CHAPTERS 12 and partly 13

The Atomic Nucleus / Nuclear Physics

 Important nomenclature and ideas
 12.1 Discovery of the Neutron
 12.2 Nuclear Properties
 12.3 The Deuteron
 12.4 Nuclear Forces
 12.5 Nuclear Stability
 12.6 Radioactive Decay
 12.7 Alpha, Beta, and Gamma Decays
 12.8 Radioactive Nuclides
 13.4 Fission
 13.5 Fission Reactors
 13.6 Fusion
It is said that Cockroft and Walton were interested in raising the voltage of their
equipment, its reliability, and so on, more and more, as so often happens when you are
involved with technical problems, and that eventually Rutherford lost patience and said,
“If you don’t put a scintillation screen in and look for alpha particles by the end of the
week, I’ll sack the lot of you.” And they went and found them (the first nuclear
transmutations). - Sir Rudolf Peierls in Nuclear Physics in Retrospect 1
 A Z  N
Z Atomic _ symbol as Z is the ordering
principle of the periodic
table of the elements, it
A Z  N
Atomic _ symbol is often dropped

4
He 49Be126C  01n A and charge conserved in nuclear reactions, first an
2 2
alpha particle, last a neutron
12.2: Nuclear Properties
 The nuclear charge is +e times the number (Z) of protons.

 Hydrogen’s isotopes:
 Deuterium: Heavy hydrogen. Has a neutron as well as a proton in its
nucleus.
 Tritium: Has two neutrons and one proton, is radioactive, about 40 tons
on earth.

 The nuclei of the deuterium and tritium atoms are called deuterons
and tritons.
 Atoms with the same Z, but different mass number A, are called
isotopes.

3
Nuclear Properties
 The symbol of an atomic nucleus is .
where Z = atomic number (number of protons)
N = neutron number (number of neutrons)
A = mass number (Z + N)
X = chemical element symbol
 Each nuclear species with a given Z and A is called a nuclide.
 Z characterizes a chemical element.
 The dependence of the chemical properties on N is negligible,
certain physical properties, e.g thermal expansion show
measurable differences due to isotope effects.

 Nuclides with the same neutron number are called isotones and
the same value of A are called isobars.

4
Sizes and Shapes of Nuclei
 Rutherford concluded that the range of the nuclear force must be le
ss than about 10−14 m.
 Assume that nuclei are spheres of radius R.
 Particles (electrons, protons, neutrons, and alphas) scatter when pr
ojected close to the nucleus.

 The nuclear force is often called the strong force.

 There is no simple closed form equation for this force, so we don’t h

ave a simple potential energy function that we could put into the Sc
hrödinger Equation, but quantum mechanics reigns supreme in the
nuclear realm as well

5
Sizes and Shapes of Nuclei
 The nuclear radius may be approximated to be R = r0A1/3
where r0 ≈ 1.2 × 10−15 m.

 We use the femtometer with 1 fm = 10−15 m, also called a fermi.

6
Note the three orders of magnitude
difference between μnuclear and μBohr

7
 Positrons have same
mass and spin as
electron but positive
charge

e- and e+ are also called beta radiation

8
12.1: Discovery of the Neutron
 Rutherford proposed the atomic structure with the massive nucleu
s in 1911.
 the components of nucleus were known only in 1932
 Three reasons why electrons cannot exist within the nucleus:
1) Nuclear size
The uncertainty principle puts a lower limit on its kinetic energy tha
t is much larger that any kinetic energy observed for an electron e
mitted from nuclei (its actually the result of β-decay).
2) Nuclear spin
If a deuteron nucleus were to consist of protons and electrons, the
deuteron must contain 2 protons and 1 electron. A nucleus compo
sed of 3 fermions must result in a half-integral spin. But it has bee
n measured to be 1. So no electrons can possible in the nucleus
(but they apparently come out of atoms or their nucleus)

9
Discovery of the Neutron
 In 1930 the German physicists Bothe and Becker used a
radioactive polonium source that emitted α particles. When
these α particles bombarded beryllium, the radiation penetrated se
veral centimeters of lead but was readily absorbed
by paraffin wax,

4
2 He Be C  n
9
4
12
6
1
0

10
Discovery of the Neutron
 In 1932 Chadwick proposed that the new radiation produced by α
+ Be consisted of neutrons. His experimental data estimated the n
eutron’s mass as somewhere between 1.005 u and 1.008 u, not fa
r from the modern value of 1.0087 u.

