Download Chapter 30: Nuclear Physics What will we learn in this chapter?

Chapter 30: Nuclear Physics
What will we learn in this chapter?
Contents:
Properties of nuclei
Nuclear masses
Nuclear stability
Radioactivity
Alpha decay
Beta decay
Radiocarbon dating
Radiation and life sciences
Nuclear reactions
Nuclear fission and fusion
Chernobyl after the catastrophe 1986
Properties of nuclei
Composition of nuclides:
Protons! ! total number is the atomic number Z, determines
! ! ! ! chemical properties of an element.
Neutrons! ! total number is the neutron number N.
Properties of nuclei:
The total number of particles (nucleons) is called the nucleon (or
mass) number and denoted by A = Z + N.
The size of a nucleus is 20,000 to 200,000 times smaller than the
atom.
To a good approximation, the size of a
nucleus depends on the atomic
number A.
Radii of nuclei
Radii of nuclei: The radii of nuclei are given approximately by the
formula
R = R0 A1/3
here R0 is an empiric constant: R0 = 1.2 fm.
Note:
The volume of a sphere is 4!/3 R3, thus the volume of a nucleus is
proportional to A.
This means that the density of nuclei is approximately constant.
How dense are nuclei? For example, iron cores have a density of
approximately 1017 kg/m3!
Nuclear masses and isotopes
Several elements exist with the same Z (electronic properties) but
different N. These are called isotopes.
Examples:
Isotopes contd.
Properties of isotopes:
Chemically, isotopes of an element are basically the same.
Slight differences in the physical properties due to differences in
mass:
Melting & boiling temperatures
Diffusion rates (example U238 and 238 are separated with
centrifuges)
Nomenclature used:
Element El with Z protons and atomic mass A is usually called A
Z El
This means that El has N = A – Z neutrons.
Example:
14
6 C
represents Carbon 14 with Z = 6, A = 14, N = 8.
Atomic mass units.
Masses of nuclear constituents:
Proton ! ! mp = 1.6726171(29) 10-27 kg
Neutron! ! mn = 1.67492728(29) 10-27 kg
These are nearly equal. For precise measurements the unified atomic
mass unit (1 u) is introduced (1/12 of 12
6 C ):
1 u ! ! ! ! = 1.66053886(28) 10-27 kg
Masses of atomic constituents and H in UAM:
Proton!! ! mp = 1.00727646688(13) u
Neutron! ! mn = 1.00866491560(55) u
Electron! ! me = 0.00054857990945(24) u
Hydrogen!! mH = mp + me = 1.0078250 u
Atomic masses of light elements
Einstein relativity interlude…
Einstein postulated that energy and mass are equivalent:
Every mass has an energy associate with it.
Every energy has a mass associated with it.
This is expressed by the equation (c the velocity of light):
E = mc2
Note:
This equation follows from the symmetry of space and time.
A small amount of matter can produce a large amount of energy.
Example: One dollar bill weighs about 1g. This corresponds to
approximately 90 TJ (or 21.5 kilotons of TNT, Hiroshima 13
kilotons).
Atomic masses contd.
Note:
1 mole of particles with a mass of 1 u each would have a total
mass of exactly 1 gram.
Tables of atomic masses in UAM are for neutral atoms with Z
electrons. If you want only the nucleus or an ionized atom, you
need to subtract the corresponding mass of the electrons.
What is the energy equivalent of 1u?
Use E = mc2 = 931.494 MeV.
Does the mass of an atom agree with the sum of the masses of the
constituents?
No. Why? Some mass corresponds to the binding energy of the
atom, i.e.,EB = (∆M )c2.
Mass defect
Mass defect: The mass defect ∆M for a nucleus with mass M that has
Z protons and N neutrons is defined as
∆M = Zmp + N mn − M
Note:
There is no mass defect in 11 H . Why?
