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22
created
vacancies
orbital
ofNumber
s vacancie
shell
K of
Number
where hv is the energy of the photon and BE is the binding energy of the electron in the
shell (Figure 3). If the photon energy is slightly higher than the binding energy (BE) then
the chance of PEE is high. For example a photon of energy 100 keV has high probability of
undergoing PEE when it interacts with Pb atom for which the K shell binding energy is 88
keV. Rest of the (100-88) 12 keV energy will be carried away by the ejected electron as its
kinetic energy. The ejection of electron creates a hole in the inner shell, which is filled by
an electron from any one of the outer shells. Since the electron in outer shells posses higher
energy than those in the inner shells, the difference in their energy is released as x-ray
photon. The K, L, M, ... shells of a given atom have fixed energy so the difference in their
energies is also fixed and the emitted radiation because of any transition between them is
termed as characteristic x-rays.
Interaction of Radiation with Matter
Figure 3: Process of photoelectric absorption. The incoming photon disappears (absorbed) and
orbital electron is knocked out. Electron from outer shell falls (dotted line) into the inner shell to
fill up the vacancy.
Three types of possibilities exists during photoelectric effect:
(i) Radiative transitions
As has been explained above, during the electron transition from outer orbit to inner
one, a photon is emitted with energy equal to the difference of the binding energies of the
orbits involved. The vacancy moves to a higher shell and consequently a characteristic
photon of lower energy follows. The probability of emission of a photon is expressed as the
fluorescent yield.
emitted photonsray -X ofNumber
Fluorescent yield =
Mostly it is the K-shell that is responsible for fluorescent yield
emitted photonsray -XK ofNumber
K shell fluorescent yield (k) =
Interaction of Radiation with Matter
The fluorescent yield increases with increase in atomic number.
23
(ii) Auger electrons
The characteristic X-ray photon, instead of being emitted out, has a probability to eject
another orbital electron from the atom. These electrons are called Auger electrons (Figure
4). The energy of Auger electron is equal to the difference of the x-ray photon energy and
the binding energy of the shell involved in the process. The process competes with radiative
transition. The Auger yield is expressed as the ratio of electrons emitted due to vacancies in
subshell i and the total number of atoms with a vacancy in subshell i.
Figure 4: Mechanism of Auger electron emission
Coster-Kronig electrons
The process is exactly like Auger transition except that the electron filling the vacancy
comes from the subshell of the same principal shell in which the vacancy lies. The kinetic
energy of the emitted electrons can be calculated exactly as for Auger electrons. The energy
of Coster-Kronig electrons is so small that they are quickly absorbed in the medium.
Summary of Photo Electric Effect
The probability is very high when the photon is just enough energy to eject out
electron from the shell
The process involves bound electrons
Effect is proportional to cube of the atomic number (Z3) and is inversely proportional
to cube of the photon energy (1/E3).
Pair production
When a photon with energy in excess of 1.02 MeV passes close to the nucleus of an
atom, it may disappear and in its place two anti particles (negatron and positron) may be
produced as shown in figure 5. In this process energy converts into mass in accordance with
Einstein mass energy equation (E = m.c2). After traversing some distance through medium,
the positron loses its energy and combines with an electron and annihilates. During
24
Interaction of Radiation with Matter
combination both the antiparticles disappear (annihilation) and two photons of 0.511 MeV
are emitted in opposite direction.
Figure 5: Schematic representation of pair production
Summary of pair production
This involves interaction between photon and the nucleus.
Threshold energy for this process is 1.022MeV and the interaction is proportional to
the energy in excess of 1.022MeV.
The probability of this type of interaction is proportional to the atomic number (Z).
Two annihilated photon each of 0.511MeV are produced per interaction and radiated
from site of interaction in opposite direction.
Photo nuclear reaction
When photon energy is too high, either a neutron or proton may be knocked out (more
likely the neutron) from the nucleus. For majority of atoms the threshold energy for this
effect is about 10 MeV and probability increases with increasing energy till a maximum is
reached above which the probability falls rapidly.
