# Basic Physics of Nuclear Medicine/Atomic & Nuclear Structure

![](Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png "Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png"){width="150"}

You will have encountered much of what we will cover here in your high
school physics. We are going to review this material again below so as
to set the context for subsequent chapters. This chapter will also
provide you with an opportunity to check your understanding of this
topic.

The chapter covers atomic structure, nuclear structure, the
classification of nuclei, binding energy and nuclear stability.

## Atomic Structure

The atom is considered to be the basic building
block of all matter. Simple atomic theory tells us that it consists of
two components: a nucleus surrounded by
an electron cloud. The situation can be
considered as being similar in some respects to planets orbiting the
sun.

From an electrical point of view, the nucleus is said to be positively
charged and the electrons negatively charged.

From a size point of view, the radius of an atom is about 10^-10^ m
while the radius of a nucleus is about 10^-14^ m, i.e. about ten
thousand times smaller. The situation could be viewed as something like
a cricket ball, representing the nucleus, in the middle of a sporting
arena with the electrons orbiting somewhere around where the spectators
would sit. This perspective tells us that the atom should be composed
mainly of empty space. However, the situation is far more complex than
this simple picture portrays in that we must also take into account the
physical forces which bind the atom together.

Chemical phenomena can be thought of as
interactions between the electrons of individual atoms.
Radioactivity on the other hand can be
thought of as changes which occur within the nuclei of atoms.

## The Nucleus

A simple description of the nucleus tells us that it is composed of
protons and neutrons.
These two particle types are collectively called **nucleons**, i.e.
particles which inhabit the nucleus.

From a mass point of view the mass of a proton is roughly equal to the
mass of a neutron and each of these is about 2,000 times the mass of an
electron. So most of the mass of an atom is concentrated in the small
region at its core.

From an electrical point of view the proton is positively charged and
the neutron has no charge. An atom all on its own (if that were possible
to achieve!) is electrically neutral. The number of protons in the
nucleus of such an atom must therefore equal the number of electrons
orbiting that atom.\

## Classification of Nuclei

The term **Atomic Number** is defined in nuclear physics as the number
of protons in a nucleus and is given the symbol **Z**. From your
chemistry you will remember that this number also defines the position
of an element in the Periodic Table of
Elements.

The term **Mass Number** is defined as the number of nucleons in a
nucleus, that is the number of protons plus the number of neutrons, and
is given the symbol **A**.

Note that the symbols here are a bit odd, in that it would prevent some
confusion if the Atomic Number were given the symbol A, and the Mass
Number were given another symbol, such as M, but its not a simple world!

It is possible for nuclei of a given element to have the same number of
protons but differing numbers of neutrons, that is to have the same
Atomic Number but different Mass Numbers. Such nuclei are referred to as
**Isotopes**. All elements have isotopes and the number ranges from
three for hydrogen to over 30 for elements such as caesium and barium.

Chemistry has a relatively simple way of classifying the different
elements by the use of symbols such as H for hydrogen, He for helium and
so on. The classification scheme used to identify different isotopes is
based on this approach with the use of a superscript before the chemical
symbol to denote the Mass Number along with a subscript before the
chemical symbol to denote the Atomic Number. In other words an isotope
is identified as:

```{=html}
<div class="center">
```
${}_{\mathbf{Z}}^{\mathbf{A}}\mathbf{X}$

```{=html}
</div>
```
where X is the chemical symbol of the element; A is the \"Mass Number,\"
(protons+ neutrons); Z is the \"Atomic Number,\" (number identifying the
element on the periodic chart).

Let us take the case of hydrogen as an example.
It has three isotopes:

-   the most common one consisting of a single proton orbited by one
    electron,
-   a second isotope consisting of a nucleus containing a proton and a
    neutron orbited by one electron,
-   a third whose nucleus consists of one proton and two neutrons, again
    orbited by a single electron.

A simple illustration of these isotopes is shown below. Remember though
that this is a simplified illustration given what we noted earlier about
the size of a nucleus compared with that of an atom. But the
illustration is nevertheless useful for showing how isotopes are
classified.

```{=html}
<div class="center">
```
![](NM2_6Ani.gif "NM2_6Ani.gif")

```{=html}
</div>
```
The first isotope commonly called **hydrogen** has a Mass Number of 1,
an Atomic Number of 1 and hence is identified as:

```{=html}
<div class="center">
```
${}_1^1\mathbf{H}$

```{=html}
</div>
```
The second isotope commonly called **deuterium** has a Mass Number of 2,
an Atomic Number of 1 and is identified as:

```{=html}
<div class="center">
```
${}_1^2\mathbf{H}$

```{=html}
</div>
```
The third isotope commonly called **tritium** is identified as:

```{=html}
<div class="center">
```
${}_1^3\mathbf{H}$

```{=html}
</div>
```
The same classification scheme is used for all isotopes. For example,
you should now be able to figure out that the uranium isotope,
${}_{92}^{236}\mathbf{U}$ , contains 92 protons and 144 neutrons.