Example: Deuteron (D = 21 H )
∆M = mH + mn − mD
= 1.007825u + 1.008665u − 2.014101u = 0.00239u
the binding energy to pull a deuteron apart is thus
EB = 0.00239u(931.5MeV/u) = 2.23MeV
Notes on energy scales
In high-energy reactions the binding energies per nucleon are
generally ~ 8 MeV. This is HUGE.
We can therefore assume atoms are in their ground state when we
talk about nuclear reactions.
Note:
When atoms are bombarded with high-energy particles by a
radioactive transformation, they can decay to the ground state by
the emission of gamma rays which have energies between a few
tenths to a few MeV.
Protons and neutrons are also spin-1/2 particles. Therefore there
is a nuclear spin associated to a nucleus.
Nuclear stability: binding energies
Nearly all stable nuclei have binding energies in the
range from 6 to 9 MeV.
The curve reaches a peak at about 8.8 MeV/nucleon
at A = 62 (nickel).
The spike at A = 4 shows the unusual stability of
Helium 4.
The forces that hold protons and neutrons together is
the “strong interaction.”
Nuclear force (a.k.a. strong interaction)
Characteristics of the nuclear force:
It does not depend on charge (both n and p are bound).
It is strong enough to hold protons together, i.e., stronger than
the electric force.
It has a short range, on the order of 10-15 m. Why?
Not all particles in the nucleus interact at a given point in time
(saturation), unlike the electric forces.
It favors the binding of pairs (pairs of protons or pairs of
neutrons) with each pair having total spin zero. This explains the
unusual stability of alpha particles.
Note:
These qualitative characteristics of the nuclear force help
understand why only about 300/2500 nuclei are stable.
Unstable nuclei
Properties of unstable nuclei:
Unstable nuclei are called radioactive.
They formed from other nuclei or from the primordial time of
the universe (or supernovae).
They decay to form other nuclei by emitting particles and
electromagnetic radiation.
The decay time scale ranges from microseconds to billions of
years.
What happens when nuclei decay?
They emit particles and radiation (energy).
This energy can be used (power plants), at the “small” cost of
storing nasty byproducts…
Segrè chart
Use:
Helps visualize atomic structure and decays.
Explanation of graph:
The axes are N (neutron number) and Z (proton number).
Because A = Z + N, it follows that Z = A – N. Hence the blue lines
with Z = N represent a given value of A.
Note: the graph is rotated by 90º such that it fits on the slide and
is legible on the projector (see book).
Segrè chart of stable nuclides
Features seen on the Sègre chart
Most lines of constant A pass trough only one or two stable
nuclides, i.e., for a given mass number there are only 1 or 2 stable
nuclides (examples are A = 20, 40, 60, and 80).
In 4 cases the lines pass trough 3 stable nuclides (A = 96, 124, 130,
136).
Only 4 nuclides have both odd Z and odd N (odd-odd nuclides):
2
1H
6
3 Li
10
5 B
14
7 N
There is no stable nuclide for A = 5 or A = 8. Reason: alpha particles
are very stable and do not accept a fifth particle. Furthermore, a
nuclide with A = 8 splits rapidly into two alpha particles.
The stable region is very narrow.
For small mass number N = Z approximately. N/Z increases gradually
with A to about 1.6 (competition of electric/strong forces).
For A > 209 (Z > 83) there are no stable nuclides.
When are nuclides unstable?
The stability/instability of a nucleus is determined by the competition
between the attractive nuclear force and the repulsive electric force.
If there were no electrical interactions, Z = N would be most stable.
The electric repulsion shifts the balance in favor of the neutrons, but
if there are too many neutrons, the nucleus is unstable because they
cannot pair.
When A increases, the electric force grows faster than the nuclear
force.
Summarizing:
A nucleus is unstable if it is too big (A > 209, Z > 83).
A nucleus is unstable if the proton–neutron ratio is wrong.
A unstable nucleus will undergo radioactive decay.
Alpha decay
When a nucleus disintegrates and emits alpha particles, it is said to
undergo alpha decay.
