Chapter 3: Modern Physic
Ch 3-2 Radioactivity
Chapter 3-2: Radioactivity
3-2-1 Introduction
At the end of the last century a phenomenon was noted which provided considerable
knowledge about the constitution of atoms. Becquerel discovered while working with uranium
salts that they emitted particles or radiation which could affect photographic plates.
Investigation showed that this was true of all uranium salts of whatever type, and it was
therefore clear that this was a property of the uranium atoms and not of another
constituent of the salt. Rutherford and others began an extensive investigation of the
phenomenon, the main lines of research being into (a) what sort of particles were being
emitted, and (b) what sort of laws the emission mechanism obeyed.
3-2-2 The Nature of Radioactive Emissions
As regards the first line of investigation, it was found that the emanations must
consist of three different types, the first being easily absorbed, the second rather less
easily absorbed, and the third scarcely absorbed at all. If electric and magnetic fields
were applied to the emissions, the easily absorbed constituent deflected in such a way as to
show that it consisted of positively charged particles. The slightly less easily absorbed
emanation deflected in such a way as to show that it consisted of negatively charged
particles, and the remaining emanation was unaffected by such fields. The positively
charged particles were called -particles and the negative ones -particles; and the
undeflected emanation, probably radiation, was called rays. The negatively charged
particles were obviously very light on the evidence of the ease with which they were
scattered and the extent of their deflection in an electric field. Their (e/m) value was
found to be identical with that of the electron, and it was therefore clear that -particles
and electrons were the same thing.
In a famous experiments Rutherford established beyond doubt the identity of these
particles.
Particles and radiation are quite differently absorbed in passage through matter. A particle
can lose its energy gradually, but a single ray, X-ray, or photon must normally lose all of
its energy in one event. The laws of absorption of particles and of radiation are therefore
quite different. The way in which -rays were absorbed was characteristic of radiation. The
frequency of the -rays is in general found to be higher than that for X-rays, although the
two types of radiation slightly overlap in frequency. The difference between X-rays and -
CHAPTER 3: Modern Physics
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rays is that the former is emitted from the electronic parts of an atom, the latter from
the nucleus.
The particles and radiation emitted by the radioactive isotopes can be detected by a
number of instruments. The most usual instruments employed in biological and medical fields
are ionization, Geiger and scintillation counters. The scintillation detector is briefly
described in the following section to provide the reader with some knowledge of how
counters work.
3-2-3 Scintillation Detectors.
There are substances that emit a flash of light following the deposition of
energy in them by the passage of a fast charged particle. These substances are known as
scintillators and may be liquid, crystalline, or plastic.
Scintillators are all characterized by the possession of atomic or molecular optical
levels that are excited by the Coulomb fields of passing charged particles. The optical
levels are usually supplied by a trace impurity of a special salt dissolved in an otherwise
highly purified medium. Sodium iodide crystals containing a trace of thallium are very
common. Because of the high atomic number of the iodine, they are quite sensitive to 
radiation, which ejects fast photoelectrons from the iodine atom.
The amount of light emitted by the scintillators when a particle passes through it is
very small and is usually far below the level that may be detected by the human eye or a
photographic plate. For this reason, the light is collected by reflection from the interior
of the crystal mirrored wall and allowed to fall on the faces of highly sensitive
phototubes. In this tube, weak light pulses fall onto a sensitive photo-cathode, which
then emits a few electrons into the interior of the tube. These electrons are then
accelerated in a high electrical field and fall onto a second electrode, where they 'splash'
out more electrons. This larger group is then accelerated in turn to fall onto a third
electrode to "splash" out yet more electrons. This cascade sequence is made to proceed
through as many as 12 or 14 stages until the original charge produced by the light, is
multiplied by 109 or more. The resulting current from the tube produces a voltage pulse
that is easily measured and that can be made proportional to the amount of light
collected and to the energy deposited by the charged particle in the scintillators.
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Figure 3-2-1 is a scintillation detector in conjunction with a photo-multiplier tube.
Incoming charged particles or  rays produce a flash at the crystal. Then, by the
photoelectric effect, an electron in the photo-cathode is released. More electrons are
produced by secondary emission, until the effect of the single electron has been
multiplied many times. The accelerating potential between two consecutive electrodes is
about 100 V. The amplified signal is finally collected and detected by a sensitive
electronic circuit. A recorder, multi-channel analyzer, then monitors the voltage pulse.
Figure 3-2-2 Scintillation detector used with a photo-multiplier tube.
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3-2-4 Gamma camera
The basic design of the most common type of gamma camera
used today was developed by an American physicist, Hal Anger
and is therefore sometimes called the Anger Camera. It consists
of a large diameter NaI (Tl) scintillation crystal which is viewed
by a large number of photomultiplier tubes.
Free reading
3-2-5 The Laws of Radioactive Decay
On the second line of investigation mentioned in the introductory section, the law
obeyed by the emitted radiation was not at first easy to discover.
Once it had been discovered what types of particle were being emitted from radioactive
elements, the picture was easier to see. An atom of element X, which has an atomic mass
number A, the nearest whole number to its mass in a.m.u., and an atomic number Z, the
number of positive charges on its nucleus or the number of electrons it possesses, is
denoted by the symbol AXZ. If it emits an particle, it turns into an atom A-4YZ-2. Similarly,
an atom A`PZ` on emitting a particle will become an atom of A`QZ`+1. Thus if 238U92 emits a
-particle, it turns into an atom of atomic mass 234 and atomic number 90. If this atom is
also radioactive, as it is, and emits a  particle, it becomes element 91. This particular
isotope of element 91, which has a mass of 234, is also radioactive and emits a -particle.
The element now formed is an isotope of uranium of mass 234. It also is radioactive
emitting -particle, and so on. When the radioactivity from natural uranium is being
investigated, what is in fact being examined is a complex radioactive emission from a whole
chain of radioactive elements. This obviously makes the task of finding the law of
radioactive emission almost impossible, since, while some elements are decaying and their
radioactivity is consequently decreasing, other elements are being formed and this
radioactivity is increasing. However, if the uranium isotope of mass 234 is separated
chemically from a uranium mixture and its products are continually removed, it is found to
emit -particles only and the -activity is found to decay exponentially. In fact if any
radioactive element is chemically separated out and the products formed by the action of
its radioactivity are continually removed, it is always found that the activity decays
exponentially.
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Fig 3-2-3 The activity of a radioactive isotope as a function of time
(a) Shows the exponential decay of , and (b) the linear decay of ln 
If the activity  of a radioactive element is defined as the number of particles
emitted per second, then the decay curve of any radioactive substance is as shown in Fig 4.
The number of atoms remaining of the element at any time is
N(t)=Noe-
3-2-1
where N0 is the number of atoms originally present and  is the decay constant.
Alternatively, one may say that the number of atoms decaying per second, which is the same
as the activity, is proportional to the number of atoms present at any time.
For, from Eq.(3-1)

