CENTRE OF APPLIED RADIATION SCIENCES
Introduction to Nuclear Physics
ARSM 611: Nuclear Physics
Lecture: Moyo Elvis
MODULE OUTLINE
1. Basic Concepts
1.1. Terminology
1.2. Units, dimensions and physical constants
1.3. Nuclear Radius
1.4. Nuclear Forces
2. Mass defect and binding energy
2.1. Chart of nuclides
2.2. Mass defect
2.2. Binding energy
3. Radioactive decay
3.1. Alpha decay
3.2. Beta decay
3.3. Gamma decay
3.4. Spontaneous fission
3.5. Branching Ratios
ARSM 611: Nuclear Physics
1.
Basic Concepts
In this chapter we review some notations and basic concepts in Nuclear Physics. The chapter is meant to setup a common
language for the rest of the material we will cover as well as rising questions that we will answer later on.
1.1.Terminology
A given atom is specified by the number of

neutrons: N

protons: Z

electrons: there are Z electron in neutral atoms
Atoms of the same element have same atomic number Z. They are not all equal, however. Isotopes of the same element
have different number of neutrons N.
A
Isotopes are denoted by: ZX
where X is the chemical symbol and A = Z + N is the mass number. E.g.: 235
92U, [the Z number is redundant; thus, it is
often omitted]. When talking of different nuclei, we can refer to them as

Nuclide: atom/nucleus with a specific N and Z.

Isobar: nuclides with same mass number A but different number of protons (Z) and neutrons (N)

Isotone: nuclides with same N, but different number of protons (Z) and different mass (A)

Isotope: Nuclei with the same number of protons (Z), but a different number of neutrons (N) and a different mass (A)
ARSM 611: Nuclear Physics
Example
What is the notation for a nucleus with Z = 30 and N = 32 (i.e.. 30 protons and 32
neutrons)?
• What is the chemical symbol for an element with Z = 30?
ARSM 611: Nuclear Physics
Examples
State the name of the element and the number of protons, electrons, and neutrons in the nuclides
listed below.
Solutions
ARSM 611: Nuclear Physics
1.2. Units, dimensions and physical constants
 Nuclear energies are measured in powers of the unit Electron volts: 1eV = 1.6 × 10−19 J.
Nuclear energies are usually in the range of MeV (mega-electron volt, or 106eV).
 Nuclear masses are measured in terms of the atomic mass unit : 1 amu or 1u =1.66 × 10−27
kg.
Because of the mass-energy equivalence, we will often express masses in terms of energy
units. To convert between energy (in MeV) and mass (in amu) the conversion factor is of course
the speed of light square (since E = mc2). In these units we have: c 2 =931.502 MeV/u.
 Proton mass: 938.280 MeV/c2 .
 Neutron mass: 938.573 MeV/c2 .
 Electron mass: 0.511 MeV/c2 .
Physical constants that we will encounter include:
 speed of light, c = 299, 792, 458 m s−1
 electron charge, e =1.602176487 × 10−19 C
 Planck constant h =6.62606896 × 10−34 J s
 Avogadro’s number Na =6.02214179 × 1023 mol−1
 permittivity of vacuum 𝜖0 =8.854187817 × 10−12 Fm−1 (F=Faraday
ARSM 611: Nuclear Physics
1.3. Nuclear Radius