Properties:
Alpha particle: 2 neutrons, 2 protons (He nucleus), zero total spin.
Occurs predominantly when the nuclei are too large to be stable.
When a nucleus emits an alpha particle N → N − 2
Z →Z −2
A→A−4
After that the nucleus is closer to stable territory on the Sègre
chart.
Alpha particles are emitted with well-defined energies
(conservation laws) and can penetrate solids a few µm.
Alpha decay example:
A typical alpha emitter is radium 226 Ra :
226
Ra →222 Rn + α
The speed of the alpha particle can be
determined from the curvature of its
trajectory in a magnetic field: 1.5 107 m/s.
With a mass of 6.64 10-27 kg, it has a
kinetic energy of 4.7 MeV. One can use
momentum conservation to determine
their energy.
Note:
Because alpha particles are slow, they only penetrate very little
into a material. A piece of paper should be enough to shield them.
Beta decay
Nuclei decaying can also emit electrons. This are known as beta–
particles.
How does this happen?
A neutron decays into a proton and an electron (beta– particle).
Note that free neutrons have an average lifetime of 15 min.
Properties:
Occurs predominantly when the ratio N/Z is too large.
A does not change, but N → N − 1 and Z → Z + 1 .
Beta particles have speed of 0.9995c and appear in a spectrum of
energies. Therefore, there is another particle, the antineutrino
−
emitted (neutral): n → p + β + ν e .
Can be shielded with thick clothing, used in medical applications.
Gamma decay
After a nucleus emits alpha or beta particles, it may still be in an
excited state.
It can emit a high-energy photon often called gamma-ray photon to
go back to its ground state.
Properties:
The energy of gamma radiation is 10 keV to 5 MeV.
Requires heavy shielding (lead or concrete wall).
Example: Radium decay.
Alpha particles emitted have two
possible kinetic energies.
Likely source for M. Curies early
death.
Decay series
When a radioactive nucleus decays, the resulting products might also
be radioactive.
In this case there is a series of decays until a stable configuration is
obtained.
Sègre chart representation of decays:
Alpha emission: N and Z decrease by 2.
Beta emission: N decreases by 1 and Z increases by 1.
Example: 238 U
14 decays with 8 alpha and 6 beta emissions.
Terminates in the stable isotope 206 P b .
Sègre chart for 238U (rotated by 90º)
lala
half-life
Radioactive decay rates
In any radioactive sample the number of radioactive nuclei decreases
as the nuclei decay.
If we have N nuclei at time t, we want to compute the rate of change
Rate of decay of radioactive nuclei:
∆N
= −λN
∆t
The constant λ is called the decay constant. It is material dependent.
Note:
A large value of λ corresponds to a fast decay.
Definition: Activity
Number of decays per unit time.
SI unit: becquerel, 1 Bq = 1 decay/s.
Unit: Curie, 1Ci = 3.7 1010 decays/s (~1g Ra).
exponential
decay
Radioactive decay contd.
It is possible to derive an expression for the number N of nuclei
remaining after a time t if the number at t = 0 is N0.
Number of radioactive nuclei remaining after time t:
N = N0 e−λt
This assumes N0 nuclei at t = 0 with a decay constant λ .
The half-life T1/2 of a radioactive substance is the time required for
the number of radioactive nuclei to decrease by 50%.
Decay constant and half-life:
ln 2
= 0.693λ−1
λ
In particle physics the life of a nucleus is described by the lifetime Tmean
T1/2
1
Tmean = =
= 1.443T1/2
λ
ln 2
T1/2 =
14C
dating
Application of radioactivity:
Dating of specimens (archeological, geological, …).
Idea: Measure the concentration of radioactive isotopes.
Why 14C?
14C is produced in the atmosphere by cosmic-ray bombardment.
Therefore there is a small fraction in the atmospheric CO2.
Plants that obtain the carbon from the atmosphere have the same
proportion of 14C as the atmosphere.