Relative contribution of various types of interactions
When a photon interacts with matter there is probability of all type of interactions
mentioned above provided the photon energy is above the threshold needed for the
interactions. However, depending upon the energy of the photon and type of matter through
which it passes and the chances of a given interaction vary. The relative probability of each
type of interaction is proportional to the cross section for that process. The probability of an
interaction is proportional to the sum of all cross sections (Figure 6).
Interaction of Radiation with Matter
Figure 6: Relative contribution of PEE, Compton scattering and pair production in a NaI(Tl)
detector
25
The total attenuation coefficient, , is thus the sum of the four components:
(total) =(photo) + (elastic) + (Compton) + (pair)
In materials with low atomic number (Z), (elastic) is usually very small and can be
neglected for practical purposes. One can say with certainty that with increase in energy the
sum will decrease initially due to rapid fall in photoelectric effect particularly with high Z
materials. The decrease is slow between 200 keV and 5 MeV due to predominance of
Compton scatter in this range and increase in later part due to pair production. For water,
the total attenuation coefficient is almost constant from 10 to 100 MeV because the decrease
in Compton effect is compensated by increase in pair production. But the same is not true
for high Z materials (e.g. lead), where the total effect increases with energy due to
predominance of pair production.
Further reading
1. Physics in Nuclear Medicine, SR Cherry, JA Sorenson and ME Phelps, 3rd edition, Saunders,
Philadelphia, USA, 2003.
2. Nuclear Physics, DC Tayal, Himalaya Publishing House, Mumbai, 1980.
3. Physics of Radiology, HE. Johns and JR Cunningham, Charles C. Thomas Publisher, 1971.
4. Introductory Physics of Nuclear Medicine, R Chandra, Lea & Febiger Publisher, USA, 1995.
5. Fundamental Physics of Radiology, WJ Meredith and JB Massey, John Wright and Sons Ltd., Bristol,
UK, 1974.
Radioactivity
G.S. Pant and A.K. Shukla
With his experiment with a uranium salt (potassium uranyl sulfate) in 1896 Henry
Becquerel could demonstrate that uranium emits radiation without an external source of
energy. He showed that radiation emitted by uranium shared certain characteristics with
x rays but, unlike x rays, they could be deflected by a magnetic field due to presence of
charged particles. He was awarded the 1903 Nobel Prize for physics for his discovery, which
he shared with Marie Curie and Pierre Curie. Although Henri Becquerel discovered the
phenomenon but Marie Curie coined the term radioactivity.
Marie Curie further investigated the phenomenon of radioactivity. After chemical
extraction of uranium from the ore, she observed that the residual material was more “active”
than the pure uranium. Marie concluded that the ore contained, in addition to uranium, new
elements that were also radioactive and led to their discoveries of the elements of polonium
and radium. In recognition of her services to the advancement of chemistry by the discovery
of the elements radium and polonium she was awarded the 1911 novel prize in chemistry;
thus becoming the first person to receive two Nobel prizes. In her honor, the Radiology
Congress chose the curie as the basic unit of radioactivity: the quantity of radon in equilibrium
with one gram of radium (1 Ci = 3.7 × 1010 dps). A newer unit (SI unit) of activity is the
Becquerel named after Henry Becquerel who is credited with the discovery of radioactivity.
One Becquerel is equal to one disintegration per second. (The SI unit of radioactivity is
Becquerel abbreviated as Bq, 1 Bq=1dps).
