Chapter 29
Nuclear Physics
Milestones in the Development
of Nuclear Physics

1896 – the birth of nuclear physics


Becquerel discovered radioactivity in
uranium compounds
Rutherford showed the radiation had
three types
Alpha (He nucleus)
 Beta (electrons)
 Gamma (high-energy photons)

More Milestones

1911 Rutherford, Geiger and Marsden
performed scattering experiments



Established the point mass nature of the
nucleus
Nuclear force was a new type of force
1919 Rutherford and coworkers first
observed nuclear reactions in which
naturally occurring alpha particles
bombarded nitrogen nuclei to produce
oxygen
Milestones, final





1932 Cockcroft and Walton first used
artificially accelerated protons to produce
nuclear reactions
1932 Chadwick discovered the neutron
1933 the Curies discovered artificial
radioactivity
193 Hahn and Strassman discovered nuclear
fission
1942 Fermi and collaborators achieved the
first controlled nuclear fission reactor
Some Properties of Nuclei

All nuclei are composed of protons and neutrons




Exception is ordinary hydrogen with just a proton
The atomic number, Z, equals the number of
protons in the nucleus
The neutron number, N, is the number of
neutrons in the nucleus
The mass number, A, is the number of nucleons
in the nucleus



A=Z+N
Nucleon is a generic term used to refer to either a
proton or a neutron
The mass number is not the same as the mass
Symbolism
A
Z


X
X is the chemical symbol of the element
Example:

27
13

Al



Mass number is 27
Atomic number is 13
Contains 13 protons
Contains 14 (27 – 13) neutrons
The Z may be omitted since the element
can be used to determine Z
More Properties
The nuclei of all atoms of a particular
element must contain the same number
of protons
 They may contain varying numbers of
neutrons


Isotopes of an element have the same Z
but differing N and A values
14
13
12
 Example: 11
C C C C
6
6
6
6
Charge
The proton has a single positive charge,
+e
 The electron has a single negative
charge, -e
 The neutron has no charge



Makes it difficult to detect
e = 1.60217733 x 10-19 C
Mass

It is convenient to use atomic mass
units, u, to express masses
1 u = 1.660559 x 10-27 kg
 Based on definition that the mass of one
atom of C-12 is exactly 12 u


Mass can also be expressed in MeV/c2
From ER = m c2
 1 u = 931.494 MeV/c2

Summary of Masses
Masses
Particle
kg
u
MeV/c2
Proton
1.6726 x 10-27 1.007276
938.28
Neutron
1.6750 x 10-27 1.008665
939.57
Electron
9.101 x 10-31
5.486x10-4 0.511
The Size of the Nucleus



First investigated by
Rutherford in scattering
experiments
He found an expression for
how close an alpha particle
moving toward the nucleus
can come before being
turned around by the
Coulomb force
The KE of the particle
must be completely
converted to PE
Size of the Nucleus, cont
d gives an upper limit for the size of the
nucleus
 Rutherford determined that

4k e Ze 2
d
mv 2



For gold, he found d = 3.2 x 10-14 m
For silver, he found d = 2 x 10-14 m
Such small lengths are often expressed in
femtometers where 1 fm = 10-15 m

Also called a fermi
Size of Nucleus, Current

Since the time of
Rutherford, many other
experiments have
concluded the following


Most nuclei are
approximately spherical
Average radius is
r  ro A

1
3
ro = 1.2 x 10-15 m
Density of Nuclei
The volume of the nucleus (assumed to
be spherical) is directly proportional to
the total number of nucleons
 This suggests that all nuclei have nearly

the same density

Nucleons combine to form a nucleus as
though they were tightly packed
spheres
Nuclear Stability

There are very large repulsive electrostatic
forces between protons


These forces should cause the nucleus to fly apart
The nuclei are stable because of the presence
of another, short-range force, called the
nuclear force


This is an attractive force that acts between all
nuclear particles
The nuclear attractive force is stronger than the
Coulomb repulsive force at the short ranges within
the nucleus
Nuclear Stability, cont


Light nuclei are most
stable if N = Z
Heavy nuclei are most
stable when N > Z


As the number of protons
increase, the Coulomb
force increases and so
more nucleons are
needed to keep the
nucleus stable
No nuclei are stable
when Z > 83
Binding Energy

The total energy of the bound system
(the nucleus) is less than the combined
energy of the separated nucleons

