Alpha particles are nuclei of Helium atoms, consisting of two protons and two neutrons.

1. ENTC 4390
MEDICAL IMAGING
RADIOACTIVE DECAY

2. Nuclear Particles & Radiation
 Only a few of the many different nuclear
emanations are used in medicine.
 In order of importance, the entities are:
• x-rays
• Electromagnetic waves of very short wavelength that
behave in many ways like particles.
• Gamma (γ) rays
• Electromagnetic waves similar to x-rays, but of even
shorter wavelength.
• Neutrons
• Actual particles that are produced during the decay of
certain radioacitve materials.

3. Radioactivity
Don’t be confused by
this picture!
A single radioactive
source does not emit
all three types α, β
and γ.

4. 3 Types of Radioactivity
B field
into
screen
Radioactive detector
sources
α particles: helium nuclei Easily Stopped
β particles: electrons Stopped by metal
γ : photons (more energetic than x-rays) penetrate!

5.  The nucleus of an atom consists of
neutrons and protons, referred to
collectively as nucleons.
 In a popular model of the nucleus (the
“shell model”), the neutrons and protons
reside in specific levels with different
binding energies.

6. Materials Science Fundamentals
1. The structure of an atom:

7. Materials Science Fundamentals
2. Elements/Atomic Number (Z) & Atomic
Masses
Key: Chemical Behavior Determined by Z
and Ionization

8. Materials Science Fundamentals
 Atomic Number: # of Protons
 Mass Number: # of Protons and
Neutrons
 Atomic Weight: Total Mass of Atom

9.  If a vacancy exists at a lower energy level, a
neutron or proton in a higher level may fall to fill
the vacancy
• This transition releases energy and yields a more
stable nucleus.
• The amount of energy released is related to the
difference in binding energy between the higher and
lower levels.
• The binding energy is much greater for neutrons and
protons inside the nucleus than for electrons outside the
nucleus.
• Hence, energy released during nuclear transitions is much
greater than that released during electron transitions.

10.  If a nucleus gains stability by transition of a neutron
between neutron energy levels, or a proton between
proton energy levels, the process is termed an isometric
transition.
• In an isomeric transition, the nucleus releases energy
without a change in its number of protons (Z) or neutrons
(N).
• The initial and final energy states of the nucleus are said to be
isomers.
• A common form of isomeric transition is gamma decay (γ) in
which the energy is released as a packet of energy (a quantum
or photon) termed a gamma (γ) ray
• An isomeric transition that competes with gamma decay is
internal conversion, in which an electron from an extranuclear
shell carries the energy out of the atom.

11.  It is also possible for a neutron to fall to a lower
energy level reserved for protons, in which
case the neutron becomes a proton.
 It is also possible for a proton to fall to a lower
energy level reserved for neurons, in which
case the proton becomes a neuron.
• In these situations, referred to collectively as beta (β)
decay, the Z and N of the nucleus change, and the
nucleus transmutes from one element to another.
• In beta (β) decay, the nucleus loses energy and gains
stability.

12.  In any radioactive process the mass
number of the decaying (parent) nucleus
equals the sum of the mass numbers of
the product (progeny) nucleus and the
ejected particle.
• That is, mass number A is conserved in
radioactive decay

13.  In alpha (α) decay, an alpha particle (two
protons and two neutrons tightly bound
4
as a nucleus of helium 2 He ) is ejected
from the unstable nucleus.
• The alpha particle is a relatively massive,
poorly penetrating type of radiation that can
be stopped by a sheet of paper.

14.  An example of alpha decay is:
226
88 Ra→ 222Rn+ 2 He
86
4
Radium Radon alpha particle

15. ENTC 4390
MEDICAL IMAGING
DECAY SCHEMES

16. A decay scheme depicts the decay
processes specific for a nuclide (nuclide
is a generic term for any nuclear form).
• Energy on the y axis, plotted against the
• Atomic number of the nuclide on the x axis.