When a plant dies, it stops taking carbon, and the 14C has already
absorbed decays with a half-life of 5730 years.
By measuring the proportion of 14C, we can determine when
something died (apply corrections due to pollution since 1900…).
Similar approach with 40K/40Ar ratios in in rock specimens.
What are the effects or radiation on tissue?
Radiation:
Radioactivity (alpha, beta, gamma).
X rays
Interactions with tissue:
Molecular bonds are broken, creating ions.
Charged particles interact directly with the electrons in tissues.
Electromagnetic radiation interacts via the photoelectric effect.
Neutrons can be absorbed by nuclei which then decay.
Effects on tissue:
Range from a sunburn to death.
Alteration of genetic material, bone marrow destruction.
Radiation doses
The quantitative description of the effect of radiation on living tissue
is called radiation dosimetry.
The absorbed dose is the amount of energy delivered to the tissue
per unit mass.
Unit of absorbed radiation dose: The SI unit is called gray (old: rad)
!
!
!
1 Gy = 1 J/kg
1 rad = 0.01 J/kg = 0.01 Gy = 1 cGy
Note:
Because different radiation
sources affect tissue
differently, the relative
biological effectiveness (RBE)
is introduced.
Biological effect of radiation
The biological effect of radiation is measured by the product of the
absorbed dose and the RBE (biologically equivalent dose).
Unit of equivalent dose: The SI unit is called Sievert (old rem)
!
!
!
equivalent dose (Sv) = RBE x absorbed dose (Gy)
A more common unit is the ‘rem’ which is equivalent to the definition
of the rad
!
!
!
equivalent dose (rem) = RBE x absorbed dose (rad)
Hence, 1 rem = 0.01 Sv.
Radiation: pros
Pros:
Radiation is used for diagnosis (angiograms,
tiroid disease, liver disease, tracers) and
treatment of diseases (tumor therapy).
Wide variety of analytical applications.
Typical radiation exposures:
Chest X ray! ! ! 0.2 - 0.4 mSv on 5kg tissue, no effect
Cosmic rays! ! ! 1.0 mSv per year at sea level
! ! ! ! ! ! 2.0 mSv per year at 5000 ft altitude (pilots!)
Soil, building materials, … (similar to cosmic rays).
82% of the average exposure is from natural sources,
18% man-made.
A whole-body 5 Sv dose causes death within days.
A localized 100 Sv dose causes complete tissue destruction.
Radiation: cons
Cons:
Long-term exposure causes different cancers and genetic defects.
Safety levels in the US:
2 - 5 mSv per person per year
should be safe.
For persons working with radiation,
maximally 50 mSv per year.
These doses are high. For example,
the EU allows maximally 1 mSv for
regular exposures.
Radon
222Rn
is an inert, colorless, odorless radioactive gas.
It is part of the 238U decay series and occurs naturally in rocks and
soil.
Why is this a problem?
Radon is a gas, i.e., when produced in the soil, it can seep into
households trough basements.
Radon decays; when inhaled, the emitted alpha particles can
damage tissue in the lungs.
Activity inside American homes: 1 pCi/year, reduces life
expectancy by about a month (cigarettes are worse).
Unfortunately, activities of 3500 pCi/year have also been
measured…
Nuclear reactions
Rutherford proposed in 1919 that a heavy particle with sufficient
kinetic energy might be able to penetrate a nucleus.
Result:
A new, heavier nucleus.
A decay of the original nucleus.
17
1
Example: 42 He + 14
(note that 2+7 = 8+1)
7 N → 8 O + 1H
Such a process is called a nuclear reaction.
Nuclear reactions obey conservation laws:
Energy, momentum, angular momentum
Electric charge
Spin
Total number of nucleons (Z and A are invariant).
Not that the initial and final rest masses are not the same…
Reaction energy
The differences between the rest masses before and after the
reaction correspond to the reaction energy.
