Download Nuclear Physics

Nuclear Physics
This Lecture: Nuclear structure, Strong Force,
Radioactivity
Previous lecture:
More on Atomic Physics
Electron Spin and Exclusion Principle
Emission and absorption spectra for atoms
with more electrons
Lasers
Final
Mon. May 12, 12:25-2:25, Ingraham B10
New material:
Particle in a box (Ch 40.4-5, 40.10)
Hydrogen Atom quantum numbers, wave functions, probability
(Ch 41.1-2)
Electron Spin and Pauli exclusion principle (Ch 41.3-6)
Lasers (Ch 41.8)
Nuclear Physics: nuclear structure (Ch 42.1-3) and Radioactivity
(Ch 42.5-7)
MTE1-3 material (see past lecture notes and Exam web page)
Final Exam
• Final is 25% of final grade
• In the final about 30% on new material, rest is
material in MTE1-3
• 2 sheets allowed (HAND WRITTEN!)
Notify NOW any potential and VERY serious problem you have with this
time
From last lecture: building atoms
4
Measuring the Moon-Earth
distance with a laser
NASA Apollo Laser Ranging Experiment: begun 25 yrs ago
when Apollo 11 deployed a reflector in the Sea of tranquillity
Lunar ranging involves sending a laser beam
through an optical telescope
At the Moon's surface the beam is
roughly four miles wide
Highly collimated beam from
stimulated emission, almost
monochromatic
5
http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.html
Nuclear Structure
Neutron
Size of electron orbit is
5x10-11 m
Nucleus is 5,000 times
smaller than the atom!
Nucleus size ~10-14 m
Proton
1 fermi = 10-15m
Spacing between
nucleons 10-15 m
Neutron: zero charge (neutral)
Proton: positive charge
(equal and opposite to electron)
6
Nucleons are not building blocks of matter
• We now know that
protons and neutrons
are not fundamental
particles.
• They are composed
of quarks, which
interact by
exchanging gluons.
7
Notation for nuclei
• Zero net charge ->
# protons in nucleus = # electrons orbiting.
• The number of electrons determines which element.
– 1 electron → Hydrogen
– 2 electrons → Helium
– 6 electrons → Carbon
A
Z
• How many neutrons?
6
3
Li
Nucleus =Protons+ Neutrons
nucleons
A = # of nucleons=
atomic mass number
A=N+Z
Z = atomic number (# of
protons or # of electrons)
8
N = # of neutrons
Example: Carbon
•Carbon has 6 electrons (Z=6)
•Zero net charge => 6 protons in
the nucleus.
•Most common form of carbon
has 6 neutrons in the nucleus.
12
C
6
Another form of Carbon has
6 protons, 8 neutrons in the nucleus. This is 14C.
9
different
mass
Quiz
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
10
Isotopes of Hydrogen
D2O has 20 nucleons and H2O has 18. So heavy water is
heavier than water by (20-18)/18= 10%
Number of nucleons determines the mass of atoms 11
Women Nobel Prizes
The only 2 female Nobel Prizes in Nuclear
Physics! (we need more!!!)
1903 Marie Curie (with Pierre)
in recognition of the extraordinary services they
have rendered by their joint researches on the
radiation phenomena discovered by Professor
Henri Becquerel
Maria Goeppert-Mayer
1963 Shell Model of Nucleus
Nuclear Force (Strong Interaction)
• 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.
Gravitational effects are negligible at atomic and nuclear level
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 14
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.
Attractive energy must be larger than the Coulomb repulsion,
so nuclear binding energies are at least
A. 5000 eV
B. 500,000 eV =0.5 MeV
C. 5,000,000 eV
Experimentally,
nucleons bound by ~ 8 MeV / nucleon
(8,000,000 eV / nucleon)
15
A convenient unit of Mass
• It is convenient to use atomic mass units, u, to
express masses
– 1 u = 1.660 539 x 10-27 kg
– mass of one atom of 12C = 12 u
⇒ 1 u = 1.66 x 10-27 kg
• Mass can also be expressed in MeV/c2
– From rest energy of a particle ER = mc2
– 1 u = 931.494 MeV/c2
16
€
Nuclear density
• Experimentally,
r0=1.2 fm
– 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
ρ nuc
m
Au
Au
u
1.66 ×10−27 kg
= =
=
=
=
= 2.3 ×1017 kg /m 3
V 4 πr 3 4 πr 3 A 4 πr 3 4 π (1.2 ×10−15 )
0
0
3
3
3
3
Nuclear Binding Energy
• Mass of nucleus is less than
mass of isolated constituents!