This difference in energy is called the
binding energy of the nucleus

It can be thought of as the amount of energy
you need to add to the nucleus to break it
apart into separated protons and neutrons
Binding Energy per Nucleon
Binding Energy Notes
Except for light nuclei, the binding energy is
about 8 MeV per nucleon
 The curve peaks in the vicinity of A = 60



Nuclei with mass numbers greater than or less
than 60 are not as strongly bound as those near
the middle of the periodic table
The curve is slowly varying at A > 40


This suggests that the nuclear force saturates
A particular nucleon can interact with only a
limited number of other nucleons
Radioactivity

Radioactivity is the spontaneous
emission of radiation
 Experiments suggested that
radioactivity was the result of the decay,
or disintegration, of unstable nuclei
Radioactivity – Types

Three types of radiation can be emitted

Alpha particles


The particles are 4He nuclei
Beta particles

The particles are either electrons or positrons
– A positron is the antiparticle of the electron
– It is similar to the electron except its charge is +e

Gamma rays

The “rays” are high energy photons
Distinguishing Types of
Radiation
The gamma
particles carry no
charge
 The alpha particles
are deflected
upward
 The beta particles
are deflected
downward


A positron would be
deflected upward
Penetrating Ability of Particles

Alpha particles


Beta particles


Barely penetrate a piece of paper
Can penetrate a few mm of aluminum
Gamma rays

Can penetrate several cm of lead
The Decay Constant

The number of particles that decay in a given
time is proportional to the total number of
particles in a radioactive sample

ΔN = -λ N Δt


λ is called the decay constant and determines the rate
at which the material will decay
The decay rate or activity, R, of a sample is
defined as the number of decays per second
N
R
 N
t
Decay Curve

The decay curve follows
the equation


N = No e- λt
The half-life is also a
useful parameter

The half-life is defined as
the time it takes for half
of any given number of
radioactive nuclei to
decay
T1 2 
ln 2 0.693



Units

The unit of activity, R, is the Curie, Ci


1 Ci = 3.7 x 1010 decays/second
The SI unit of activity is the Becquerel,
Bq

1 Bq = 1 decay / second


Therefore, 1 Ci = 3.7 x 1010 Bq
The most commonly used units of
activity are the mCi and the µCi
QUICK QUIZ 29.1
What fraction of a radioactive sample has
decayed after two half-lives have elapsed?
(a) 1/4
(b) 1/2
(c) 3/4
(d) not enough information to say
QUICK QUIZ 29.1 ANSWER
(c). At the end of the first half-life interval,
half of the original sample has decayed and
half remains. During the second half-life
interval, half of the remaining portion of the
sample decays. The total fraction of the
sample that has decayed during the two halflives is:
1 11 3
  
2 22 4
QUICK QUIZ 29.2
The activity of a newly discovered
radioactive isotope reduces to 96% of its
original value in an interval of 2 hours.
What is its half-life?
(a) 10.2 h
(c) 44.0 h
(b) 34.0 h
(d) 68.6 h
QUICK QUIZ 29.2 ANSWER
(b). If the original activity is R0, the
activity remaining after an elapsed time t
is R = R0e-λt = R0e-(0.693/T1/2)t . Solving for
the half-life yields T1/2 = [0.693/ln(R/R0)]t. If R = 0.96R0 at t = 2.0
hr, the half-life is:
T1/2 = [-0.693/ln(0.96)](2.0 h) = 34 h.
Alpha Decay

When a nucleus emits an alpha particle
it loses two protons and two neutrons
N decreases by 2
 Z decreases by 2
 A decreases by 4


Symbolically X
A
Z
A 4
Z 2
Y He
4
2
X is called the parent nucleus
 Y is called the daughter nucleus

Alpha Decay -- Example

Decay of
226
88



226
Ra
4
Ra222
Rn

86
2 He
Half life for this decay is
1600 years
Excess mass is
converted into kinetic
energy
Momentum of the two
particles is equal and
opposite
Decay – General Rules
When one element changes into another
element, the process is called spontaneous
decay or transmutation
 The sum of the mass numbers, A, must be
the same on both sides of the equation
 The sum of the atomic numbers, Z, must be
the same on both sides of the equation
 Conservation of mass-energy and
conservation of momentum must hold