The radius of a nucleus is not well defined, since we cannot describe a nucleus as a rigid sphere with a given
radius. However, we can still have a practical definition for the range at which the density of the nucleons inside a
nucleus approximate our simple model of a sphere for many experimental situations. A simple formula that links
the nucleus radius to the number of nucleons is the empirical radius formula:
Where:
 R = nuclear radius (m)
 A = nucleon / mass number
 R0 = constant of proportionality ≈1.3 fm
Examples:
1. What is the diameter of an oxygen nucleus(nucleon number 16)? (Answer to 2 d.p. )
ARSM 611: Nuclear Physics
Solutions
1. What is the diameter of an oxygen nucleus(nucleon number 16)? (Answer to 2 d.p. )
𝟏
= (𝟏. 𝟑 × 𝟏𝟎−𝟏𝟓 )(𝟏𝟔)𝟑
= (𝟏. 𝟑 × 𝟏𝟎−𝟏𝟓 )(2.5198)
R = 𝟑. 𝟎𝟐𝟑𝟖 × 𝟏𝟎−𝟏𝟓 𝐦
Diameter = 𝟐 × 𝟑. 𝟎𝟐𝟑𝟖 × 𝟏𝟎−𝟏𝟓 = 𝟔. 𝟎𝟒𝟕𝟔 × 𝟏𝟎−𝟏𝟓 m of 6.0476 fm
ARSM 611: Nuclear Physics
1.4. Nuclear Forces
 Ernest Rutherford postulated that the positive charge in an
atom is concentrated in a small region called a nucleus at the
center of the atom with electrons existing in orbits around it.
 Niels Bohr proposed that the atom consists of a dense nucleus
of protons surrounded by electrons traveling in discrete orbits
at fixed distances from the nucleus.
 When an electron moves from one allowed orbit to another
allowed orbit, the energy difference between the two states is
emitted or absorbed in the form of a single quantum of radiant
energy called a photon
 Emission of a photon that has an energy = hv. (h = Planck's
constant = 6.63 x 10−34 J-s and v = frequency of the photon
Bohr Model of an atom
ARSM 611: Nuclear Physics
Nuclear Forces continues….
Two forces present in the nucleus are:
1) Electrostatic forces between charged particles
2) Gravitational forces between any two objects that have mass
ARSM 611: Nuclear Physics
Nuclear Forces continues….
 If only the electrostatic and gravitational forces existed in the nucleus, then it would be
impossible to have stable nuclei composed of protons and neutrons. Since stable atoms of
neutrons and protons do exist, there must be an other attractive force acting within the nucleus.
This force is called the nuclear force.
 The nuclear force is a strong attractive force that is independent of charge. It acts equally only
between pairs of neutrons, pairs of protons, or a neutron and a proton.
 The nuclear force has a very short range; it acts only over distances approximately equal to the
diameter of the nucleus (10−13 cm).
 The attractive nuclear force between all nucleons drops off with distance much faster than the
repulsive electrostatic force between protons.
ARSM 611: Nuclear Physics
2. Chart of nuclides, Binding energy and Semi-empirical mass formula
Chart of nuclides
 The Chart of the Nuclides is important to understand because it is a common tool used in the
radiation industry.
 The Chart is similar to the periodic table in that it lists all known elements, atomic numbers,
atomic mass, etc. However, it also gives all the different known isotopes for each element.