 The electromagnetic radiation (photons) are called gamma rays

which have energies on the order of MeV.

 Curie and Joliot performed several measurements to study penetr

ating high-energy gamma rays.

 There are also electrons (and positrons) emerging from atoms, be

ta rays (but they are not constituents of the nucleus themselves)

11
Intrinsic Magnetic Moment
 The proton’s intrinsic magnetic moment points in the same direction as its i
ntrinsic spin angular momentum (as it is positive).
 Nuclear magnetic moments are measured in units of the nuclear magneton
μN.

 The divisor in calculating μN is the proton mass mp, which makes the nuclea
r magneton 1836 times smaller than the Bohr magneton of the electron.
 The proton magnetic moment is μp = 2.79 μN.
 The magnetic moment of the electron is μe = −1.00116 μB. (1 in last chapter wh
ere quantum electrodynamics had been ignored)
 The neutron magnetic moment is μn = −1.91 μN.
 The nonzero neutron magnetic moment implies that the neutron has negati
ve and positive internal charge components.
Complex internal charge distribution, just like the proton.

12
 Deep
A few muons (-1e
charge, ½ spin) are
created from the energy
in the inelastic collision
and the release of
nuclear binding energy,
which gets converted
into mass
Relative
cross
sections

13
Nuclear Properties
 Atomic masses are denoted by the symbol u.
 1 u = 1.66054 × 10−27 kg = 931.49 MeV/c2

 Both neutrons and protons, collectively called nucleons, are con

structed of three other particles called quarks.

1 proton plus 1 neutron = 2.0159414 u ≈ 1877.84 MeV

mass of the nucleus of deutrium ??? Nope it’s 2.01355
u, why? 14
12.3: The Deuteron, nucleus of the deuterium atom 2H
A Z  N
1
H also called protium Z Atomic _ symbol
 The mass of a deuteron = 2.0135532 u ≈ 1875.61293 MeV
The deuterium mass = 2.01410778 (mass of a proton + mass of a
neutron + mass of an electron minus the mass equivalents of two
different types of binding energy). Chemical symbol D (isotope)
 The difference = 0.000549 u + mass of an electron and take off its

binding energy mass equivalent 13.6 eV / c2.

 The deuteron is bound by a mass-energy B .
d

 The mass of a deuterium nucleus is

 Add an electron mass to each side but ignore its binding energy

1 proton plus 1 neutron, but not bound = 2.0159414 u

15
 md + me is the deuterium atom mass M(2H) and mp + me is the most
common atomic hydrogen mass

 Because the electron masses cancel in almost all nuclear-mass

difference calculations, we use atomic masses rather than nuclear
masses.

 Convert this to energy using u = 931.5 MeV / c2.

 Even for heavier nuclei we effectively neglect the electron binding

energies (much larger than 13.6 eV) because the nuclear binding
energies (e.g. 2 MeV) are hundreds of thousands times greater.

16
 The binding energy of any nucleus = the energy required to
separate the nucleus into free neutrons and protons.

Experimental Determination of Nuclear Binding Energies

 for the 2.22-MeV binding energy by using a nuclear reaction. We

scatter gamma rays from free deuteron gas and look for the breakup of
a deuteron into a neutron and a proton:

 This nuclear reaction is called photodisintegration or a photonuclear

reaction.
 The mass-energy relation is

 where hf is the incident photon energy.

Kn and Kp are the neutron and proton kinetic energies, mn mass of
neutron.
17
The Deuteron
 The minimum energy required for the photodisintegration:
 Momentum must be conserved in the reaction if Kn, Kp ≠ 0.

