# Basic Physics of Nuclear Medicine/Radioactive Decay

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We saw in the last
chapter
that radioactivity is a process used by unstable nuclei to achieve a
more stable situation. It is said that such nuclei *decay* in an attempt
to achieve stability. So, an alternative title for this chapter is
**Nuclear Decay Processes**.

We also saw in the previous chapter that we can use the Nuclear
Stability Curve as a means of describing what is going on. So a second
alternative title for this chapter is **Methods of Getting onto the
Nuclear Stability Curve**.

We are going to follow a descriptive or phenomenological approach to the
topic here by describing in a fairly simple fashion what is known about
each of the major decay mechanisms. Once again you may have already
covered this material in high school physics. But bear with us because
the treatment here will help us set the scene for subsequent chapters.

## Methods of Radioactive Decay

Rather than considering what happens to individual nuclei it is perhaps
easier to consider a hypothetical nucleus that can undergo many of the
major forms of radioactive decay. This hypothetical nucleus is shown
below:

!A hypothetical nucleus which can undergo many forms of radioactive
decay.{width="320"}

Firstly we can see two protons and two neutrons being emitted together
in a process called **alpha-decay**. Secondly, we can see that a proton
can release a positron in a process called **beta-plus decay**, and that
a neutron can emit an electron in a process called **beta-minus decay**.
We can also see an electron being captured by a proton. Thirdly we can
see some energy (a photon) being emitted which results from a process
called **gamma-decay** as well as an electron being attracted into the
nucleus and being ejected again. Finally there is the rather
catastrophic process where the nucleus cracks in half called
**spontaneous fission**.

We will now describe each of these decay processes in turn.

## Spontaneous Fission

This is a very destructive process which occurs in some heavy nuclei
which split into 2 or 3 fragments plus some neutrons. These fragments
form new nuclei which are usually radioactive. Nuclear
reactors exploit this phenomenon for the
production of radioisotopes. Its also used for nuclear power generation
and in nuclear weaponry. The process is not of great interest to us here
and we will say no more about it for the time being.

## Alpha Decay

In this decay process two protons and two neutrons leave the nucleus
together in an assembly known as an **alpha particle**. Note that an
alpha particle is really a helium-4
nucleus.

So why not call it a helium nucleus? Why give it another name? The
answer to this question lies in the history of the discovery of
radioactivity. At the time when these radiations were discovered we
didn\'t know what they really were. We found out that one type of these
radiations had a double positive charge and it was not until sometime
later that we learned that they were in fact nuclei of helium-4. In the
initial period of their discovery this form of radiation was given the
name alpha rays (and the other two were called beta and gamma rays),
these terms being the first three letters of the Greek alphabet. We
still call this form of radiation by the name **alpha particle** for
historical purposes. Calling it by this name also contributes to the
specific jargon of the field and leads outsiders to think that the
subject is quite specialized!

But notice that the radiation really consists of a helium-4 nucleus
emitted from an unstable larger nucleus. There is nothing strange about
helium since it is quite an abundant element on our planet. So why is
this radiation dangerous to humans? The answer to this question lies
with the energy with which they are emitted and the fact that they are
quite massive and have a double positive charge. So when they interact
with living matter they can cause substantial destruction to molecules
which they encounter in their attempt to slow down and to attract two
electrons to become a neutral helium atom.

An example of this form of decay occurs in the
uranium-238 nucleus. The equation which
represents what occurs is:

```{=html}
<div style="text-align:center;">
```
${}_{\mathbf{92}}^{\mathbf{238}}\mathbf{U}$ →
${}_{\mathbf{90}}^{\mathbf{234}}\mathbf{Th}$

`+ `${}_{\mathbf{2}}^{\mathbf{4}}\mathbf{He}$

```{=html}
</div>
```
Here the uranium-238 nucleus emits a helium-4 nucleus (the alpha
particle) and the parent nucleus becomes thorium-234. Note that the Mass
Number of the parent nucleus has been reduced by 4 and the Atomic Number
is reduced by 2 which is a characteristic of alpha decay for any nucleus
in which it occurs.

## Beta Decay

There are three common forms of beta decay:

**(a) Electron Emission**

:   Certain nuclei which have an excess of neutrons may attempt to reach
    stability by converting a neutron into a proton with the emission of
    an electron. The electron is called a **beta-minus particle** -- the
    minus indicating that the particle is negatively charged.