17. A
 Given a generic nuclide, X there are four
Z
possible routes of radioactive decay.
1. A−4
α decay to the progeny nuclide Z −2 P by emission of
4
a 2 He nucleus.
2. (a) β+ (positron) decay to progeny nuclide Z −AQ by
1
emission of positive electron from the nucleus.
3. A
(b) β− (negatron) decay to progeny nuclide by Z +1 R
emission of negative electron from the nucleus.
4. γ decay reshuffles the nucleons releasing a packet of
energy with no change in Z (or N or A).

18. A
Z X
A− 4

Z −2 P 
A
 Z +1 R
Energy
A
Z −1Q 
A
Z +1 S
Z-2 Z-1 Z Z+1 Z+2
Atomic Number

19. ENTC 4390
BETA DECAY

20.  Nucleitend to be most stable if they
contain even numbers of protons and
neutrons and least stable if they contain
an odd number of both.
• Nuclei are extraordinarily stable if they contain
2, 8 ,14, 20, 28, 50, 82, or 126 protons.
• These are termed nuclear magic numbers and
• Reflect full occupancy of nuclear shells.

21.  The number of neutrons is about equal
to the number of protons in low-Z stable
nuclei.
• As Z increases, the number of neutrons
increases more rapidly than the number of
protons in stable nuclei.

23. •Can get 4 nucleons in each
energy level-
•lowest energy will favor N=Z,
•But protons repel one another
(Coulomb Force) and when Z is
large it becomes harder to put
more protons into a nucleus
without adding even more
neutrons to provide more of the
Strong Force.
•For this reason, in heavier
nuclei N>Z.

24. ENTC 4390
ISOMERIC TRANSITIONS

25.  Isomeric transitions are always preceded
by either electron capture or emission of
an α or β (+ or -) particle.
 Sometimes one or more of the excited
states of a progeny nuclide may exist for
a finite lifetime.
• An excited state is termed a metastable state
if its half-life exceeds 10-6 seconds.

26.  An isometric transition can also occur by
interaction of the nucleus with an electron in
one of the electron shells.
• This process is called internal conversion.
• The electron is ejected with kinetic energy E equal to
k
the energy Eγ released by the nucleus, reduced by the
binding energy Eb of the electron
• The ejected electron is accompanied by x rays and
Auger electrons as the extranuclear structure of the
atom resumes a stable configuration.

27.  The rate of decay of a radioactive
sample depends on the number N of
radioactive atoms in the sample.
• This concept can be stated as
∆N
= −λN
∆t
• where ∆N/∆t is the rate of decay, and the constant
λ is called the decay constant.

28.  The decay constant has units of time .
 It has a characteristic value for each nuclide.
 It also reflects the nuclides degree of
instability;
• a larger decay constant connotes a more unstable
nuclide
• i.e., one that decays more rapidly.
• The rate of decay is a measure of a sample’s activity.

29.  Theactivity of a sample depends on the
number of radioactive atoms in the
sample and the decay constant of the
atoms.
• A sample may have a high activity because it
contains a few highly unstable (large decay
constant) atoms, or
• because it contains many atoms that are only
moderately unstable (small decay constant).

30.  The SI unit of activity is the becquerel
(Bq.) defined as
• 1 Bq = 1 disintegration per second (dps)
 Anolder, less-preferred unit of activity is
the curie (Ci), defined as
• 1 Ci = 3.7 x 10 10
dps

31. Example
a. 201Tl has a decay constant of 9.49 x 10-3 hr -1. Find
81
the activity in becquerels of a sample containing 1010
atoms.
∆N 9.49 × 10 −3 atoms
Activity ( A) = − = λN = × 1010 atoms = 9.49 × 107
∆t hr hr
7 atoms 1 hr 4 atoms
A = 9.49 × 10 × = 2.64 × 10
hr 3600 sec sec
A = 2.64 × 10 4 Bq

32. Example
b. How many atoms of 11C with a decay constant of
6
2.08 hr -1 would be required to obtain the same activity
in the previous problem.
atoms atoms sec
2.64 × 10 4 2.64 × 10 4 × 3600
A sec = sec hr
N= =
λ 2.08 / hr 2.08 / hr
N = 4.57 × 107 atoms
• More atoms of 11C than of 201Tl are required to obtain
6 81
the same activity because of the difference in decay
constants.