 Experiment shows that a photon of energy less than 2.224 MeV ca

nnot dissociate a deuteron.

Deuteron Spin and Magnetic Moment

 Deuteron’s nuclear spin quantum number is 1, it’s a boson, this ind

icates also the neutron and proton spins are aligned parallel to eac
h other, add up
 The nuclear magnetic moment of a deuteron is 0.86 μ ≈ the sum o
N
f the free proton and neutron 2.79 μN − 1.91 μN = 0.88μN (difference
due to mass equivalent of binding energy)
18
 12.4: Nuclear Forces
 Neutron + proton (np) and proton + proton (pp) elastic collisions.

Very high density in the nucleolus, all nuclei are constantly moving about and
scatter of reach other

In reality
indistinguishable

Electrostatic hump

The nuclear potential energy function for two particles, similar for
many particles
19
Nuclear Forces
 The inter-nucleon potential has a “hard core” that prevents the nucle
ons from approaching each other closer than about 0.4 fm.

 The proton has “color charge radius” of about 1 fm.

 Two nucleons within about 2 fm of each other feel an attractive force.

 The nuclear force (very short range):

 falls to zero abruptly with inter-particle separation.
 The interior nucleons are completely surrounded by other nucleons
with which they interact.
 The major difference between the np and pp potentials is the Coulo
mb potential shown for r ≥ 3 fm for the pp force.

20
12.5: Nuclear Stability
 The binding energy of a nucleus
against dissociation into any
other possible combination of
nucleons. Example nuclei R and S.

 Proton (or neutron) separation

energy:
 The energy required to remove one
proton (or neutron) from a nuclide.

21
Nuclear Stability
 The “line” representing the stable nuclides is the line of stability.
 It appears that for A ≤ 40, nature prefers the number of protons a
nd neutrons in the nucleus to be about the same Z ≈ N.
However, for A ≥ 40, there is a decided preference for N > Z beca
use the nuclear force is independent of whether the particles are
nn, np, or pp.

 As the number of protons increases, the Coulomb force between

all the protons becomes stronger until it eventually affects the bin
ding significantly.

All integers, result from nucleons being fermions

22
Nuclear Stability

 Most stable nuclides have both even Z and even N (even-even

nuclides), e.g. 4 He
2

 Only four stable nuclides have odd Z and odd N (odd-odd nuclides).

23
 The Liquid Drop Model
 Treats the nucleus as a collection of interacting particles in a liquid drop.
 The total binding energy, the semi-empirical mass formula (due to
Weizäcker) is

 The volume term (av) indicates that the binding energy is approximately
the sum of all the interactions between the nucleons.

 The second term is called the surface effect because the nucleons on
the nuclear surface are not completely surrounded by other nucleons.

 The third term is the Coulomb energy (4th and 5th term next slide)

24
The Liquid Drop Model
 The fourth term is due to the so called “symmetry energy”, has a quantu
m-mechanical origin, consequence of exclusion principle. In the absence
of Coulomb forces, the nucleus prefers to have N ≈ Z.
 The last term is due to the pairing energy and reflects the fact that the nu
cleus is more stable for even-even nuclides. Use values given by Fermi t
o determine this term.

where Δ = 33 MeV·A−3/4.
 No nuclide heavier than has been found on earth. If they ever exist
ed, they must have decayed so quickly that quantities sufficient to meas
ure no longer exist.

25
one low energy (room-temperature) neutron
being absorbed by 235U, kaboom, and two to
three more medium energy neutrons to make
more “kabooms” if more fissionable uranium is
around

26
Who is the greatest person that history has forgotten
?
Marc Morgenstern, Updated July 6, 2019 · Upvoted by Travis Perry, M.A. History,
Wayland Baptist University (2020) and Brayden Swanson, Studied history
extensively for six years

You’ve probably never even heard of this man, but he’s responsible for saving
billions of lives, as well as civilization as we know it:

This is Stanislav Yevgrafovich Petrov.