A final point on classification is that we can also refer to individual
isotopes by giving the name of the element followed by the Mass Number.
For example, we can refer to deuterium as hydrogen-2 and we can refer to
${}_{92}^{236}\mathbf{U}$ as uranium-236.

Before we leave this classification scheme let us further consider the
difference between chemistry and nuclear physics. You will remember that
the water molecule is made up of two hydrogen atoms bonded with an
oxygen atom. Theoretically if we were to combine atoms of hydrogen and
oxygen in this manner many, many of billions of times we could make a
glass of water. We could also make our glass of water using deuterium
instead of hydrogen. This second glass of water would theoretically be
very similar from a chemical perspective. However, from a physics
perspective our second glass would be heavier than the first since each
deuterium nucleus is about twice the mass of each hydrogen nucleus.
Indeed water made in this fashion is called **heavy water**.

## Atomic Mass Unit

The conventional unit of mass, the kilogram, is
rather large for use in describing characteristics of nuclei. For this
reason, a special unit called the Atomic Mass
Unit (amu) is often used. This unit is
sometimes defined as 1/12th of the mass of the stable most commonly
occurring isotope of carbon, i.e. ^12^C. In terms of grams, 1 amu is
equal to 1.66 x 10^-24^ g, that is, just over one million, million,
million millionth of a gram.

The masses of the proton, m~p~ and neutron, m~n~ on this basis are:

```{=html}
<div class="center">
```
m~p~ = 1.00783 amu

```{=html}
</div>
```
and

```{=html}
<div class="center">
```
m~n~ = 1.00866 amu

```{=html}
</div>
```
while that of the electron is just 0.00055 amu.

## Binding Energy

We are now in a position to consider the subject of nuclear stability.
From what we have covered so far, we have seen that the nucleus is a
tiny region in the centre of an atom and that it is composed of
neutrally and positively charged particles. So, in a large nucleus such
as that of uranium (Z=92) we have a large number of positively charged
protons concentrated into a tiny region in the centre of the atom. An
obvious question which arises is that with all these positive charges in
close proximity, why doesn\'t the nucleus fly apart? How can a nucleus
remain as an entity with such electrostatic repulsion between the
components? Should the orbiting negatively-charged electrons not attract
the protons away from the atoms centre?

Let us take the case of the helium-4 nucleus as
an example. This nucleus contains two protons and two neutrons so that
in terms of amu we can figure out from what we covered earlier that the

```{=html}
<div class="center">
```
mass of 2 protons = 2.01566 amu,

```{=html}
</div>
```
and the

```{=html}
<div class="center">
```
mass of 2 neutrons = 2.01732 amu.

```{=html}
</div>
```
Therefore we would expect the total mass of the nucleus to be 4.03298
amu.

The experimentally determined mass of a helium-4 nucleus is a bit less -
just 4.00260 amu. In other words there is a difference of 0.03038 amu
between what we might expect as the mass of this nucleus and what we
actually measure. You might think of this difference as very small at
just 0.75%. But remember that since the mass of one electron is 0.00055
amu the difference is actually equivalent to the mass of about 55
electrons. Therefore it is significant enough to wonder about.

It is possible to consider that this missing mass is converted to energy
which is used to hold the nucleus together; it is converted to a form of
energy called **Binding Energy**. You could say, as with all
relationships, energy must be expended in order to maintain them!

Like the gram in terms of the mass of nuclei, the common unit of energy,
the joule is rather cumbersome when we consider
the energy needed to bind a nucleus together. The unit used to express
energies on the atomic scale is the **electron volt**, symbol: eV.

One electron volt is defined as the amount
of energy gained by an electron as it falls through a potential
difference of one volt. This definition on its own is not of great help
to us here and it is stated purely for the sake of completeness. So do
not worry about it for the time being. Just appreciate that it is a unit
representing a tiny amount of energy which is useful on the atomic
scale. It is a bit too small in the case of binding energies however and
the mega-electron volt (MeV) is often used.

Albert Einstein introduced us to the
equivalence of mass, m, and energy, E, at the atomic level using the
following equation:

```{=html}
<div class="center">
```
E = m c^2^ ,

```{=html}
</div>
```
where c is the velocity of light.

It is possible to show that 1 amu is equivalent to 931.48 MeV.
Therefore, the mass difference we discussed earlier between the expected
and measured mass of the helium-4 nucleus of 0.03038 amu is equivalent
to about 28 MeV. This represents about 7 MeV for each of the four
nucleons contained in the nucleus.