dN
 e-t = N (t)
dt
3-2-2
the constant of proportionality being the decay constant. Since the number of atoms
present decreases exponentially with time, so does the activity.
On the other time, the number of nuclei that have already decayed in time t is given
by
No-N(t)= No( 1- e-t )
3-2-3
Since the number of atoms decaying at any time depends only on the number present at
that time, being unaffected by pressure, temperature, or any other physical property, it is
clear that the atoms of the radioactive element are unstable and decay spontaneously owing
to this instability. The process is therefore a purely statistical one. One cannot predict
which radioactive element will decay at any given time, but over any period one can predict
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with considerable accuracy the number of atoms that will decay.
It is often preferable to work not with the decay constant but with the half-life of
the radioactive substance, this being the time it takes for the number of atoms, or the
activity, to reduce to half of the initial value, thus
1
2
No = No e-
-life period. Thus
2= e or
It follows that

ln 2= 
ln 2
fig 3-2-4


The half-life period is independent of the initial number of atoms, or the initial
activity. If a sample contains N0 atoms, it takes a time for this number to be reduced to
1
1
1
1
N0 and then a further time  for a further reduction to
of N0, i.e. to N0, and so
2
2
2
4
on. The constant s also the time for the activity to reduce by one-half.

Any radio element obeys the above laws and emits one or other but not generally both
of the possible particles. It may, in addition, emit radiation. The instability of the atom will
determine which of the particles it emits. Normally, when a particle is emitted from a
parent atom, the daughter atom formed is in its minimum possible energy state. It is,
however, possible for the particle to be emitted with less than the maximum possible
available kinetic energy, the rest of the energy being retained by the daughter, which is
then said to be in an excited state. Since atoms prefer to exist in the state of lowest
possible energy, the daughter atom gets rid of its excess energy fairly quickly by emitting
it in the form of -radiation. Experiment has shown that this is the true explanation of the
origin of -rays, because -radiation is always emitted after a particle and always from the
daughter atom.
It is now possible to produce radioactive substances artificially. By bombarding
elements with fast charged particles from accelerating machines or with neutrons in a
nuclear reactor, radioactive isotopes of any known element can be produced. These artificial
radioisotopes are of much greater use in medicine, biology, and industry than the naturally
occurring ones, as we shall see in some of the following sections.
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Note that the half-life does not express how long a material will remain radioactive but
simply the length of time for its radioactivity to halve. Examples of the half lives of some
radioisotopes are given in the following table. Notice that some of these have a relatively
short half life. These tend to be the ones used for medical diagnostic purposes because
they do not remain radioactive for very long following administration to a patient and hence
result in a relatively low radiation dose
Radioisotope Half Life (approx.)
Element
81m
Kr
131
I
137
Cs
226
Ra
Half life
13 seconds
8 days
30 years
1620 years
Element
99m
Tc
Cr
241
Am
238
U
51
Half life
6 hours
1 month
462 years
4.51 x 109 years
Solved problems
Question 1
(a) The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope
remain?
(b) Verify your answer by another means.
Answer:
(a) Starting with the relationship we established earlier between the Decay Constant and
the Half Life we can calculate the Decay Constant as follows:
Now applying the Radioactive Decay Law,
we can re-write it in the form:
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The question tells us that N0 has reduced to 1/16th of its value, that is:
Therefore
which we need to solve for t. One way of doing this is as follows:
So it will take 24 hours until 1/16th of the radioactivity remains.
(b) A way in which this answer can be verified is by using the definition of Half Life. We
are told that the Half Life of 99mTc is 6 hours. Therefore after six hours half of the
radioactivity remains.
Therefore after 12 hours a quarter remains; after 18 hours an eighth remains and after
24 hours one sixteenth remains. And we arrive at the same answer as in part (a). So we
must be right!
Note that this second approach is useful if we are dealing with relatively simple
situations where the radioactivity is halved, quartered and so on. But supposing the
question asked how long would it take for the radioactivity to decrease to a tenth of its
initial value. Deduction from the definition of half life is rather more difficult in this
case and the mathematical approach used for part (a) above will yield the answer more
readily.
Question 2 Find the radioactivity of a 1 g sample of
Avogadro's number: 6.023 x 1023.
226
Ra given that t1/2: 1620 years and
Answer:
We can start the answer like we did with Question 1(a) by calculating the Decay Constant
from the Half Life using the following equation:
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Note that the length of a year used in converting from 'per year' to 'per second' above
is 365.25 days to account for leap years. In addition the reason for converting to units of
'per second' is because the unit of radioactivity is expressed as the number of nuclei
decaying per second.
Secondly we can calculate that 1 g of
226
Ra contains:
Thirdly we need to express the Radioactive Decay Law in terms of the number of nuclei
decaying per unit time. We can do this by differentiating the equation as follows:
The reason for expressing the result above in absolute terms is to remove the minus sign
in that we already know that the number is decreasing.
We can now enter the data we derived above for λ and N:
So the radioactivity of our 1 g sample of radium-226 is approximately 1 Ci. This is not a
surprising answer since the definition of the curie was originally conceived as the
radioactivity of 1 g of radium-226!
Question 3
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What is the minimum mass of 99mTc that can have a radioactivity of 1 MBq? Assume the
half-life is 6 hours and that Avogadro's number is 6.023 x 1023.
Answer
Starting again with the relationship between the Decay Constant and the Half Life:
Secondly the question tells us that the radioactivity is 1 MBq. Therefore since 1 MBq = 1
x 106 decays per second,
Finally the mass of these nuclei can be calculated as follows:
In other words a mass of just over five pictograms of 99mTc can emit one million gammarays per second. The result reinforces an important point that you will learn about
radiation protection which is that you should treat radioactive materials just like you
would handle pathogenic bacteria.
Question 4
A sample of C14, whose half life is 5730 years, has a decay rate of 14 disintegration per
minute (dpm) per gram of natural C14. An artifact is found to have radioactivity of 4 d pm
per gram of its present C, how old is the artifact?
Using the above equation, we have:
Where:
years
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3-2-6 Production of Radioisotopes
Most of the radioisotopes found in nature have relatively long half lives. They also belong
to elements which are not handled well by the human body. As a result medical
applications generally require the use of radioisotopes which are produced artificially.
The type of radioisotope of value to nuclear medicine imaging should have characteristics
which keep the radiation dose to the patient as low as possible. For this reason they
generally have a short half life and emit only gamma-rays - that is no alpha-particle or
beta-particle emissions. From an energy point of view the gamma-ray energy should not
be so low that the radiation gets completely absorbed before emerging from the
patient's body and not too high that it is difficult to detect. For this reason most of the
radioisotopes used emit gamma-rays of medium energy that is between about 100 and
200 keV. Finally since the radioisotope needs to be incorporated into some form of
radiopharmaceutical it should also be capable of being produced in a form which is
amenable to chemical, pharmaceutical and sterile processing.
The production methods we will consider are nuclear fission, nuclear bombardment and
the radioisotope generator. The radioisotope is discussed in the following subsection.
3-2-7 Radioisotope Generator
This method is widely used to produce certain short-lived radioisotopes in a
hospital or clinic. It involves obtaining a relatively long-lived radioisotope
which decays into the short-lived isotope of interest.
A good example is 99mTc which as we have noted before is the most widely
used radioisotope in nuclear medicine today. This isotope has a half-life of six
hours which is rather short if we wish to have it delivered directly from a
nuclear facility. Instead the nuclear facility supplies the isotope 99Mo which
decays into 99mTc with a half life of about 2.75 days. The 99Mo is called the
parent isotope and 99mTc is called the daughter isotope.
So the nuclear facility produces the parent isotope which decays relatively
slowly into the daughter isotope and the daughter is separated chemically from the
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parent at the hospital/clinic. The chemical separation device is called, in this example, a
99m
Tc Generator: Shown in the figure.
It consists of a ceramic column with 99Mo adsorbed onto its top surface. A solution called
an eluent is passed through the column, reacts chemically with any 99mTc and emerges in a
chemical form which is suitable for combining with a pharmaceutical to produce a
radiopharmaceutical. The arrangement shown in the figure above is called a Positive
Pressure system where the eluent is forced through the ceramic column by a pressure,
slightly above atmospheric pressure, in the eluent vial.
The ceramic column and collection vials need to be surrounded by lead shielding for
radiation protection purposes. In addition all components are produced and need to be
maintained in a sterile condition since the collected solution will be administered to
patients.
Finally an Isotope Calibrator is needed when a 99mTc Generator is used to determine the
radioactivity for preparation of patient doses and to check whether any 99Mo is present
in the collected solution.
3-2-8 The Absorption of -Rays and X-Rays
The photons of a beam of radiation are removed from that beam by either absorption
or scattering, according to a random law. As was seen in chapter 3, this means that the form
of the law is
= e-x
3-2-5
where I0 and I are the initial and final intensities of a beam of radiation which passes
through a thickness x of absorber, and is the absorption coefficient. This law is as true for
X- and -rays as it is for light, although, of course,  depends on somewhat different factors.
We implied above that the Linear Attenuation Coefficient was useful when we were
considering an absorbing material of the same density but of different thicknesses. A
related coefficient can be of value when we wish to include the density, ρ, of the absorber in
our analysis. This is the Mass Attenuation Coefficient which is defined as the:
The main processes by which X- and -rays are absorbed are the photoelectric effect and
the Compton Effect. In the first of these processes, a photon is completely annihilated, part
of its energy being used to free an electron from an atom or molecule, the rest being given to
the freed electron in the form of kinetic energy. In the second process a photon is scattered
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by an effectively free electron, continuing with less energy, the difference having been given
to the electron in the form of energy of recoil.
The photoelectric effect is greatest for low-energy photons and increases very
rapidly with atomic number. The Compton Effect, on the other hand, does not vary much with
the energy of the photons and is only directly proportional to the atomic number. In
biological materials, for photon energies of 0.3 MeV and over, the Compton Effect is the
predominant effect. It should of course be pointed out that the degraded radiation
scattered in this effect tends to be absorbed fairly rapidly owing to the photoelectric
effect.
For photon energies in excess of 1 MeV a third effect becomes important,
which is called pair production. The photon is annihilated and its energy is used in
creating a pair of positive and negative electrons. Part of the energy is used to create
the two particles, the rest being distributed between them in the form of kinetic energy,
Fig 4. In biological materials, where the atomic number is generally low, the effect is not
very marked.
Figure 3-2-5 The absorption of -rays in different media
Question 5
The linear absorption coefficient for K and K radiation of silver are 155 cm-1 and 661
cm-1 when palladium is used as an absorber. What thickness of palladium foil reduces the
intensity of the Kradiation to one-tenth of its incident value? What is then the
percentage reduction to the intensity of the K radiation?
Solution. If the K radiation is to be reduced to one-tenth of its incident value, the
thickness required is
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 I  2.303  I 0 
ln  0  
log  
 I 