Petrov was a lieutenant colonel of the Soviet Air Defense Forces. On September
26, 1983, three weeks after the Soviet military had shot down Korean Air Lines
Flight 007, Petrov was the duty officer at the command center for the Oko nuclear
early-warning system when the system reported that a USAF Minuteman missile
had been launched from the United States, followed by up to five more.
“If notification was received from the Russian early warning systems that inbound
missiles had been detected, the Soviet Union's strategy was an immediate and
compulsory nuclear counter-attack against the United States (launch on warning),
specified in the doctrine of mutual assured destruction, or MAD.”

27
At the time, nuclear retaliation required that multiple sources confirm an attack
before launching retaliatory strikes against the offending nation. Petrov knew that
any nuclear strike from the US would be massive, and concluded that the system
had triggered a false alarm, that no missiles had been launched from the U.S., and,
disobeying orders from his superiors, stood down the retaliatory launch.
“It was subsequently determined that the false alarms were caused by a rare
alignment of sunlight on high-altitude clouds and the satellites' Molniya orbits, an
error later corrected by cross-referencing a geostationary satellite.”
Petrov’s quick thinking, as well as his refusal to obey orders, prevented what would
have most assuredly been the start of World War III, a devastating nuclear
holocaust would have ensued, and billions of people might have died, as well as
ending civilization as we know it on the Earth.
Petrov had, indeed, saved the world.
So why do we not hear more about this brave man? The glitches in the Soviets’
early-warning system embarrassed military higher ups, and the entire episode was
kept quiet until the incident became known publicly in the 1990s upon the
publication of the memoirs of Colonel General Yuriy Vsyevolodich Votintsev, a
retired commander of the Soviet Air Defense's Missile Defense Units and the officer
who had been in charge at the time of the incident.

28
“Petrov was neither rewarded nor punished for his actions, but was reassigned to
a less sensitive post, took early retirement (although he emphasized that he was
not "forced out" of the army, as is sometimes claimed by Western sources), and
suffered a nervous breakdown.”

Petrov died on May 19, 2017, of hypostatic pneumonia at 77 years old.

29
October 11, 1986, halfway between Moscow and Washington, D.C. … 30
Binding Energy Per Nucleon

 Use this to compare the relative

stability of different nuclides.
 It peaks at A = 56.
 The curve increases rapidly,
demonstrating the saturation
effect of nuclear force.
 Sharp peaks for the even-even
nuclides 4He, 12C, and 16O
tight bound.

31
32
Nuclear Models
 Current research focuses on the constituent quarks and
physicists have relied on a multitude of models to explain
nuclear force behavior.

1) Independent-particle models:
The nucleons move nearly independently in a common
nuclear potential. The shell model has been the most
successful of these.
2) Strong-interaction models:
The nucleons are strongly coupled together. The liquid drop
model has been successful in explaining nuclear masses as
well as nuclear fission.

33
Nuclear Models
The nuclear potential felt by the neutron and the proton

 The difference of the shape between the proton and the neutron are due
to the Coulomb interaction on the proton.
 Nuclei have a Fermi energy level which is the highest energy level filled
in the nucleus.
 In the ground state of a nucleus, all the energy levels below the Fermi
level are filled.

34
 Nuclear Models
 Energy-level diagrams for 12C and 16O.
Note that the
 Both are stable because they are p energy
even-even. levels are
higher

Case 1: If we add one

proton to 12C to make unstable

Filling up energy
levels up to the
Fermi level Case 2: If we add one
stable
neutron to 12C to make 13C:

35
Nuclear Models
 when we add another neutron to produce 14C, we find it is
unstable.

 neutron energy levels are lower in energy than the corresponding

proton ones.

36
 12.6: Radioactive Decay
 An empirical law that is fulfilled only statistically

 Marie Curie and her husband Pierre discovered polonium and radium in
1898.
 The simplest decay form is that of a gamma ray, which represents the nucle
us changing from an excited state to lower energy state.
 Other modes of decay include emission of α particles, β (– and +) particles,
protons, neutrons, and fission.