The Chart is in reality a graph of all the known nuclides graphing number of protons vs. number
of neutrons.
ARSM 611: Nuclear Physics
Chart of nuclides…
 The row numbers are equivalent to the atomic number of the element
 Thus each row, represents a different element
 The column numbers are equivalent to the neutron numbers of the nuclides
ARSM 611: Nuclear Physics
Chart of nuclides…
ARSM 611: Nuclear Physics
Chart of nuclides…
ARSM 611: Nuclear Physics
Chart of nuclides…
 The information given in that box includes..
 The chemical symbol & name of the element
 The atomic mass of the element
 The absorption cross section in the units of Barns (s)
 A Barn is a unit of area which is determined by the diameter of the nucleus.
Stable nuclides are gray colored boxes, they contain…
 The chemical symbol of the element
 The number of nucleons (Protons + Neutrons), which equals the atomic mass
 The % of abundance in nature
 And the capture cross section in Barns (s)
 The plot of all the stable nuclides, called the line of stability, forms a linear plot
~ 45º
ARSM 611: Nuclear Physics
Chart of nuclides…
Half-Life
 Half-life, 𝐭 𝟏 , is the time required for half the atoms of a radioactive nuclide to decay.
𝟐
 Each radioactive nuclide has its own half-life.
 More-stable nuclides decay slowly and have longer half-lives.
ARSM 611: Nuclear Physics
Chart of nuclides…
Half-Lives of Some Radioactive Isotopes
ARSM 611: Nuclear Physics
Chart of nuclides…
 Mode of decay i.e. a - alpha, b - beta, It –Isomeric Transition
 Energy of decay, given in MeV
 g - gamma emission, which is a result of decay
 Gamma energies in KeV
ARSM 611: Nuclear Physics
Chart of nuclides…
 Another type of nuclide shown on the chart are those that undergo isomeric decay.
 Isomeric decay results from a nuclide giving off an alpha or beta and becoming a
 metastable form.
 These atoms will give off energy like a gamma when they de-excite at a later time.
 These are shown on the chart as a box inside a box.
ARSM 611: Nuclear Physics
Chart of nuclides…
 Some radioactive nuclides can undergo what is called “branching” decay
 This means that under some circumstances they can give off one form of radiation, but
 under other circumstances they give off another Example – Copper 64, gives off beta – or beta +
 Both modes of decay will be given in the box on the chart
ARSM 611: Nuclear Physics
Chart of nuclides…
 Using the Chart of the Nuclides we can easily tell what a radioactive isotope changes into after decay.
 By moving from box to box based on whether or not protons or neutrons are lost or gained as a result of
radiation release, we can determine the resulting isotope.
Questions
1. How many nuclides have Z = 12?
2. How many nuclide have A = 94?
3. Is
205
80Hg
4. Does
stable?
237
90Th
exist?
ARSM 611: Nuclear Physics
Chart of nuclides…
Examples
ARSM 611: Nuclear Physics
Chart of nuclides…
Examples…
ARSM 611: Nuclear Physics
Chart of nuclides…
Assignment
 Using this information you can follow radioactive decay until it reaches stability.
 In nature, there are three naturally occurring decay chains.
 They each begin with nuclides that have long enough half-lives that they have been present since the
formation of the Earth.
 As the nuclides in the decay chains release radiation, they change into other nuclides that are also radioactive.
 They continue this process until they reach a stable isotope (usually lead).
1. Write these three naturally radioactive decay chains (30 marks)
2. Write the number of alpha in each series
ARSM 611: Nuclear Physics
Binding energy and mass defect
Mass defect
Mass defect: the difference between the mass of the atom and the sum of the masses of its parts is
called the mass defect. The mass of a particular atom is always slightly less than the sum of the
masses of the individual neutrons, protons, and electrons of which the atom consists..
Where:
ARSM 611: Nuclear Physics
Mass defect…
Example:
 Calculate the mass defect for lithium-7. The mass of lithium-7 is 7.016003 amu
Solution
ARSM 611: Nuclear Physics
Binding energy
 Binding energy is defined as the amount of energy that must be supplied to a nucleus to completely separate
its nuclear particles (nucleons).
 The loss in mass, or mass defect, is due to the conversion of mass to binding energy when the nucleus is
formed.
 It is the amount of energy that would be released if the nucleus was formed from the separate particles.
 Since nuclei are made up of neutrons and protons, there are forces of repulsion between the positive protons.
ARSM 611: Nuclear Physics
Binding energy…
From: E = mc2
Binding energy can be calculated as: 𝐵𝐸 = [ 𝑍𝑚𝑝 + 𝑁𝑚𝑛 − 𝑚 𝐴.𝑋 ]𝐶 2
Example:
Calculate the mass defect and binding energy for uranium-235. One uranium-235 atom has a mass of
235.043924 amu.
Solution
ARSM 611: Nuclear Physics
Binding Energy per Nucleon
 In order to compare nuclear stability, it is more useful to look at the binding energy per nucleon
 The binding energy per nucleon is defined as:
The binding energy of a nucleus divided by the number of nucleons in the nucleus

