrons, photons, other nuclei
• High energies produced in an accelerator facility
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Nuclear Binding Energy
• Mass of nucleus is less than
mass of isolated constituents!
• Helium nucleus energy < energy isolated nucleons.
Helium
nucleus
• Energy difference is
binding energy.
2 protons &
2 neutrons
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Nuclear binding energy
12C
has a mass of 12.00000 u (1 u = 1.661x10-27 kg)
‘Missing mass’ in He case is
4.0320 u
 4.0015 u
0.0305 u = 5.06x10-29 kg
The corresponding energy is
E  mc 2

 0.0305 u1.6611027 kg/uc 2 
 0.0305 u931.494 MeV /u
 28.41 MeV  7.1 MeV /nucleon
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Nucleus properties
• Experimentally,
– radius of nucleus r = roA1/3 (A=mass # = # nucleons)
– says that volume V proportional to A.
– says that nucleon density is constant
• Nuclear matter is ~ incompressible
– More nucleons -> larger nucleus
– Nucleons ~ same distance apart in all nuclei
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Question
Tritum is an isotope of hydrogen with three
total nucleons: two neutrons and one
proton. How many electrons does it have?
A. One
B. Two
C. Three
One electron
Trituium
One proton
two neutrons
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Even stronger
• Electron / nucleus bound by Coulomb attraction.
Strength ~10 eV.
• Protons in nucleus 50,000 times nearer.
Coulomb repulsion ~500,000 eV = 0.5 MeV
• Nuclear force must be much stronger than this.
• Experimentally,
nucleons bound by ~ 8 MeV / nucleon
(8,000,000 eV / nucleon)
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