 The decays per unit time (activity).

where dN / dt is negative because total number N decreases with time.

37
Radioactive Decay
 SI unit of activity is the Becquerel: 1 Bq = 1 decay / s.
 In common use is the Curie (Ci) 3.7 × 1010 decays / s equivalent t
o 1 g Ra (typically micro Ci to milli Ci)
 If N(t) is the number of radioactive nuclei in a sample at time t, an
d λ (decay constant) is the probability per unit time that any give
n nucleus will decay:

 If we set N(t = 0) ≡ N0
----- radioactive decay law

38
Radioactive Decay
 The number of radioactive nuclei as a function of time

39
Radioactive Decay
 The activity R is also

where R0 is the initial activity at t = 0.

 half-life t1/2 or the “mean lifetime” τ are defined on basis of decay
constant.

 The half-life is

The time it takes to arrive at No/e

 The mean lifetime is

40
41
42
Radioactive Carbon Dating
 Radioactive 14C is produced in our
atmosphere by the bombardment of 14N by
neutrons produced by cosmic rays.

 When living organisms die, their intake of 14C

ceases, and the ratio of 14C / 12C
decreases as 14C decays.
 Because the half-life of 14C is 5,730 years, it
is convenient to use the 14C / 12C ratio to
determine the age of objects over a range up
to 45,000 years ago.
 The period just before 9000 years ago had a
higher 14C / 12C ratio by factor of about 1.5
than it does today.
43
44
45
 Caused by the weak nuclear force

12
6 C is stable

46
12.7: Alpha, Beta, and Gamma Decay

When a nucleus decays, all the conservation laws must be

observed:
 Mass-energy

 Linear momentum

 Angular momentum

 Electric charge

 Conservation of nucleons

 The total number of nucleons (A, the mass number) must be

conserved in a typical (relatively low energy) nuclear reaction or
decay.

47
Alpha, Beta, and Gamma Decay
 Let the radioactive nucleus be called the parent and have the
mass

 Two or more products can be produced in the decay.

 Let the original one be My (mother) and the mass of the subsequent
one (daughter) be MD.
 The conservation of energy is

where Q is the energy released (disintegration energy) and equal to

the total kinetic energy of the reaction products.

 If Q > 0, a nuclide is unstable and may decay.

 If Q < 0, decays emitting nucleons do not occur.

48
Alpha Decay
 The nucleus 4He has a binding energy of 28.3 MeV.
 If two protons and two neutrons in a nucleus are bound by less
than 28.3 MeV, then the emission of an alpha particle (alpha
decay) is possible.

 If Q > 0, alpha decay is possible. Is also a nucleus

The appropriate masses are

49
Alpha Decay

 In order for alpha decay to occur, two neutrons and two protons
group together within the nucleus prior to decay and the alpha
particle overcomes the nuclear attraction from the remaining
nucleons and escapes through the potential energy barrier by
tunneling.

The potential energy diagram of alpha particle

50
Alpha Decay
 The barrier height VB is greater than 20 MeV.
 The kinetic energies of alpha particles emitted from nuclei range
from 4-8 MeV.
It is impossible classically for the alpha particle to escape
the nucleus, but the alpha particles are able to tunnel through the
barrier.
At higher energy, E2, α-particle h
as much higher tunneling probab
ility than at lower energy, E1, corr
esponding to shorter lifetimes.

51
Alpha Decay
 Assume the parent nucleus is initially at rest so that the total mome
ntum is zero.
 The final momenta of the daughter pD and alpha particle pα have th
e same magnitude and opposite directions.
So all alpha particles have “about” the
same momentum and kinetic energy

52
 accumulated per year

1 Sv absorbed dose causes a fatal cancer many years later in 5 out of

100 people, approx. 10 Sv per day typical natural background
53
54
 r

αdecay

Note that the total number of nucleons does not change, we discussed
α-decay in the context of tunneling and Rutherford’s scattering
experiments

55
Beta Decay
 Unstable nuclei may
move closer to the line
of stability by
undergoing beta
decay.
 The decay of a free
neutron is