A higher binding energy per nucleon indicates a higher stability
In other words, it requires more energy to pull the nucleus apart

Iron (A = 56) has the highest binding energy per nucleon, which makes it the most stable of all the elements.
ARSM 611: Nuclear Physics
Mass defect…
Example:
Helpful Constants:
 Mass of a proton: 1.007825 units
 Mass of a neutron: 1.008665 units
 1 amu = 931 MeV
1. Tritium is an isotope of hydrogen. The mass of the tritium isotope, H-3, is 3.0160490 amu.
a. What is the mass defect of this isotope?
b. What is the binding energy of this isotope?
c. Find the binding energy per nucleon.
2.
The mass of a C-12 nucleus is 12.00000 units.
a. What is the mass defect of this nucleus?
b. What is the binding energy of this nucleus?
c. Find the binding energy per nucleon.
ARSM 611: Nuclear Physics
Binding Energy per Nucleon
ARSM 611: Nuclear Physics
Radioactive decay
Atomic theory in the nineteenth century presumed that nuclei had fixed compositions. But in 1896, the French
scientist Henri Becquerel found that a uranium compound placed near a photographic plate made an image on
the plate, even if the compound was wrapped in black cloth. He reasoned that the uranium compound was
emitting some kind of radiation that passed through the cloth to expose the photographic plate. Further
investigations showed that the radiation was a combination of particles and electromagnetic rays, with its ultimate
source being the atomic nucleus. These emanations were ultimately called, collectively, radioactivity.
ARSM 611: Nuclear Physics
Radioactive decay
Following the somewhat serendipitous discovery of radioactivity by Becquerel, many prominent scientists began
to investigate this new, intriguing phenomenon. Among them were Marie Curie (the first woman to win a Nobel
Prize, and the only person to win two Nobel Prizes in different sciences—chemistry and physics), who was the
first to coin the term “radioactivity,” and Ernest Rutherford (of gold foil experiment fame), who investigated and
named three of the most common types of radiation. During the beginning of the twentieth century, many
radioactive substances were discovered, the properties of radiation were investigated and quantified, and a solid
understanding of radiation and nuclear decay was developed.
The spontaneous change of an unstable nuclide into another is radioactive decay. The unstable nuclide is called
the parent nuclide; the nuclide that results from the decay is known as the daughter nuclide. The daughter
nuclide may be stable, or it may decay itself. The radiation produced during radioactive decay is such that the
daughter nuclide lies closer to the band of stability than the parent nuclide, so the location of a nuclide relative to
the band of stability can serve as a guide to the kind of decay it will undergo.
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Alpha Particle (α)
Rutherford’s experiments demonstrated that there are three main forms of radioactive emissions. The first is
called an alpha particle, which is symbolized by the Greek letter α. An alpha particle is composed of two protons
and two neutrons and is the same as a helium nucleus. (We often use 24He to represent an alpha particle.) It has
a 2+ charge. When a radioactive atom emits an alpha particle, the original atom’s atomic number decreases by
two (because of the loss of two protons), and its mass number decreases by four (because of the loss of four
nuclear particles). We can represent the emission of an alpha particle with a chemical equation—for example, the
alpha-particle emission of uranium-235 is as follows:
Rather than calling this equation a chemical equation, we call it a nuclear equation to emphasize that the
change occurs in an atomic nucleus. How do we know that a product of this reaction is 231
90Th? We use the law of
conservation of matter, which says that matter cannot be created or destroyed. This means we must have the
same number of protons and neutrons on both sides of the nuclear equation. If our uranium nucleus loses 2
protons, there are 90 protons remaining, identifying the element as thorium. Moreover, if we lose four nuclear
particles of the original 235, there are 231 remaining. Thus we use subtraction to identify the isotope of the Th
atom—in this case, 231
90Th.
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Beta Particle (β)
The second type of radioactive emission is called a beta particle, which is symbolized by the Greek letter β. A
beta particle is an electron ejected from the nucleus (not from the shells of electrons about the nucleus) and has
a -1 charge. We can also represent a beta particle as -10e. The net effect of beta particle emission on a nucleus is
that a neutron is converted to a proton. The overall mass number stays the same, but because the number of
protons increases by one, the atomic number goes up by one. Carbon-14 decays by emitting a beta particle:
Again, the sum of the atomic numbers is the same on both sides of the equation, as is the sum of the mass
numbers. (Note that the electron is assigned an “atomic number” of –1, equal to its charge.)
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Positron Emission (β+ decay).
In addition to the three major types of radioactive particles listed above, two additional less common types of
emissions have been discovered. These include positron emission and electron capture.
Positron emission (β+ decay) is the emission of a positron from the nucleus. Oxygen-15 is an example of a
nuclide that undergoes positron emission:
Positron emission is observed for nuclides in which the n:p ratio is low. These nuclides lie below the band of
stability. Positron decay is the conversion of a proton into a neutron with the emission of a positron. The n:p ratio
increases, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. The positron
has the mass of an electron, but a positive charge. Thus, the overall mass of the nuclide doesn’t change, but the
atomic number is decreased by one, which causes a change in the elemental identity of the daughter isotope.
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Gamma Radiation (γ)
The third major type of radioactive emission is not a particle but rather a very energetic form of electromagnetic