QUICK QUIZ 29.3
If a nucleus such as 226Ra that is initially at rest
undergoes alpha decay, which of the following
statements is true? (a) The alpha particle has
more kinetic energy than the daughter nucleus.
(b) The daughter nucleus has more kinetic
energy than the alpha particle. (c) The daughter
nucleus and the alpha particle have the same
kinetic energy.
QUICK QUIZ 29.3 ANSWER
(a). Conservation of momentum requires the
momenta of the two fragments be equal in
magnitude and oppositely directed. Thus,
from KE = p2/2m, the lighter alpha particle
has more kinetic energy that the more
massive daughter nucleus.
Beta Decay
During beta decay, the daughter
nucleus has the same number of
nucleons as the parent, but the atomic
number is one less
 Symbolically

A
Z
X Y  e

A
Z
X Y  e

A
Z 1
A
Z 1
Beta Decay, cont

The emission of the electron is from the
nucleus
The nucleus contains protons and neutrons
 The process occurs when a neutron is
transformed into a proton and an electron
 Energy must be conserved

Beta Decay – Electron Energy
The energy released
in the decay process
should almost all go
to kinetic energy of
the electron
 Experiments showed
that few electrons
had this amount of
kinetic energy

Neutrino
To account for this “missing” energy, in 1930
Pauli proposed the existence of another
particle
 Enrico Fermi later named this particle the

neutrino

Properties of the neutrino




Zero electrical charge
Mass much smaller than the electron, probably not
zero
Spin of ½
Very weak interaction with matter
Beta Decay – Completed

Symbolically

XZA1Y  e   
A
Z
X Y  e  
A
Z 1

 is the symbol for the neutrino
is the symbol for the antineutrino
To summarize, in beta decay, the following pairs of
particles are emitted
 An electron and an antineutrino
 A positron and a neutrino


A
Z
Gamma Decay

Gamma rays are given off when an excited
nucleus “falls” to a lower energy state

Similar to the process of electron “jumps” to lower
energy states and giving off photons
The excited nuclear states result from
“jumps” made by a proton or neutron
 The excited nuclear states may be the result
of violent collision or more likely of an alpha
or beta emission

Gamma Decay – Example

Example of a decay sequence




The first decay is a beta emission
The second step is a gamma emission

12
5
B C *  e  
12
6
C*126 C  
12
6
The C* indicates the Carbon nucleus is in an
excited state
Gamma emission doesn’t change either A or Z
Uses of Radioactivity

Carbon Dating



Beta decay of 14C is used to date organic samples
The ratio of 14C to 12C is used
Smoke detectors



Ionization type smoke detectors use a radioactive
source to ionize the air in a chamber
A voltage and current are maintained
When smoke enters the chamber, the current is
decreased and the alarm sounds
More Uses of Radioactivity

Radon pollution
Radon is an inert, gaseous element
associated with the decay of radium
 It is present in uranium mines and in
certain types of rocks, bricks, etc that may
be used in home building
 May also come from the ground itself

Natural Radioactivity

Classification of nuclei

Unstable nuclei found in nature


Nuclei produced in the laboratory through nuclear
reactions


Give rise to natural radioactivity
Exhibit artificial radioactivity
Three series of natural radioactivity exist



Uranium
Actinium
Thorium
Decay Series
of 232Th



Series starts
with 232Th
Processes
through a
series of alpha
and beta
decays
Ends with a
stable isotope
of lead, 208Pb
Nuclear Reactions

Structure of nuclei can be changed by
bombarding them with energetic
particles


The changes are called nuclear reactions
As with nuclear decays, the atomic
numbers and mass numbers must
balance on both sides of the equation
QUICK QUIZ 29.4
Which of the following are possible reactions?
QUICK QUIZ 29.4 ANSWER
(a) and (b). Reactions (a) and (b) both
conserve total charge and total mass number
as required. Reaction (c) violates
conservation of mass number with the sum
of the mass numbers being 240 before
reaction and being only 223 after reaction.
Q Values


Energy must also be conserved in nuclear
reactions
The energy required to balance a nuclear
reaction is called the Q value of the reaction
 An exothermic reaction




There is a mass “loss” in the reaction
There is a release of energy
Q is positive
An endothermic reaction



There is a “gain” of mass in the reaction
Energy is needed, in the form of kinetic energy of the incoming
particles
Q is negative
Threshold Energy