 The beta decay of 14C

(unstable) to form 14N, The electron energy spectrum from the beta decay
a stable nucleus, can The electron does not exist in the
be written as nucleus, it is created from the
+ something
energy that results from the decay
exceedingly
(which is due to the weak force)
tiny
Observed experimentally, but should be impossible according to the
56
prevailing understanding of physics before Pauli’s neutrino
 Beta Decay
 There was a problem in neutron decay, the spin ½ neutron cannot
decay to two spin ½ particles, a proton and an electron. 14C has
spin 0, 14N has spin 1, and the electron has spin ½.
we cannot combine spin ½ & 1 to obtain a spin 0.

 Wolfgang Pauli proposed a new particle, the neutrino, that must

be produced in beta decay. It has spin quantum number ½, charge
0, and carries away the energy that is apparently missing in the fig.
in the previous slide
 Momentum seemed not to be conserved either, so Pauli predicts a
particle that must exist and carry away just the right amount of
energy so that momentum will also be conserved and everything is
Oki-Doki again

That particle will actually be much later, 1956, experimentally observed, 1995 Nobel priz
57
Frederick Reines
Beta Decay

 An occasional electron is detected with the kinetic energy close to

the required Kmax (to conserve energy), but in most cases the
electron’s kinetic energy is less than Kmax.
the neutrino has very very very little mass, and most of its
energy is kinetic.

 Neutrinos have no charge and do not interact electromagnetically.

 They are not affected by the strong force of the nucleus.
 They are due to the weak interaction (result from the weak force).
 The unification of the electromagnetic and weak force is the
electroweak force.

58
β- Decay
 There are actually antineutrinos . (In beta-minus decay)
 The beta decay of both a free neutron and 14C is written as

 In the general beta decay of the parent nuclide to the daughter

, the reaction is

 The disintegration energy Q is Note that A is constant

 In order for β− to occur, we must have Q > 0.

 The total number of nucleons A is constant, but Z charges to Z + 1.

59
β+ Decay
 Is what happens for unstable nuclides with too many protons
 Positive electron (positron) is produced.
 Positron is the antiparticle of the electron.
 A free proton might decay with t1/2 > 1032 y, nobody knows for sure
 The nucleus 14O is unstable and decays by emitting a positron and
a neutrino to become stable 14N.

 The general β+ decay is

60
Electron Capture
 Classically, inner K-shell and L-shell electrons are tightly bound a
nd L-orbits are highly elliptical, possibility of atomic electron capt
ure.
 The reaction for a proton is p + e− n+v
 The general reaction is

 The disintegration energy Q is

61
Gamma Decay
 If the decay proceeds to an
excited state of energy Ex
rather than to the ground
state, then Q for the
transition to the excited
state can be determined
with respect to the
transition to the ground
state. The disintegration
energy Q to the ground
state Q0.

 Q for a transition to the

excited state Ex is

62
63
Gamma Decay
 The excitation energies tend to be much larger, many keV or
even MeV.
 The possibilities for the nucleus to rid itself of this extra energy is
to emit a very high energy photon (gamma ray).
 The gamma-ray energy hf is given by the difference of the higher
energy state E> and lower one E<.

 The decay of an excited state of AX* (where * is an excited state)

to its ground state is

 A transition between two nuclear excited states E> and E< is

64
Gamma Decay
 The gamma rays are normally emitted soon after a nucleus is put
into an excited state.

 Sometimes selection rules prohibit a certain transition, and the

excited state may live for a long time.
 These states are called isomers or isomeric states and are
denoted by a small m for metastable.

 Example: one state of at 0.271 MeV excitation energy does

not gamma decay because of a large spin difference transition.

65
12.8: Radioactive Nuclides
 The unstable nuclei found in nature exhibit natural radioactivity.