• Helium nucleus energy < energy isolated nucleons.
mp=1.6726 x 10-27kg/1.66 x 10-27 kg/u= 1.0078u
mn=1.6749 x 10-27kg/1.66 x 10-27 kg/u= 1.0087u
• Energy difference is
binding energy.
2 protons &
2 neutrons
1.0078u
Helium
nucleus
1.0078u
Arises from E=mc2
Equivalence of mass
and energy.
18
Binding energy
Nucles mass
mnucleus
Mass of Z protons and
N neutrons: Zmp + Nmn
Experiment says:
mnucleus < Zmp + Nmn
• Binding energy: energy you would need to supply to disassemble
the nucleus into nucleons: Ebinding = (Zmp+Nmn-mnucleus)c2
• Example: deuteron = 1 proton and 1 neutron bounded together
• Free particles: mp = 1.0078u, mn= 1.0087u, mp+mn=2.01649u
• Atomic mass of deuteron 2H = 2.01410u
• Binding energy =0.002388u x 931.494MeV/u = 2.224MeV
• Binding energy/nucleon = 2.224/2
19
Binding energy of different nuclei
For nuclei smaller than Fe the binding energy increases with A: you have to
supply more energy to win nuclear bounds.
Fe with A = 56 nucleons has 8.79 MeV/nucleon (amount of energy to
remove one nucleon from Fe nuclei)
Peaks at 4He, 12C and 16O because these nuclei are more tightly bond.
Nuclear force is short range: as nucleus grows nuclear bonds are saturated
and nuclei interact only with neighbors => Ebinding almost constant
20
Binding energy released:
fusion and fission
Combine p and n to form
4He
7MeV/nucleon
binding energy
is released
fusion
of 2 light
nuclei in
a heavier one
smaller energy
is released in fission
of a heavy nuclei into
2 lighter nuclei
21
Stable and Unstable Isotopes
Isotope = same Z
Isotone = same N
Isobar = same A
Stability of nuclei
•
Dots: naturally occurring isotopes.
•
Shaded region: isotopes created in
the laboratory.
•
•
•
Light nuclei are most stable if N=Z
Heavy nuclei are most stable if N>Z
As # of p increases more neutrons are
needed to keep nucleus stable
•
No nuclei are stable for Z>83
Radioactivity
• Discovered by Becquerel in 1896
• spontaneous emission of radiation as result of
decay or disintegration of unstable nuclei
• Unstable nuclei can decay by emitting some
form of energy
• Three different types of decay observed:
Alpha decay ⇒ emission of 4He nuclei (2p+2n)
Beta decay⇒ electrons and its anti-particle (positron)
Gamma decay⇒ high energy photons
Penetrating power of radiation
• Alpha radiation barely penetrate a piece of
paper (but dangerous!)
• Beta radiation can penetrate a few mm of Al
• Gamma radiation can penetrate several cm of
lead
Is the radiation charged?
• Alpha radiation positively charged
• Beta radiation negatively charged
• Gamma radiation uncharged
•
232Th
Decay: an exponential decrease
−rt
N(t) = N 0e
has a half-life
t1/2=14 x109 yr
• Sample initially
contains: N0 = 106
232Th atoms
• Every 14 billion
years, the number
of 232Th nuclei goes
down by a factor of
two.
N0
−rt1 / 2
N(t1/ 2 ) =
= N 0e
2
N0
€
N0/2
N0/4
N0/8
−rt1/ 2 = ln(1/2) ⇒ r = ln2 /t1/ 2
The Decay Rate
• probability that a nucleus decays during Δt
Prob(in Δt) = rΔt
Constant of proportionality r = decay rate (in s-1)
• number of decays (decrease)= NxProb=rNΔt =
=-ΔN
N=number of independent nuclei
€
N(t) = N 0e−rt
ΔN
= −rN
Δt
# radioactive
nuclei at time t
# rad. nuclei
at t=0
The number of decays per second is the activity
€
€
ΔN
R=
= rN
Δt
1
τ=
r
time constant