In 1898 Ernest Rutherford reported the existence of alpha and beta rays in uranium
radiation and indicated some of their properties. With Frederick Soddy at McGill University,
Montreal, Rutherford showed that elements such as uranium and thorium became different
elements (i.e., transmuted) through the process of radioactive decay. From his experiments
with bombardment of thin gold foil with alpha particles he concluded that the atom’s mass
must be concentrated in a small positively charged nucleus while the electrons inhabit the
farthest reaches of the atom. Although this planetary model of the atom has been greatly
refined over the years, it remains as valid today as when it was originally formulated by
Rutherford. For his extensive work, Rutherford won the 1908 Nobel Prize in chemistry. He
2 6
Radioactivity
27
used the exponential equation to calculate the decay of radioactive substances and was the
first to elucidate the related concepts of the half-life and decay constant.
The nucleus can be regarded as a combination of two fundamental particles neutrons and
protons. These particles are together termed as nucleons. The stability of a nucleus depends
on at least two different forces, the repulsive Coulomb force between any two or more
protons and strong attractive force between any two nucleons (nuclear forces). The nuclear
forces are strong but effective over very short distances whereas the weaker coulomb forces
are effective over much longer distance. The stability of a nucleus depends upon the
arrangement of its nucleons particularly the ratio of the number of neutrons to the number
of protons. To keep a number of protons at a very close distance within the nucleus, the
presence of adequate number of neutrons is essential but the situation is rather complicated.
Amongst the many possible combinations of protons and neutrons only around 260 nuclides
are stable and the rest are unstable.
Figure 1: The line of stability and different regions around it
It seems that there are favoured neutron-to-proton ratios amongst the stable nuclides.
Figure 1 shows the function of number of neutron (N) against the number of proton (Z) for
all available nuclides. The stable nuclides gather around an imaginary line, which is called the
line of stability. For light elements (A<50) this line corresponds to N=Z, but with increasing
atomic number neutron-to-proton ratio increases up to 1.5 (N=1.5Z). The line of stability
ends at A=209 (Bi) and all nuclides above that and those which are not close to this line are
unstable. Nuclides that lie on the left of the line of stability (Area I) have an excess of
neutrons, those lying on the right of the line (Area II) are neutron deficient and those above
the line (Area III) are too heavy (excess of both neutrons and protons) to be stable.
28
n p energy
Radioactivity
An unstable nucleus sooner or later (nanoseconds to thousands of years) changes to a
more stable proton-neutron combination by emitting particle(s) such as alpha (), beta ()
and gamma (). The emission of gamma rays is associated with or emissions. The
phenomenon of spontaneous emission of such particles from the nuclides is called radioactivity
and such nuclides are called radionuclides. The change from the unstable nuclide (parent)
to a more stable nuclide (daughter) is called radioactive decay or disintegration. In some
cases the daughter may also be radioactive and finally decays to a stable nuclide. During
disintegration, there is emission of nuclear particle(s) and release of energy. The process is
spontaneous and cannot be influenced by any external factor. It is also not possible to
predict as to which radioactive atom will disintegrate first.
Radioactivity is a nuclear phenomenon in which no orbital electron participates. Therefore,
the chemical properties of the atom, whether radioactive or non-radioactive, are not expected
to alter. The change, if any, may be so small to be of any consequence in nuclear medicine.
Modes of radioactive decay
Radionuclides normally decay by alpha, beta and gamma emissions. Other processes such as
fission will also be discussed here in brief. The decay of a radionuclide (parent) is actually
an attempt to attain stability. The resulting nuclide after decay of the parent is called
daughter. The daughter nuclide may be stable or unstable. All unstable nuclides (radionuclides)
undergo transformation by any one of the following modes:
Nuclides having excess neutrons
Beta emission
Nuclides having excess number of neutrons (Area I in figure 1) attempt to acquire a stable
form by converting a neutron to proton within the nucleus. In this process – (negatron) and
an antineutrino are emitted. The nuclear equation that explains the process may be given as
follows:
where n, p, , represent the neutron, the proton, the negatron (beta minus) and the
antineutrino respectively. Antineutrino is a particle with no mass and charge produced in
beta decay. The proton stays in the nucleus but the electron and the antineutrino are ejected out
carrying the released energy as their kinetic energy. In this mode of decay, atomic number
of the daughter nuclide increases by one with no change in mass number. The mass of the
neutron is more than the mass of the proton, the electron and the antineutrino combined
together. This difference in mass (mass defect) is converted into energy and randomly shared
by beta particle and antineutrino. The beta particle may have energy between zero to a
certain maximum level. The antineutrino has no mass and charge and has no application in
nuclear medicine.