All living people are

somewhat radioactive, e.g.
depending on how much
NaCl they eat (it is obtained
from mines, where there is
some KCl present as well

Produced in nuclear reactors

for medical purposes

66
Radioactive Nuclides
 There are only four paths that the heavy naturally occurring
radioactive nuclides may take as they decay.
 Mass numbers expressed by either:
 4n
 4n + 1
 4n + 2
 4n + 3

Three of these paths lead to different types of isotopes of Pb

67
Radioactive Nuclides
 The sequence of one of the radioactive series Th
232

 Bi can decay by either alpha or beta decay (branching).

212

68
Time Dating Using Lead Isotopes
 A plot of the abundance ratio of 206Pb / 204Pb versus 207Pb / 204Pb
can be a sensitive indicator of the age of lead ores. Such
techniques have been used to show that meteorites and the earth,
believed to be left over from the formation of the solar system, are
4.55 billion years old.

69
70
71
A Z  N
Z Atomic _ symbol

72
73
Thermal Neutron Fission
 Fission fragments are highly unstable because
they are so neutron rich.
 Prompt neutrons are emitted simultaneously
with the fissioning process. Even after prompt
neutrons are released, the fission fragments
undergo beta decay, releasing more energy.
 Most of the ~200 MeV released in fission goes
to the kinetic energy of the fission products, but
the neutrons, beta particles, neutrinos, and
gamma rays typically carry away 30–40 MeV of
the kinetic energy.

74
75
 Chain Reactions
 Because several neutrons are produced in
fission, these neutrons may subsequently
produce other fissions. This is the basis of the
self-sustaining chain reaction.
 If slightly more than one neutron, on the
average, results in another fission, the chain
reaction becomes critical.
 A sufficient amount of mass is required for a
neutron to be absorbed (a statistical process),
called the critical mass.
 If less than one neutron, on the average,
produces another fission, the reaction is
subcritical.
 If more than one neutron, on the average,
produces another fission, the reaction is
supercritical.
 An atomic bomb is an extreme example of a
supercritical fission chain reaction.

76
Chain Reactions
 A critical fission reaction can be controlled by absorbing
neutrons. A self-sustaining controlled fission process requires
that not all the neutrons are prompt. Some of the neutrons are
delayed by several seconds and are emitted by daughter
nuclides. These delayed neutrons allow the control of the
nuclear reactor.

 Control rods regulate the absorption of neutrons to sustain a

controlled reaction.

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13.5: Fission Reactors
 Several components are important
for a controlled nuclear reactor:
1) Fissionable fuel
2) Moderator to slow down neutrons
3) Control rods for safety and to
control criticality of reactor
4) Reflector to surround moderator
and fuel in order to contain
neutrons and thereby improve
efficiency
5) Reactor vessel and radiation shield
6) Energy transfer systems if
commercial power is desired

 Two main effects can “poison”

reactors: (1) neutrons may be
absorbed without producing fission
[for example, by neutron radiative
capture], and (2) neutrons may
escape from the fuel zone.

78
Core Components
 Fission neutrons typically have 1–2 MeV of kinetic energy, and because
the fission cross section increases as 1/v at low energies, slowing down
the neutrons helps to increase the chance of producing another fission.
A moderator is used to elastically scatter the high-energy neutrons and
thus reduce their energies. A neutron loses the most energy in a single
collision with a light slow moving particle. Heavy hydrogen (in heavy
water), carbon (graphite), and beryllium are all good moderators.
 The simplest method to reduce the loss of neutrons escaping from the
fissionable fuel is to make the fuel zone larger. The fuel elements are
normally placed in regular arrays within the moderator.

79
Core Components
 The delayed neutrons produced
in fission allow the mechanical
movement of the rods to control
the fission reaction. A “fail-safe”
system automatically drops the
control rods into the reactor in
an emergency shutdown.
 If the fuel and moderator are
surrounded by a material with a
very low neutron capture cross
section, there is a reasonable
chance that after one or even
many scatterings, the neutron
will be backscattered or
“reflected” back into the fuel
area. Water is often used both
as moderator and reflector.