To conserve both momentum and energy,
incoming particles must have a minimum
amount of kinetic energy, called the threshold
energy
KEmin



 m
 1   Q
 M
m is the mass of the incoming particle
M is the mass of the target particle
If the energy is less than this amount, the
reaction cannot occur
QUICK QUIZ 29.5
If the Q value of an endothermic reaction is
-2.17 MeV, the minimum kinetic energy
needed in the reactant nuclei if the reaction
is to occur must be (a) equal to 2.17 MeV,
(b) greater than 2.17 MeV, (c) less than 2.17
MeV, or (d) precisely half of 2.17 MeV.
QUICK QUIZ 29.5 ANSWER
(b). In an endothermic reaction, the
threshold energy exceeds the magnitude
of the Q value by a factor of (1+ m/M),
where m is the mass of the incident
particle and M is the mass of the target
nucleus.
Radiation Damage in Matter
Radiation absorbed by matter can cause
damage
 The degree and type of damage depend on
many factors




Type and energy of the radiation
Properties of the absorbing matter
Radiation damage in biological organisms is
primarily due to ionization effects in cells

Ionization disrupts the normal functioning of the
cell
Types of Damage

Somatic damage is radiation damage to
any cells except reproductive ones
Can lead to cancer at high radiation levels
 Can seriously alter the characteristics of
specific organisms


Genetic damage affects only
reproductive cells

Can lead to defective offspring
Units of Radiation Exposure

Roentgen [R] is defined as
That amount of ionizing radiation that will
produce 2.08 x 109 ion pairs in 1 cm3 of air
under standard conditions
 That amount of radiation that deposits
8.76 x 10-3 J of energy into 1 km3 of air


Rad (Radiation Absorbed Dose)

That amount of radiation that deposits 10-2
J of energy into 1 kg of air
More Units

RBE (Relative Biological Effectiveness)



The number of rad of x-radiation or gamma
radiation that produces the same biological
damage as 1 rad of the radiation being used
Accounts for type of particle which the rad itself
does not
Rem (Roentgen Equivalent in Man)

Defined as the product of the dose in rad and the
RBE factor

Dose in rem = dos in rad X RBE
Radiation Levels

Natural sources – rocks and soil, cosmic rays



Upper limit suggested by US government



Background radiation
About 0.13 rem/yr
0.50 rem/yr
Excludes background and medical exposures
Occupational



5 rem/yr for whole-body radiation
Certain body parts can withstand higher levels
Ingestion or inhalation is most dangerous
Applications of Radiation

Sterilization
Radiation has been used to sterilize
medical equipment
 Used to destroy bacteria, worms and
insects in food
 Bone, cartilage, and skin used in graphs is
often irradiated before grafting

Applications of Radiation, cont

Tracing

Radioactive particles can be used to trace
chemicals participating in various reactions


Example,
131I
to test thyroid action
CAT scans
Computed Axial Tomography
 Produces pictures with greater clarity and
detail than traditional x-rays

Applications of Radiation, final

MRI
Magnetic Resonance Imaging
 When a nucleus having a magnetic
moment is placed in an external magnetic
field, its moment processes about the
magnetic field with a frequency that is
proportional to the field
 Transitions between energy states can be
detected electronically

Radiation Detectors





A Geiger counter is the most
common form of device used
to detect radiation
It uses the ionization of a
medium as the detection
process
When a gamma ray or
particle enters the thin
window, the gas is ionized
The released electrons
trigger a current pulse
The current is detected and
triggers a counter or speaker
Detectors, 2

Semiconductor Diode Detector



A reverse biased p-n junction
As a particle passes through the junction, a brief
pulse of current is created and measured
Scintillation counter



Uses a solid or liquid material whose atoms are
easily excited by radiation
The excited atoms emit visible radiation as they
return to their ground state
With a photomultiplier, the photons can be
converted into an electrical signal
Detectors, 3

Track detectors

Various devices used to view the tracks or paths of
charged particles

Photographic emulsion
– Simplest track detector
– Charged particles ionize the emulsion layer
– When the emulsion is developed, the track becomes visible

Cloud chamber
–
–
–
–
Contains a gas cooled to just below its condensation level
The ions serve as centers for condensation
Particles ionize the gas along their path
Track can be viewed and photographed
Detectors, 4

Track detectors, cont

Bubble Chamber




Contains a liquid near its boiling point
Ions produced by incoming particles leave tracks of
bubbles
The tracks can be photographed
Wire Chamber




Contains thousands of closely spaced parallel wires
The wires collect electrons created by the passing
ionizing particle
A second grid allows the position of the particle to be
determined
Can provide electronic readout to a computer