I 
2.303

log( 10)
155cm 1
 0.0149cm.
x
1
For the K radiation for this thickness of absorber,
ln( I 0' I ')  x  661cm 1  0.0149cm  9.82
therefore
log( I 0' / I ' )  9.82 / 2.303  4.264,
therefore
( I 0' / I ' )  1.84  10 4 ,
therefore
I 0'  I '
 100  99.995.
I 0'
The percentage reduction in the intensity of the Kradiation is 99.995%.
3-2-9 Radiation Units
Units of measure and exposure
In order to specify the amount of radioactivity contained in a sample and the amount of
radiation absorbed by an object, we make use of two units-the curie (Ci) and the rad. A
curie of radioactivity represents exactly 3.7 x 1010 decay events per second (regardless
of the type or energy of the radiation).
A clinical source of 60Co might contain several kilocuries (1 kCi= 103 Ci) , whereas a
millicurie (1 mCi = 10-3 Ci) of some radioisotope might be administered for internal
radiotherapy
The measure of X-rays ionizing ability is called the exposure:

The coulomb per kilogram (C/kg) is the SI unit of ionizing radiation exposure, and
it is the amount of radiation required to create one coulomb of charge of each
polarity in one kilogram of matter.
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The roentgen (R) is an obsolete traditional unit of exposure, which represented
the amount of radiation required to create one electrostatic unit of charge of each
polarity in one cubic centimeter of dry air. 1.00 roentgen = 2.58×10−4 C/kg
However, the effect of ionizing radiation on matter (especially living tissue) is more
closely related to the amount of energy deposited into them rather than the charge
generated. This measure of energy absorbed is called the absorbed dose:

Radiation exposure is measured in terms of a unit called the rad, which stands for
radiation absorbed dose. If 1 kg of material absorbs 0.01 J of radiation energy,
the dose is said to be 1 rad:
rad = 0.01 J/kg
3-2-6
1

The gray (Gy), which has units of (Joules/kilogram), is the SI unit of absorbed
dose, and it is the amount of radiation required to deposit one joule of energy in
one kilogram of any kind of matter.
1.00 gray =100 rad = 1J/kg
3-2-7
The equivalent dose is the measure of the biological effect of radiation on human
tissue. For X-rays it is equal to the absorbed dose.

The sievert (Sv) is the SI unit of equivalent dose, which for X-rays is numerically
equal to the gray (Gy).

The Roentgen equivalent man (rem) is the traditional unit of equivalent dose. For Xrays it is equal to the rad or 10 millijoules of energy deposited per kilogram. 1.00
Sv = 100 rem.
Reported dosage due to dental X-rays seems to vary significantly. Depending on the
source, a typical dental X-ray of a human results in an exposure of perhaps, 3, 40,
300, or as many as 900 mrems (30 to 9,000 μSv).
A person standing at a distance of 1 m from a 1-Ci source of 60Co for one hour
would receive a dose of approximately 1.2 rad at the front surface of his or her
body and a dose of about half this amount at a depth of 10 cm (because of the
attenuation of the radiation in the body). It is important to remember that the rad
is a measure of the absorbed radiation dose per kilogram.
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3-2-10 Radiation Exposures
The biological effect of radiation depends not only on the absorbed dose in rads
but on several other factors as well. These factors include the LET value of the
radiation, the rad distribution within the tissue, as well as certain biological and
chemical variables. It has therefore become standard practice to specify the
biological damage produced by radiation in terms of a dose equivalent measured in
rem:
Dose equivalent in rem = (absorbed dose in rad) x QF
3-2-8
where QF is the quality factor of the particular radiation. When a 5-MeV 
particle deposits its energy in a dense ionization track through a section of tissue,
it does considerably more damage to the tissue than when a number of electrons
deposit the same amount of energy in the tissue. Thus, we say that the quality
factor of particles is much greater than that for electrons. QF values can only be
approximate because the effectiveness of a particular radiation in producing
biological damage depends on many variables. Some working values for the quality
factors for different radiations are listed in the following table.
_______________________________
Radiation
QF(approximate)
_______________________________
X or  ray
1
Electron ( particles)
1
 particles
20
Protons
10
Fast neutrons (~MeV)
10
Slow neutrons (~eV)
5
_______________________________
Thus, if a person receives a 0.2-rad dose of particles, the exposure is
measured as (0.2 rad) x (20) = 4 rem. If the exposure is entirely to X a radiation or
electrons, the dose equivalent in rem is equal to the dose in rad.
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Question 6
. A source emits  - radiation and even when shielded the dose rate is 0.15 rad h-1 at a
distance of 1 m. if the maximum permissible dose rate is 6.25 millirad h -1, how close to
the shielded source may a scientific worker approach?
Solution. The intensity of the radiation falls off at least as rapidly as the square
distance from the source because of the normal geometrical factors involved. We wish to
find the distance r at which the dose rate will have fallen to the permissible, and we can
therefore say that, at the worst,
0.15 rad h-1  1/(1 m)2
6.25 x 10-3rad h-1  1/r2
Therefore
r2
0.15