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Energy Transfer
 The most common method is to pass hot
water heated by the reactor through some
form of heat exchanger.
 In boiling water reactors (BWRs) the
moderating water turns into steam, which
drives a turbine producing electricity.
 In pressurized water reactors (PWRs) the
moderating water is under high pressure and
circulates from the reactor to an external
heat exchanger where it produces steam,
which drives a turbine.
 Boiling water reactors are inherently simpler
than pressurized water reactors. However,
the possibility that the steam driving the
turbine may become radioactive is greater
with the BWR. The two-step process of the
PWR helps to isolate the power generation
system from possible radioactive
contamination.
81
Types of Reactors
 Power reactors produce commercial electricity.
 Research reactors are operated to produce high
neutron fluxes for neutron-scattering experiments.
 Heat production reactors supply heat in some cold
countries.
 Some reactors are designed to produce radioisotopes.
 Several training reactors are located on college
campuses.

82
Nuclear Reactor Problems
 The danger of a serious accident in which radioactive elements are
released into the atmosphere or groundwater is of great concern to
the general public.
 Thermal pollution both in the atmosphere and in lakes and rivers
used for cooling may be a significant ecological problem.
 A more serious problem is the safe disposal of the radioactive wastes
produced in the fissioning process, because some fission fragments
have a half-life of thousands of years.
 Three widely publicized accidents at nuclear reactor facilities—one
at Three Mile Island in Pennsylvania in 1979, the others two at
Chernobyl in Ukraine in 1986 and Fukushima in Japan in 2011 —
have significantly dampened the general public’s support for nuclear
reactors.
 Large expansion of nuclear power can succeed only if four critical
problems are overcome: lower costs, improved safety, better nuclear
waste management, and lower proliferation risk.

83
 ≈ 5,000
Bq
inside an
healthy
adult

Due to a tsunami that was triggered by a magnitude 9.0 earthquake 84

Breeder Reactors
 A more advanced kind of reactor is the breeder reactor, which
produces more fissionable fuel than it consumes.
 The chain reaction is:

 The plutonium is easily separated from uranium by chemical means.

 Fast breeder reactors have been built that convert 238U to 239Pu. The
reactors are designed to use fast neutrons.
 Breeder reactors hold the promise of providing an almost unlimited
supply of fissionable material.
 One of the downsides of such reactors is that plutonium is highly
toxic, and there is concern about its use in “unauthorized” weapons
production.
85
 13.6: Fusion
 If two light nuclei fuse together, they also form a
nucleus with a larger binding energy per nucleon and
energy is released. This reaction is called nuclear
fusion.

 The most energy is released if two isotopes of

hydrogen fuse together in the reaction.

1
0 n Li  H  He
6
3
3
1
4
2

86
The European Fusion project, 1991 87
 1
0 n Li  H  He
6
3
3
1
4
2

Future fusion plants – Iter included – are expected to make

Quasi unlimited their own tritium fuel by using high-energy neutrons,
amount of deuterium released when deuterium and tritium fuse, to split the
in oceans common metal lithium into tritium and helium 88
Formation of Elements
 The proton-proton chain includes a series of reactions that starts
with two protons and ends with an ordinary alpha particle.

 As stars form due to gravitational attraction of interstellar matter, the

heat produced by the attraction is enough to cause protons to
overcome their Coulomb repulsion and fuse by the following
reaction:

 The deuterons are then able to combine with 1H to produce 3He:

 The 3He atoms can then combine to produce 4He:

89
Formation of Elements
 As the reaction proceeds, however, the temperature increases, and
eventually 12C nuclei are formed by a process that converts three 4He
into 12C.
 Another cycle due to carbon is also able to produce 4He. The series of
reactions responsible for the carbon or CNO cycle are

 Proton-proton and CNO cycles are the only nuclear reactions that can
supply the energy in stars.

90
91
92
93
Alpha Decay
 From the conservation of energy and conservation of linear
momentum, determine a unique energy for the alpha particle.

94
Sizes and Shapes of Nuclei
The shape of the Fermi distribution

 If we approximate the nuclear shape as a sphere,

 The nuclear mass density is 2.3 × 1017 kg / m3.

95
96