33.  Note that the equation
∆N
= −λN
∆t
• can be written as
dN
= −λN
dt

34.  Rearranging and solving for N,
dN
= −λdt
N
∫ ∫
natural log format dN
= ln N = − λdt = −λt
N
e ln N = e − λt
N = N o e − λt
• where No is the number of atoms at time to .

35.  The physical half-life, T1/2, of a radioactive nuclide is
the time required for decay of half of the atoms in a
sample of the nuclide.
N = N o e − λt
N 1 − λT 1 / 2
T 1 / 2⇒ = =e
No 2
1
ln 
 2  =T = 0.693
1/ 2
−λ λ

36. Example
 The half-life is 1.7 hours for 113mIn
(Indium).
a. A sample of In has a mass of 2µg.
113m

37. ENTC 4390
MEDICAL IMAGING
DECAY SCHEMES

38. X-Rays
 Strong or high energy x-rays can
penetrate deeply into the body.
 Weak or soft x-rays are used if only
limited penetration is needed
 The energy of x-rays, as well as other
nuclear particles is measured in
• electron-volts (ev)
• thousands of electron-volts (kev)
• millions of electron-volts (Mev)

39.  The diagnostic use of x-ray depends on
the fact that various types of absorbs x-
rays to a greater or lesser degree.
• Absorption by bone is quite high,
• Absorption by fatty tissue is low.
 Thisallows the use of the x-ray beam for
delineating the details of body structure.

40. Gamma Rays
 X-rays are generally produced
electrically.
 γ_rays are the result of a radioactive
transition in a substance that has been
activated in a nuclear reactor.
 Once again, energy is measured in
• electron-volts (ev)
• thousands of electron-volts (kev)
• millions of electron-volts (Mev)

41. higher energy γ-rays penetrate all
 The
human tissue quite easily.
 γ-rays are used in conjunction with scanning
systems to detect anomalies due to disease or
neoplastic growth.

42. Neutrons
 Neutron applications in medicine are
limited.
 Again, energy is measured in
• electron-volts (ev)
• thousands of electron-volts (kev)
• millions of electron-volts (Mev)

43. Preflight - Gamma Ray Emission
Gamma rays are emitted due to electrons
making transitions to nuclear energy levels.
• true
• false
No, gamma rays are high energy photons
emitted when nucleons make transitions
between their allowed quantum states.

44. Beta rays are produced when the atom spontaneously
Preflight - Nuclear Beta Decay
repels all its electrons from its orbits.
• true
• false
Beta particles are electrons. However, the atom does
not emit its atomic electrons.
Beta electrons are emitted by a nucleus along with a
neutral weakly interacting particle called the neutrino
when one of the neutrons in the nucleus decays.
Free neutrons are unstable - they decay.
Sometimes in atoms with large numbers
p + -
υ
n → e of neutrons, one of its neutrons may be
loosely bound - spontaneous decay!

45. Preflight - Positrons
Beta particles are:
• Always negatively charged.
• Always positively charged.
• Some beta decays could produce positively
charged particles with properties similar to
those of electrons.
Some radioactive elements emit a positively
charged particle which is in all other respects
similar to an electron! Anti-matter!! Positrons!!!

46. Preflight - Alpha Particles
Alpha particles are:
• Electrons
• Protons.
• Nuclei of Helium atoms
• nuclei of Argon of protons and many more
Some Nuclei have lots atoms
protons. Lowest energy bound-states require about
equal numbers of protons and neutrons. Those
nuclei emit most tightly bound nuclear matter, i.e.,
Helium nuclei with two protons and two nuclei.