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```

:   We can represent what occurs as follows:

```{=html}
<div class="center">
```
n^0^ → p^+^ + e^-^

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</div>
```

:   where a neutron converts into a proton and an electron. Notice that
    the total electrical charge is the same on both sides of this
    equation. We say that the electric charge is
    conserved.

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```

:   We can consider that the electron cannot exist inside the nucleus
    and therefore is ejected.

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```

:   Once again there is nothing strange or mysterious about an electron.
    What is important though from a radiation safety point of view is
    the energy with which it is emitted and the chemical damage it can
    cause when it interacts with living matter.

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```

:   An example of this type of decay occurs in the
    iodine-131 nucleus which decays into xenon-131
    with the emission of an electron, that is

```{=html}
<div class="center">
```
${}_{\mathbf{53}}^{\mathbf{131}}\mathbf{I}$

`→ `${}_{\mathbf{54}}^{\mathbf{131}}\mathbf{Xe}$` + `${}_{\mathbf{-1}}^{\mathbf{0}}\mathbf{e}$

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

:   The electron is what is called a beta-minus particle. Note that the
    Mass Number in the above equation remains the same and that the
    Atomic Number increases by 1 which is characteristic of this type of
    decay.

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```

:   You may be wondering how an electron can be produced inside a
    nucleus given that the simple atomic description we gave in the
    previous chapter indicated that the nucleus consists of protons and
    neutrons only. This is one of the limitations of the simple
    treatment presented so far and can be explained by considering that
    the two particles which we call protons and neutrons are themselves
    formed of smaller particles called **quarks**. We are not going to
    consider these in any way here other than to note that some
    combinations of different types of quark
    produce protons and another combination produces neutrons. The
    message here is to appreciate that a simple picture is the best way
    to start in an introductory text such as this and that the real
    situation is a lot more complex than what has been described. The
    same can be said about the treatment of beta-decay given above as we
    will see in subsequent chapters.

**(b) Positron Emission**

:   When the number of protons in a nucleus is too large for the nucleus
    to be stable it may attempt to reach stability by converting a
    proton into a neutron with the emission of a positively-charged
    electron.

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```

:   That is not a typographical error! An electron with a positive
    charge also called a **positron** is emitted. The positron is the
    **beta-plus particle**.

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```

:   The history here is quite interesting. A brilliant Italian
    physicist, Enrico Fermi developed a
    theory of beta decay and his theory predicted that
    positively-charged as well as negatively-charged electrons could be
    emitted by unstable nuclei. These particles could be called pieces
    of anti-matter and they were
    subsequently discovered by experiment. They do not exist for very
    long as they quickly combine with a normal electron and the
    subsequent reaction called **annihilation** gives rise to the
    emission of two gamma rays.

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:   Science fiction writers had a great time following the discovery of
    anti-matter and speculated along with many scientists that parts of
    our universe may contain negatively-charged protons forming nuclei
    which are orbited by positively-charged electrons. But this is
    taking us too far away from the topic at hand!

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```

:   The reaction in our unstable nucleus which contains one too many
    protons can be represented as follows:

```{=html}
<div class="center">
```
p^+^ → n^0^ + e^+^

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

:   Notice, once again, that electric charge is conserved on each side
    of this equation.

```{=html}
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```

:   An example of this type of decay occurs in
    sodium-22 which decays into neon-22 with the
    emission of a positron:

```{=html}
<div class="center">
```
${}_{\mathbf{11}}^{\mathbf{22}}\mathbf{Na}$ →
${}_{\mathbf{10}}^{\mathbf{22}}\mathbf{Ne}$ +
${}_{\mathbf{+1}}^{\mathbf{0}}\mathbf{e}$

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

:   Note that the Mass Number remains the same and that the Atomic
    Number decreases by 1.

**(c) Electron Capture**

:   In this third form of beta decay an inner orbiting electron is
    attracted into an unstable nucleus where it combines with a proton
    to form a neutron. The reaction can be represented as:

```{=html}
<div class="center">
```
e^-^ + p^+^ → n^0^

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

:   This process is also known as **K-capture** since the electron is
    often attracted from the K-shell of the atom.

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```

:   How do we know that a process like this occurs given that no
    radiation is emitted? In other words the event occurs within the
    atom itself and no information about it leaves the atom. Or does it?
    The signature of this type of decay can be obtained from effects in
    the electron cloud surrounding the nucleus when the vacant site left
    in the K-shell is filled by an electron from an outer shell. The
    filling of the vacancy is associated with the emission of an
    X-ray from the electron cloud and it is
    this X-ray which provides a signature for this type of beta decay.

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```

:   This form of decay can also be recognised by the emission of
    gamma-rays from the new nucleus.

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```

:   An example of this type of radioactive decay occurs in
    iron-55 which decays into manganese-55
    following the capture of an electron. The reaction can be
    represented as follows:

```{=html}
<div class="center">
```
${}_{\mathbf{26}}^{\mathbf{55}}\mathbf{Fe}$ +
${}_{\mathbf{-1}}^{\mathbf{0}}\mathbf{e}$ →
${}_{\mathbf{25}}^{\mathbf{55}}\mathbf{Mn}$

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

:   Note that the Mass Number once again is unchanged in this form of
    decay and that the Atomic Number is decreased by 1.

## Gamma Decay

Gamma decay involves the emission of energy from an unstable nucleus in
the form of electromagnetic radiation.