For a reaction A + B → C + D the reaction energy Q is
Q = (MA + MB − MC − MD )c2
Note:
When Q > 0, the total mass decreases and we have an exoergic
reaction; the kinetic energy increases.
When Q < 0, the total mass increases and we have an endoergic
reaction; the kinetic energy decreases.
An endoergic reaction cannot occur unless the initial kinetic
energy is at least as great as |Q|; called the threshold energy.
Nuclear fission
Definition:
! Decay process in which an unstable nucleus splits into two
! fragments of comparable mass (and often some neutrons),
! instead of emitting alpha or beta particles.
Properties:
The energy released in the fission is enormous (about 200MeV
per nucleus) and appears as kinetic energy of the fragments.
Induced fission: induced by neutron absorption.
Spontaneous fission: nuclei break up without initial neutrons.
Fission fragments always have too many neutrons to be stable,
i.e., N/Z ~ 1.55.
In general, the fragments also break up and might emit further
neutrons.
Example: 23xU
238U
(99.3%) breaks
up with neutrons that
have at least 1.2 MeV.
235U (0.7%) breaks up
with slow neutrons.
More than 100 different
nuclides (~20 different
elements) are produced.
The different fragments
also produce neutrons.
Why is the curve
symmetric?
distribution of A of fission products of U
Chain reaction in 235U
The initial reaction is triggered by neutron
bombardment.
The released neutrons (~2.5) can trigger
more fissions, i.e., a chain
reaction occurs.
The speed of the
reaction determines
the use of the material:
Controlled/slowly: nuclear
reactor.
Uncontrolled/explosive:
atomic bomb.
How can this be used to generate electricity?
Nuclear reactor
Idea:
Control the fission to produce a steady energy flux.
On average, 2.5 neutrons are produced in 235U fission. Therefore
40% are needed to keep the chain reaction alive.
Technical considerations:
Slow neutrons are more efficient in triggering reactions. Hence
the radioactive material is submerged in a moderator (H20) which
slows the neutrons via collisions.
To ensure the right amount of neutrons are in the reactor, control
rods can be inserted/removed. Cadmium works best since it
absorbs neutrons and does not react further.
238U absorbs neutrons, but cannot sustain the reaction. Thus U
needs to be enriched, i.e., the amount of 235U is increased to 3%.
The produced heat then drives a steam turbine yielding ~ 1GW.
Nuclear reactors
highly radioactive
Dangers/problems of nuclear reactors
Meltdown:
Even when the control rods are fully inserted, there is a residual
heat due to beta decays. Thus generators are never in the “off”
position.
Chernobyl: A poorly planned test of the cooling system produced
a core meltdown releasing 108 Ci into the atmosphere (600 yrs).
Nuclear waste:
The produced waste is radioactive and presents huge storage
challenges. Usually encased in glass and buried underground.
Ecology (never discussed…):
Water for the chillers is taken from and returned to rivers. The
water temperature rises destroying the local biotopes.
Nuclear fusion
Definition:
! Two or more (light) nuclei combine to form a larger nucleus.
Properties:
Energy is released because the binding energy per nucleon
increases after the reaction.
Example reaction:
!
!
!
!
1
1
2
+
1 H + 1 H → 1 H + β + νe
1
2
3
1 H + 1 H → 2 He + γ
3
3
4
1
1
2 He + 2 He → 2 He + 1 H + 1 H
The positron β + combines with an electron and produces gamma
radiation. Thus 4 protons produce a He atom and radiation. The
produced energy is 26.7 MeV. This proton-proton chain occurs in
the sun.
Nuclear fusion contd.
Initial energy for thermonuclear reactions:
The nuclei must come very close together, ~ 2 fm to overcome
the electrical repulsion.
The necessary energy is ~ 0.7 MeV, which corresponds to the
fusion reactor
initial reaction energy.
Such energies are available at very
high temperatures of ~109 K.
Where do we find fusion?
Stars
Hydrogen bombs (uncontrolled
thermonuclear reaction).
Fusion reactors (not functional
yet).
plasma