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.
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
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
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.
22.
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.
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
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.