You should remember from your high school physics that electromagnetic
radiation is the biggest
physical phenomenon we have so far discovered. The radiation can be
characterised in terms of its frequency, its wavelength and its energy.
Thinking about it in terms of the energy of the radiation we have very
low energy electromagnetic radiation called **radio waves**, **infra-red
radiation** at a slightly higher energy, **visible light** at a higher
energy still, then **ultra-violet radiation** and the higher energy
forms of this radiation are called **X-rays** and **gamma-rays**. You
should also remember that these radiations form what is called the
Electromagnetic Spectrum.

```{=html}
<div class="center">
```
![](NM3_11.gif "NM3_11.gif")

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```
Before proceeding it is useful to pause for a moment to consider the
difference between X-rays and gamma-rays. These two forms of radiation
are high energy electromagnetic rays and are therefore virtually the
same. The difference between them is not **what** they consist of but
**where** they come from. In general we can say that if the radiation
emerges from a nucleus it is called a gamma-ray and if it emerges from
outside the nucleus from the electron cloud for example, it is called an
X-ray.

One final point is of relevance before we consider the different forms
of gamma-decay and that is what such a high energy ray really is. It has
been found in experiments that gamma-rays (and X-rays for that matter!)
sometimes manifest themselves as waves and other times as particles.
This wave-particle duality can be
explained using the equivalence of mass and energy at the atomic level.
When we describe a gamma ray as a wave it has been found useful to use
terms such as frequency and wavelength just like any other wave. In
addition when we describe a gamma ray as a particle we use terms such as
mass and electric charge. Furthermore the term electromagnetic
photon is used for these particles. The
interesting feature about these photons however is that they have
neither mass nor charge!

There are two common forms of gamma decay:

**(a) Isomeric Transition**

:   A nucleus in an excited state may reach its ground or unexcited
    state by the emission of a gamma-ray.

```{=html}
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```

:   An example of this type of decay is that of
    technetium-99m -- which by the way is the
    most common radioisotope used for diagnostic purposes today in
    medicine. The reaction can be expressed as:

```{=html}
<div class="center">
```
${}_{\mathbf{43}}^{\mathbf{99m}}\mathbf{Tc}$ →
${}_{\mathbf{43}}^{\mathbf{99}}\mathbf{Tc}$ +
`<b>`{=html}`<big>`{=html}$\gamma$`</big>`{=html}`</b>`{=html}

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

:   Here a nucleus of technetium-99 is in an excited state, that is, it
    has excess energy. The excited state in this case is called a
    **metastable state** and the nucleus is therefore called
    technetium-99m (m for metastable). The excited nucleus looses its
    excess energy by emitting a gamma-ray to become technetium-99.

**(b) Internal Conversion**

:   Here the excess energy of an excited nucleus is given to an atomic
    electron, e.g. a K-shell electron.

## Decay Schemes

Decay schemes are widely used to give a
visual representation of radioactive decay. A scheme for a relatively
straight-forward decay is shown below:

![](NM3_12.gif){width="150"}

This scheme is for hydrogen-3 which decays to helium-3 with a half-life
of 12.3 years through the emission of a beta-minus particle with an
energy of 0.0057 MeV.

A scheme for a more complicated decay is that of caesium-137.

![](NM3_13.gif){width="150"}

This isotope can decay through through two beta-minus processes. In one
which occurs in 5% of disintegrations a beta-minus particle is emitted
with an energy of 1.17 MeV to produce barium-137. In the second which
occurs more frequently (in the remaining 95% of disintegrations) a
beta-minus particle of energy 0.51 MeV is emitted to produce barium-137m
-- in other words a barium-137 nucleus in a metastable state. The
barium-137m then decays via isomeric transition with the emission of a
gamma-ray of energy 0.662 MeV.

![](NM3_14.gif)

The general method used for decay schemes is illustrated in the diagram
on the right.

The energy is plotted on the vertical axis and atomic number on the
horizontal axis -- although these axes are rarely displayed in actual
schemes. The isotope from which the scheme originates is displayed at
the top -- X in the case above. This isotope is referred to as the
**parent**. The parent loses energy when it decays and hence the
products of the decay referred to as **daughters** are plotted at a
lower energy level.

The diagram illustrates the situation for common forms of radioactive
decay. Alpha-decay is illustrated on the left where the mass number is
reduced by 4 and the atomic number is reduced by 2 to produce daughter
**A**. To its right the scheme for beta-plus decay is shown to produce
daughter **B**. The situation for beta-minus decay followed by
gamma-decay is shown on the right side of the diagram where daughters
**C** and **D** respectively are produced.

## Multiple Choice Questions

Click
`<b>`{=html}here`</b>`{=html}
to access multiple choice questions on radioactive decay.

## External links

-   Basics about
    Radiation --
    overview of the different types of ionising radiation from the
    Radiation Effects Research Foundation -- a cooperative Japan-United
    States Research Organization which conducts research for peaceful
    purposes.
-   Radiation and Life
    -- from the World Nuclear Association website.
-   Radiation and
    Radioactivity
    -- a self-paced lesson developed by the University of Michigan\'s
    Student Chapter of the Health Physics Society, with sections on
    radiation, radioactivity, the atom, alpha radiation, beta radiation
    and gamma radiation.