 24,
2
(1m)
6.25  10 3
Therefore
r = 4.9 m.
Question 7
How much aluminum is required to reduce the intensity of a 200 keV gamma-ray beam to
10% of its incident intensity? Assume that the Half Value Layer for 200 keV gamma-rays
in Al is 2.14 cm.
Answer
The question phrased in terms of the symbols used above is:
,
when x = ?
We are told that the Half Value Layer is 2.14 cm. Therefore the Linear Attenuation
Coefficient is
Now combining all this with the exponential attenuation equation:
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we can write:
Therefore
So the thickness of aluminum required to reduce these gamma-rays by a factor of ten is
about 7 cm. This relatively large thickness is the reason why aluminum is not generally
used in radiation protection - its atomic number is not high enough for efficient and
significant attenuation of gamma-rays. You might like to try this question for the case
when Pb is the absorber - but you will need to find out the Half Value Layer for the 200
keV gamma-rays yourself!
Here's a hint though: have a look at one of the tables above.
And here's the answer for you to check when you've finished: 2.2 mm.
In other words a relatively thin thickness of Pb is required to do the same job as 7 cm of
aluminium.
Question 8
A 105 MBq source of 137Cs is to be contained in a Pb box so that the exposure rate 1 m
away from the source is less than 0.5 mR/hour. If the Half Value Layer for 137Cs gammarays in Pb is 0.6 cm, what thickness of Pb is required? The Specific Gamma Ray Constant
for 137Cs is 3.3 R hr-1 mCi-1 at 1 cm.
Answer
This is a fairly typical question which arises when someone is using radioactive materials.
We wish to use a certain quantity of the material and we wish to store it in a lead
container so that the exposure rate when we are working a certain distance away is below
some level for safety reasons. We know the radioactivity of the material we will be using.
But its quoted in SI units. We look up a reference book to find out the exposure rate for
this radioisotope and find that the Specific Gamma Ray Constant is quoted in traditional
units. Just as in our question!
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So let us start by getting our units right. The Specific Gamma Ray Constant is given as:
3.3 R hr-1 mCi-1 at 1 cm from the source.
This is equal to:
3300 mR hr-1 mCi-1 at 1 cm from the source,
which is equal to:
mR hr-1 mCi-1 at 1 m from the source,
on the basis of the Inverse Square Law. This result expressed per becquerel is
mR hr-1 (Bq-1 at 1 m ) from the source,
since 1 mCi = 3.7 x 107 Bq. And therefore for 105 MBq, the exposure rate is:
mR hr-1 (105MBq)-1 at 1 m from the source,
That is the exposure rate 1 meter from our source is 891.9 mR hr-1.
We wish to reduce this exposure rate according to the question to less than 0.5 mR hr -1
using Pb. You should be able at this stage to use the exponential attenuation equation
along with the Half Value Layer for these gamma-rays in Pb to calculate that the
thickness of Pb required is about 6.5 cm.
3-2-11 Radiations Hazards and Protection
3-2-11-a Radiation Biology
It is well known that exposure to ionizing radiation can result in damage to living tissue.
We've already described the initial atomic interactions. What's important in radiation
biology is that these interactions may trigger complex chains of bimolecular events and
consequent biological damage.
We've seen above that the primary means by which ionizing radiations lose their energy
in matter is by ejection of orbital electrons. The loss of orbital electrons from the atom
leaves it positively charged. Other interaction processes lead to excitation of the atom
rather than ionization. Here, an outer valence electron receives sufficient energy to
overcome the binding energy of its shell and moves further away from the nucleus to an
orbit that is not normally occupied. This type of effect alters the chemical force that
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binds atoms into molecules and a regrouping of the affected atoms into different
molecular structures can result. That is, excitation is an indirect method of inducing
chemical change through the modification of individual atomic bonds.
Ionizations and excitations can give rise to unstable chemical species called free radicals.
These are atoms and molecules in which there are unpaired electrons. They are chemically
very reactive and seek stability by bonding with other atoms and molecules. Changes to
nearby molecules can arise because of their production.
In the case of X- and gamma-ray interactions, the energy of the photons is usually
transferred by collisions with orbital electrons, e.g. via photoelectric and Compton
effects. These radiations are capable of penetrating deeply into tissue since their
interactions depend on chance collisions with electrons. Indeed, nuclear medicine imaging
is only possible when the energy of the gamma-rays is sufficient for complete emission
from the body, but low enough to be detected.
The interaction of charged particles (e.g. alpha
and beta particles), on the other hand, can be
by collisions with atomic electrons and also via
attractive and repulsive electrostatic forces.
The rate at which energy is lost along the track
of a charged particle depends therefore on the
square of the charge on that particle. That is,
the greater the particle charge, the greater
the probability of it generating ion pairs along
its track. In addition, a longer period of time is
available for electrostatic forces to act when a
charged particle is moving slowly and the ionization probability is therefore increased as
a result.
The situation is illustrated in the following figure where tracks of charged particles in
water are depicted. Notice that the track of the relatively massive α-particle is a
straight line, as we've discussed earlier in this chapter, with a large number of
interactions (indicated by the asterisks) per unit length. Notice also that the tracks for
electrons are tortuous, as we've also discussed earlier, and that the number of
interactions per unit length is considerably less.
It is clear that exposure to ionizing particles or radiation is very harmful to all living
organisms and, in particular, to human beings. Many of the earliest pioneers in these fields
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suffered serious injury to their skins and this drew attention to the problem. It was soon
found that other cells of the body could be destroyed and that gene mutations could be
produced. High doses of radiation can produce cancer with latent period of up to 20 years,
though the most serious risk appears to be leukemia, which normally appears within a few
years after irradiation. The gene mutations produced are generally detrimental and, since
most of them are recessive, the effect may not be observed until the mutant genes have
been distributed throughout a large population.
The population is subjected to radiation from naturally occurring sources, the main
agents being cosmic rays, natural radioactive materials in the soil and rocks, and small
amounts of radioisotopes, principally 40K, found in the human body. The dosages from these
sources are approximately 0.05, 0.05, and 0.025 rem per year. The total natural dosage per
year is thus 0.125 and in an average lifetime around 9 rem. The lethal dose of radiation is
400 rem, 50% of people who receive such a dose over a short period dying. The body has, or
course, considerable recuperative ability, and 400 rem spread over several years will not be
likely to cause death, although health may be seriously impaired. A dose of 200 rem over a
short period is likely to lead to leukemia.
The International Commission on Radiological Protection has laid down safety
standards for the protection of radiological workers and for the population as a whole. If a
person is exposed in his occupation to radiation hazards, he must receive a dosage of no more
than 5 rem per year (40 times the natural dosage) and no more than 3 rem in any period of
13 weeks. Anyone working in the vicinity of a radioactive area must receive no more than 1.5
rem per year ; and the population as a whole must not receive a dosage of more than 0.5 rem
per individual per year.
The increasing use of X-rays in diagnostic and therapeutic medicine and the
testing of atomic weapons with consequent fall-out, represent the greatest hazards to the
population as a whole. The dosage per individual from these sources is still small in
comparison with that from natural sources. All radiation causes biological damage and, in
particular, gene mutation. From naturally occurring sources the mutation rate is already very