## Nuclear Stability

In most stable isotopes the binding
energy per nucleon lies between 7 and 9
MeV. There are two competing forces in the nuclei, electrostatic
repulsion between protons and the attractive nuclear force between
nucleons (protons and neutrons). The electrostatic force is a long range
force that becomes more difficult to compensate for as more protons are
added to the nucleus. The nuclear force, which arises as the residual
strong force (the strong force binds the quarks together within a
nucleon), is a short range force that only operates on a very short
distance scale (\~ 1.5 fm) as it arises from a Yukawa potential.
(Electromagnetism is a long range force as the force carrier, the
photon, is massless; the nuclear force is a short range force as the
force carrier, the pion, is massive). Therefore, larger nuclei tend to
be less stable, and require a larger ratio of neutrons to protons (which
contribute to the attractive strong force, but not the long-range
electrostatic repulsion). For the low Z nuclides the ratio of neutrons
to protons is approximately 1, though it gradually increases to about
1.5 for the higher Z nuclides as shown below on the **Nuclear Stability
Curve**.

!The nuclear stability
curve.

In other words to combat the effect of the increase in electrostatic
repulsion when the number of protons increases the number of neutrons
must increase more rapidly to contribute sufficient energy to bind the
nucleus together.

As we noted earlier there are a number of isotopes for each element of
the Periodic Table. It has been found that the most stable isotope for
each element has a specific number of neutrons in its nucleus. Plotting
a graph of the number of protons against the number of neutrons for
these stable isotopes generates what is called the **Nuclear Stability
Curve**:

Note that the number of protons equals the number of neutrons for small
nuclei. But notice also that the number of neutrons increases more
rapidly than the number of protons as the size of the nucleus gets
bigger so as to maintain the stability of the nucleus. In other words
more neutrons need to be there to contribute to the binding energy used
to counteract the electrostatic repulsion between the protons.

## Radioactivity

There are about 2,450 known isotopes of the approximately one hundred
elements in the Periodic Table. You can imagine the size of a table of
isotopes relative to that of
the Periodic Table! The unstable isotopes lie above or below the Nuclear
Stability Curve. These unstable isotopes attempt to reach the stability
curve by splitting into fragments, in a process called **Fission**, or
by emitting particles and/or energy in the form of radiation. This
latter process is called **Radioactivity**.

It is useful to dwell for a few moments on the term radioactivity. For
example what has nuclear stability to do with radio? From a historical
perspective remember that when these radiations were discovered about
100 years ago we did not know exactly what we were dealing with. When
people like Henri Becquerel and Marie
Curie were working initially on these strange
emanations from certain natural materials it was thought that the
radiations were somehow related to another phenomenon which also was not
well understood at the time - that of radio communication. It seems
reasonable on this basis to appreciate that some people considered that
the two phenomena were somehow related and hence that the materials
which emitted radiation were termed *radio-active*.

We know today that the two phenomena are not directly related but we
nevertheless hold onto the term radioactivity for historical purposes.
But it should be quite clear to you having reached this stage of this
chapter that the term radioactive refers to the emission of particles
and/or energy from unstable isotopes. Unstable isotopes for instance
those that have too many protons to remain a stable entity are called
**radioactive isotopes** - and called **radioisotopes** for short. The
term **radionuclide** is also sometimes used.

Finally about 300 of the 2,450-odd isotopes mentioned above are found in
nature. The rest are man-made, that is they are produced artificially.
These 2,150 or so artificial isotopes have been made during the last 100
years or so with most having been made since the second world war.

We will return to the production of radioisotopes in a later
chapter
of this wikibook and will proceed for the time being with a description
of the types of radiation emitted by radioisotopes.

## Multiple Choice Questions

Click
`<b>`{=html}here`</b>`{=html}
to access multiple choice questions on atomic and nuclear structure.

## External Links

-   Novel Periodic
    Table - an
    interactive table providing information about each element.
-   Marie and Pierre Curie and the Discovery of Polonium and
    Radium - an
    historical essay from The Nobel Foundation.
-   Natural
    Radioactivity -
    an overview of radioactivity in nature - includes sections on
    primordial radionuclides, cosmic radiation, human produced
    radionuclides, as well as natural radioactivity in soil, in the
    ocean, in the human body and in building materials - from the
    University of Michigan Student Chapter of the Health Physics
    Society.
-   The Particle
    Adventure -
    an interactive tour of the inner workings of the atom which explains
    the modern tools physicists use to probe nuclear and sub-nuclear
    matter and how physicists measure the results of their experiments
    using detectors - from the Particle Data Group at the Lawrence
    Berkeley National Lab, USA and mirrored at CERN, Geneva.
-   WebElements - an excellent web-based
    Periodic Table of the Elements which includes a vast array of data
    about each element - originally from Mark Winter at the University
    of Sheffield, England.

ca:Física bàsica de la medicina nuclear/Estructura atòmica i
nuclear