radiation called gamma rays, symbolized by the Greek letter γ. Electromagnetic radiation can be characterized
into different categories based on the wavelength and photon energies. The electromagnetic spectrum shown in
the figure below shows the major categories of electromagnetic radiation. Note that the human sensory
adaptations of sight and hearing have evolved to detect electromagnetic radiation, with radio waves having
wavelengths between 1 mm and 100 km and visible light having wavelengths between 380 – 700 nm.
Technological advances have helped humankind utilize other forms of electromagnetic radiation including X-rays
and microwaves.
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Gamma Radiation (γ)…
Some electromagnetic radiation with very short wavelengths are active enough that they may knock out electrons out of atoms in a sample
of matter and make it electrically charged. The types of radiation that can do this are termed ionizing radiation. X-rays and Gamma rays are
examples of ionizing radiation. Some radioactive materials, emit gamma radiation during their decay. For example, in the decay of
radioactive technetium-99, a gamma ray is emitted. Note that in radioactive decay where the emission of gamma radiation occurs, that
the identity of the parent material does not change, as no particles are physically emitted.
Sometimes the radioactive decay of a sample can result in the release of multiple forms of radioactivity. For
example, in the radioactive decay of radon-222, both alpha and gamma radiation are emitted, with the latter
having an energy of 8.2 × 10−14 J per nucleus decayed:
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Gamma Radiation (γ)…
Alpha, beta, and gamma emissions have different abilities to penetrate matter. The relatively large alpha particle
is easily stopped by matter (although it may impart a significant amount of energy to the matter it contacts). Beta
particles penetrate slightly into matter, perhaps a few centimeters at most. Gamma rays can penetrate deeply into
matter and can impart a large amount of energy into the surrounding matter. The table below summarizes the
properties of the three main types of radioactive emissions and the figure below summarizes the ability of each
radioactive type to penetrate matter.
The Three Main Forms of Radioactive Emissions
ARSM 611: Nuclear Physics
Major Forms of Radioactivity
Gamma Radiation (γ)
The relative abilities of three different types of ionizing radiation to penetrate solid matter.
ARSM 611: Nuclear Physics
Radioactivity
Electron Capture (k-capture).
Electron capture occurs when one of the inner electrons in an atom is captured by the atom’s nucleus. For
example, potassium-40 undergoes electron capture:
Electron capture occurs when an inner shell electron combines with a proton and is converted into a neutron. The
loss of an inner shell electron leaves a vacancy that will be filled by one of the outer electrons. As the outer
electron drops into the vacancy, it will emit energy. In most cases, the energy emitted will be in the form of an Xray. Like positron emission, electron capture occurs for “proton-rich” nuclei that lie below the band of stability.
Electron capture has the same effect on the nucleus as does positron emission: The atomic number is decreased
by one and the mass number does not change. This increases the n:p ratio, and the daughter nuclide lies closer
to the band of stability than did the parent nuclide. Whether electron capture or positron emission occurs is
difficult to predict. The choice is primarily due to kinetic factors, with the one requiring the smaller activation
energy being the one more likely to occur.
ARSM 611: Nuclear Physics
Radioactivity
These types of decay, along with their equations and changes in atomic and mass numbers.
ARSM 611: Nuclear Physics
Radioactivity
Nuclear Fission
Occasionally, an atomic nucleus breaks apart into smaller pieces in a radioactive process called spontaneous
fission (or fission). Typically, the daughter isotopes produced by fission are a varied mix of products, rather than a
specific isotope as with alpha and beta particle emission. Often, fission produces excess neutrons that will
sometimes be captured by other nuclei, possibly inducing additional radioactive events. Uranium-235 undergoes
spontaneous fission to a small extent. One typical reaction is:
where 10n is a neutron. As with any nuclear process, the sums of the atomic numbers and mass numbers must
be the same on both sides of the equation. Spontaneous fission is found only in large nuclei. The smallest
nucleus that exhibits spontaneous fission is lead-208. (Fission is the radioactive process used in nuclear power
plants and one type of nuclear bomb).
ARSM 611: Nuclear Physics
Multiple choice
ARSM 611: Nuclear Physics
.
ARSM 611: Nuclear Physics
Radioactivity
Activity
 The activity (A) of a sample is the rate of decay of that sample.
 This rate of decay is usually measured in the number of disintegrations that occur per second.
 The activity is the product of the decay constant and the number of atoms present in the sample
ARSM 611: Nuclear Physics
Radioactivity
Units of Measurement for Radioactivity
 Two common units to measure the activity of a substance are the curie (Ci) and becquerel (Bq).
 A curie is a unit of measure of the rate of radioactive decay equal to 3.7 x 1010 disintegrations per second.
 This is approximately equivalent to the number of disintegrations that one gram of radium-226 will undergo in
one second.
 A becquerel is a more fundamental unit of measure of radioactive decay that is equal to 1 disintegration per
second
 1 curie = 3.7 x 1010 becquerels (Bq)
Variation of Radioactivity Over Time
Derive an expression which can be used to calculate how the number of atoms present will change over time
ARSM 611: Nuclear Physics
Radioactivity
Variation of Radioactivity Over Time
 Activity and the number of atoms are always proportional.
ARSM 611: Nuclear Physics
Radioactivity
Radioactive half-life
The radioactive half-life is the amount of time required for the activity to decrease to one-half of its original value.
The half-life can be calculated by solving Equation below for the time, t, when the current activity, A, equals onehalf the initial activity 𝐴0 .