high, resulting at the moment in gross abnormality in around 3% of all births. Any increase in
the dosage rate of the population will increase the number of mutations, the most noticeable
likely result being an increase in mental diseases.
3-2-11-b Medical and Biological Effects of Radiation
Each quantum of X-rays (or -rays or high frequency ultraviolet light) carries energy
of 1000 eV or more. If this energy is imparted to a cell, biochemical effects are
produced similar to those produced by radioactive particles. All the applications
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mentioned in chapter 6 therefore apply to X-rays also.
The effects of high energy radiation, such as X- rays from television sets or
detail to give general information about the biological effects of radiation.
The more energetic X- rays and rays can penetrate to any point in the human
body, whereas ultraviolet radiation is absorbed completely in the skin. Therefore, X and 
radiation can affect the internal organs and nervous system, whereas the effects of UV
radiation are generally limited to the exposed areas of the skin. Overexposure to UV
radiation will result in sunburn, but a long-term effect of repeated overexposure can be
the development of skin cancer.)
The high-energy radiation to which the general public is exposed is almost
exclusively in the form of X rays or rays. Radiation workers, on the other hand,
sometimes come into contact with materials that emit  and  particles. All of these
radiations can produce biological damage by virtue of their ionizing action in living tissue.
The doubly charged, slowly moving  particles from radioactive substances interact very
effectively with the atomic electrons in matter and produce a high degree of ionization.
The rate at which a single 5-MeV  particle deposits energy through ionization in a
medium such as biological tissue is approximately 100 keV/m. Consequently; in the wake
of a moving  particle we find a dense collection of ions and electrons.
The electrons that are emitted in radioactive -decay have energies in the range
from a few keV to 1 MeV or so. The corresponding electron velocities are very much
greater than those of radioactive a particles. For this reason, an electron passing through
matter does not remain near any atom for a time sufficient to interact effectively with
the atomic electrons; the degree of ionization that is produced is therefore low. The rate
at which a 1-MeV electron deposits energy through ionization in a medium such as tissue
is only about 0.25 keV/m. Consequently, in the wake of a moving electron we find only a
diffuse collection of ions and knocked-out electrons.
The much smaller rate of energy loss with distance (or linear energy transfer for
an electron compared with an  particle implies that electrons will penetrate much
farther into biological material. In fact, -decay electrons have ranges in tissue of a few
millimeters, whereas radioactive particles will penetrate only to a depth of about 40
m (0.04 mm). (The range of a 1-MeV electron in tissue is 4.2 mm, whereas the range of a
5-MeV  particle is 37 m.)
When rays or X rays pass through matter, they interact with the medium via,
the photoelectric effect or the Compton effect or by pair production if the photon
energy is greater than 2mec2 = 1.02 MeV and release energetic electrons. These electrons
ionize the surrounding atoms in the same way that - decay electrons do. Therefore, the
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characteristics of the ionization produced by decay electrons and by rays and X
rays are the same. The difference between the effects of - decay electrons and
energetic photons is that the latter can penetrate to a substantial depth in matter
before the first interaction. For example, the 1.2- and 1.3-MeV rays that follow 60Co
decay will penetrate about 10 cm of tissue before the incident intensity has been
reduced by 50 percent. Consequently, the effect on, for example, the internal organs of
the body will be much greater due to an exposure to rays or X rays than to an equal
exposure to  particles or a particles from an external source. (Of course, if a radioactive material is inhaled or ingested, the effect on the internal organs due to  and 
particles can be large.)
Gamma rays and X rays penetrate deeply into matter because they have no electric
charge and therefore do not lose energy until they produce photoelectric or Compton
electrons. All of the ionization that accompanies the passage of  rays and X rays
through matter is produced by the secondary electrons. Similarly a neutron does not
directly produce any ionization in passing through matter. When the neutron strikes a
nucleus, the nucleus recoils as a result of the collision. As the nucleus moves through the
surrounding atoms, some of the atomic electrons are stripped away. Thus, the collision
produces ionization along the path of the recoiling nucleus. In biological material, which
contains a large fraction of hydrogen, neutrons interact primarily with the nuclear
protons of the hydrogen atoms. The knocked-on protons are the particles that produce
almost all of the ionization in such materials when irradiated with neutrons.
3-2-12 Radiation Protection
For the protection of radiation workers all radioactive materials must be shielded
in store, normally by being surrounded by a lead container thick enough to absorb all the
particles and most of the
remote control or at a safe distance (the dosage falling off at least as rapidly as the inverse
square of the distance from the source). All equipment producing radiation must be
adequately shielded and the operators must be protected from scattered radiation. All
workers are required to wear film badges or pocket ionization chambers which, are checked
regularly to calculate dosages received, and must adhere strictly to codes of practice, which
have been laid down by legislation. If it is found that any worker has received more than the
permitted dose, he is immediately removed from radiation work for a stipulated period. Since
genetic effects are the most serious for the population as a whole, it is recommended that,
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where appropriate, workers wear lead-rubber aprons to protect the gonads or ovaries.
Shielding against X-Rays
Lead is the most common shield against X-rays because of its high density (11340 kg/m3),
stopping power, ease of installation and low cost. The maximum range of a high-energy
photon such as an X-ray in matter is infinite; at every point in the matter traversed by
the photon, there is a probability of interaction. Thus there is a very small probability of
no interaction over very large distances. The shielding of photon beam is therefore
exponential (with an attenuation length being close to the radiation length of the
material); doubling the thickness of shielding will square the shielding effect.
The following table shows the recommended thickness of lead shielding in function of Xray energy, from the Recommendations by the Second International Congress of
Radiology.
X-Rays generated by peak Minimum
voltages
thickness
not exceeding
of Lead
200 kV
4.0 mm
225 kV
5.0 mm
500 kV
22.0 mm
600 kV
34.0 mm
900 kV
51.0 mm
3-2-13 Applications
3-2-13-a Carbon and Uranium Dating
A simple direct use of radioactivity is in dating. It is often necessary in biology,
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geology, and other fields to determine when a particular fossil was alive, when an artifact
was made, or when a geological stratum was laid down. The use of radioactivity, where this
is possible, is almost always the most accurate method of dating and is sometimes the only
one available.
In living plants and animals the carbon is mainly 12C, the normal isotope, but a small
but detectable quantity of 14C atoms are also present. These result from the bombardment
of atmospheric nitrogen by cosmic rays. The 14C isotope is radioactive, with a half-life of
5.76 x 103years. In living organisms the 14C atoms will be decaying but, since the atoms are
continually renewed by uptake from the environment, the ratio of 14C to 12C atoms is found
to remain constant at all times. It is further believed that this ratio has not altered
significantly over a considerable period of time.
A quite different situation arises as soon as the organism dies. No further renewal of
the radioactive carbon takes place and the number of 14C atom decays exponentially with
time, as therefore does the radioactivity exhibited. If the activities of a quantity of carbon
from a recently alive organism and of the same quantity of carbon from a subject to be
dated are and , then

