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
1938 Hahn and Strassman discovered
nuclear fission
1942 Fermi and collaborators achieved
the first controlled nuclear fission
reactor
Ernest Rutherford




1871 – 1937
Discovery of
atoms being
broken apart
Studied
radioactivity
Nobel prize in
1908
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

Symbol:


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
Example: 11C 13C 13C 14C
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 = 1.602 177 33 x 10-19 C
Mass

It is convenient to use unified mass
units, u, to express masses



1 u = 1.660 559 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/c
2
Proton
1.6726 x 10-27 1.007276
938.28
Neutron 1.6750 x 10-27 1.008665
939.57
Electron 9.109 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
4ke Ze2
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:


Most nuclei are
approximately
spherical
Average radius is
1
3
r  ro A

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
Example 1
Consider the hydrogen atom to be a sphere of radius equal
to the Bohr radius, 0.53 × 10−10 m, and calculate the
approximate value of the ratio of the nuclear density to the
atomic density.
Maria Goeppert-Mayer



1906 – 1972
Best known for
her development
of shell model of
the nucleus
Shared Nobel
Prize in 1963
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
Example 2
Calculate the average binding energy per nucleon of
and
197
79
Au.
93
41
Nb
Marie Curie




1867 – 1934
Discovered new
radioactive
elements
Shared Nobel
Prize in physics in
1903
Nobel Prize in
Chemistry in
1911
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




A radioactive beam is
directed into a region
with a magnetic field
The gamma particles
carry no charge and
they are not deflected
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
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


A
Z
XAZ42Y 42 He
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
Beta Decay


During beta decay, the daughter
nucleus has the same number of
nucleons as the parent, but the
atomic number is changed by one
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 (KEmax)
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ZA1Y  e   
 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 photons are called gamma rays, very high
energy relative to light
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
Example 3
Radon gas has a half-life of 3.83 days. If 3.00 g of radon
gas is present at time t = 0, what mass of radon will
remain after 1.50 days have passed?
Enrico Fermi



1901 – 1954
Produced transuranic
elements
Other contributions




Theory of beta decay
Free-electron theory
of metals
World’s first fission
reactor (1942)
Nobel Prize in 1938
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

See table 29.2
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
Nuclear Reactions –
Example


Alpha particle colliding with
nitrogen:
4
14
1
He

N

X

2
7
1H
Balancing the equation allows for
the identification of X
X

17
8
17
8
X O
So the reaction is
4
14
17
1
2 He  7 N  8 O  1 H
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
m

KEmin  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
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]



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 kg of air
Rad (Radiation Absorbed Dose)

That amount of radiation that deposits 10-2
J of energy into 1 kg of absorbing material
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 = dose 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 to reduce the chances of
infection
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
Example 4
The first known reaction in which the product nucleus was
radioactive (achieved in 1934) was one in which was
bombarded with alpha particles. Produced in the reaction
were a neutron and a product nucleus. (a) What was the
product nucleus? (b) Find the Q value of the reaction.
Example 5
A person whose mass is 75.0 kg is exposed to a wholebody dose of 25.0 rads. How many joules of energy are
deposited in the person’s body?