Radioactivity
, ,
H C P
35
S
I Xe
Co
131
I
P
29
Radionuclides in which the daughter comes to ground or stable state by emitting only
beta particles are called pure beta emitters such as
3 14 32
and
. Those, which cannot
attain a stable state after beta emission and still remain in one of the excited states of the
daughter, emit gamma photon(s) either in a single transition or in cascades to come to
ground state. In such situations more than one gamma photons are emitted per beta emission.
For example,
131 132
,
(a, b) shows beta minus decay with and without gamma photon (e.g.
and
60
emit beta particles followed by gamma emissions. Figure 2
32
and
Figure 2a: Decay scheme of 32P
).
Similarly 14C decays to 14N followed by beta emission
14
C = 14N + –+
Figure 2b : Decay scheme of
131
I
30
p n energy
, ,
C N O
F
p e n
Radioactivity
Nuclides deficient in neutrons
There are two alternatives for such nuclides to come to a stable state:
(a) Positron emission
In this mode of decay a proton transforms to a neutron followed by emission of a
positron and a neutrino
The positron and neutrino share the emitted energy as their kinetic energy. Thus the
spectrum of positron also shows a continuous spectrum like negatron. The positron is the
antiparticle of the electron/negatron. They are very much alike but with opposite charge.
Figure 3 shows the decay mode of beta plus from 11C.
In positron decay, the atomic number of the daughter is decreased by one but the mass
number remains the same. The emitted positron on coming to rest annihilates with an
electron and two photons of 511 keV are emitted in opposite directions in accordance with
law of conservation of momentum. Some of the positron emitting radionuclides (
68
18
,
Ga and 82Rb) are very useful for PET imaging in nuclear medicine.
11 13 15
,
(b) Electron capture
by attracting one of its own orbital electrons (usually k electron) to the nucleus. The electron
combines with the proton producing a neutron and a neutrino in the process.
Figure 3: Decay scheme of 11C
A nucleus with excess number of protons has an alternative way to acquire a stable state
Radioactivity
67 111 123
, ,
Ga In I
125
I
125
I
Nd Sm Hf
,
Li Li
U Th He
Ra Rn He
31
The electron capture is an important phenomenon as it creates a vacancy in the orbit,
which is filled by an electron from outer orbit. The transition of electron from outer to inner
orbit leads to the emission of characteristic x-rays. These photons may either leave the atom
or knock out electrons from the higher orbits. Such electrons are called Auger electrons and
are of low energies and extremely short range in tissue. They are therefore found to be
extremely useful for therapeutic application particularly in targeted therapy.
Electron capture is more likely to occur in heavy elements (electrons more close to the
nucleus) whereas positron emission is more likely in lighter elements. Radionuclides such
as
decay mode of
and
.
decay partially or fully by electron capture. Figure 4 shows the
Figure 4: Decay scheme of
125
I
Nuclides with excess protons and neutrons
There are two ways for this kind of nucleus (region III) to attempt to attain a stable
state.
(a) Alpha decay
Nuclides with excess protons and neutrons try to get rid of the extra mass by emitting an
alpha particle (2 neutrons and 2 protons). The atomic number of the daughter in such decay
is reduced by 2 and mass number by 4. The alpha decay may be followed by gamma
emission to enable the daughter nucleus to come to its ground or stable state. Many isotopes
with atomic number greater than 83 are alpha emitters. However, Some rare earth elements
114 146 174
(
, ,...
) and some light elements (
8 9
etc.) also decay by alpha emission.
Some typical examples of alpha decays are:
235 132 4
92 90 2
226 222 4
88 86 2
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