e-t
Therefore
t=
1

ln(

ln 3-2-9
ln 2
The time t so calculated is the time for which the subject has been dead.
Since the half-life of 14C is 5.76 x 103 years, and the activity of carbon found in
organisms is in any case small, the limit to the carbon-dating process is around 50000 years.
For geological purposes this is a negligibly small period, and uranium dating is used for
events more distant in time. In many rocks, uranium, which consists mainly of the isotope
238, is found in conjunction with the lead isotope 206. This is not surprising, since 238U is
the first member of one of the naturally occurring radioactive series, the end product of
which is stable 206Pb. It is believed that when the rocks were formed, only 238U were
present, the 200Pb now found representing the product of the radioactivity, which has taken
place since that time. The half-life of 238U is 4.5 x l09 years, and all radioactive elements in
the series have half-lives very much smaller than this. When a radioactive series is in equilibrium, the numbers or atoms of each element present at any time are in the direct ratio of
their half-lives. The numbers of atoms present of elements other than 238U and 206 Pb are
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therefore negligibly small and may be ignored in any calculation.
In any sample the number of atoms nu and np of 238U and 206Pb respectively, are
calculated from the respective masses and Avogadro's number. It is believed that the
number of atoms, of 238U present at the formation of the rocks was nou = nu + np.
Therefore, if t is the time since the rocks were laid down,
Nu=nou e-t
Therefore
t=

ln (nu + np)/nu
ln 2
3-2-10
Question 9
A sample of C14, whose half life is 5730 years, has a decay rate of 14 disintegration per
minute (dpm) per gram of natural C. An artifact is found to have radioactivity of 4 dpm
per gram of its present C, how old is the artifact?
Using the above equation, we have:
Where:
years
years
3-2-13-b Radioactive Isotopes as Tracers
Many elements are taken up by biological organisms, but their role in the functioning
of the organism is not always clear. Chemical and biochemical techniques are not always able
to provide the answers to the problems raised, and the use of radioactive isotopes as
tracers has allowed many obscure points to be cleared up. Although the normal isotope of an
element cannot be identified after it has entered a biological system, the absorption,
metabolic uptake, movement to particular sites, etc., of a radioactive isotope can be
followed by the activity it exhibits. This can be done without operating on the system or in
any way interfering with its functioning.
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The unit of radioactivity is the curie, originally chosen to be the activity of 1 g of
radium, but now internationally defined as 3.7x1010 disintegrations per second. For biological
and medical purposes activities of this order are far too high and would kill the host
material into which such radioactivity was introduced. Activities of mill curies and micro
curies are much more usual.
It should, however, be made clear that any counter, even when far removed from a
radioactive sample, will still record counts. This is because of the cosmic radiation, natural
radioactivity in the air and the ground, and various type of manmade radioactivity around us.
A background count should therefore always be recorded before, after, and often during, a
series of tests. This is subtracted from the count made during an investigation to give the
count due to the sample alone. If the sample activity is of the same order as, or less than,
the background count, the counter may require to be shielded to reduce the background
effect and increase the accuracy of the result.
The next few sections will be concerned with dealing with a few examples of the use
of tracer techniques to indicate the type of problem that can be tackled and to show the
simplicity and usefulness of the method.
3-2-13-c Studies of Metabolic Uptake
In patients suffering from pernicious anemia, the absorption of vitamin B12 is low, It
is difficult, however, by normal methods to determine just how much of the vitamin, is being
absorbed by the body. Since vitamin B12 contains a cobalt atom, it is possible to synthesize
the vitamin with the radioactive isotope 58Co and to feed a known dose to the patient.
Comparison of the activity of the dose given with the subsequent activity of the feces
allows the calculation of the fraction of the dose, which has been absorbed by the gut.
The thyroid takes up practically all iodine ingested and, absorbed by the gut. This
stored iodine is used to form the hormone thyroxin and di-iodo-tyrosine, which are then
circulated through the body. A measured dose of the radioactive isotope 131I can be given
by mouth to normal subjects and the activity can be measured with a standard configuration
at the neck in the region of the thyroid gland. A fixed blood sample taken after 48 h will
also show activity because of the labeled iodine in the hormones.
A patient suffering from hyperthyroidism has an over-active thyroid, which absorbs
too much iodine too quickly and thus produces an excessive amount of hormone. By feeding
such patient radioactive iodine and comparing the activity of the thyroid and of blood
samples with the data obtained from normal subjects, one can easily and quickly diagnose
the complaint.
In the two examples dealt with, how the ingested substance was used by the system
was of no great interest. It is often important in biochemical work to know which portion of
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an ingested molecule is used in the synthesis of another compound, and tracer techniques
can answer this type of question. For example, glycine is used in the formation of
protoporphyrin. Its structural chemical formula is
The two carbon atoms being colourde, red and blac, for identification purposes. It is
possible to synthesize glycine with either C1, or C2 the radioactive 14C isotope. If C is
radioactive, the radioactivity appears in the porphyrin ring; it does not if C is radioactive.
This shows that glycine is used in the synthesis of protoporphyrin but that the carboxyl
carbon is removed during the synthesis.
3-2-13-d Transport Studies
Carbon dioxide is absorbed by the leaves of plants and takes part in the process of
photosynthesis, in which carbohydrates are produced. A simple method of determining
where the carbohydrates go in the plant after they are produced is provided by radioactive
tracer techniques. Carbon dioxide is made from radioactive carbon 14C, and a leaf of a
growing plant is enclosed in a transparent container through which the prepared gas is
passed. After several hours a Geiger counter placed at various parts of the plant will
indicate where the labeled carbon atoms are now located.
Figure 3-2-6 Auto radiograph of a leaf which has been maintained in an atmosphere of
radioactive carbon dioxide, showing the uptake of the labeled carbohydrates.
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More usually a technique called auto radiography is employed. Leaves and portions of
the stem can be removed from the plant and placed between photographic plates. The particles from the 14C atoms strike the emulsion of the plates, each one producing a
developable spot. The more radioactive atoms there are at a particular part of a leaf the
more spots will be produced at that point of a film. If the carbohydrate is spread
throughout a leaf, a picture of the whole leaf will be produced on the film; but the regions
where the concentration is highest will appear darker than the others. It is found that the
concentration is greater in the vascular system of the leaf than elsewhere (Fig. 3-2-6).
It is further found that if a young leaf is used in the experiment, all the radioactive
atoms remain in that leaf, the hydrocarbon being needed for the growth of the leaf itself.
On the other hand, if the leaf is a mature one, some of the radioactive carbohydrate is
passed on to young leaves, which are unable to supply all their own needs. It would have been
very difficult to obtain such information by any means other than the use of radioactive
tracers.
The use of radioactive tracers allied to auto radiography has been extremely useful in the
study of replication. As an example of this, let us consider chromosome division in broadbeam root tips, which are often used for this type of purpose, since the chromosomes, or
their auto radiographs, can be made clearly visible in a microscope. If thymidine labeled
with 3H is used in growing the specimens, the 3H is incorporated only into the chromosomes
and auto radiographs of cells will therefore show the chromosomes, or portions of them,
clearly.
Cell division may be inhibited with colchicines, which does not affect the division of
chromosomes. If cells containing labeled chromosomes are treated with colchicines,
chromosome division will proceed to different stages in different cells. After the process is
completed, some cells will contain two sets of chromosomes, some four sets, and so on. If an
auto radiography film is placed over the preparation, pictures of these cells will be obtained
and the distribution of 3H after one, two, three, etc., divisions can be followed. In this way
one obtains information about the manner in which the actual material of the chromosome
divides and how it replicates from the medium,
3-2-13-e Isotopic Dilution
Radioactive techniques may also be used to determine the total volume occupied by a
fluid. If the activity of a known quantity of suitably labeled fluid is measured and this fluid
is then injected into the volume, when the radioactive tracer has dispersed throughout the
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whole region, the activity of an extracted sample indicates by how much the tracer has
been diluted. The total volume may therefore be calculated.
In one such experiment 5 x 10-6m3 of water, with 3
isotope was injected into the antecubital vein of a human subject. The activity of 10 -6 m3 of
the injected sample was 30200 counts per second. After 0.5, 1, 2, and 3h blood samples
were withdrawn from the same vein and the plasma was separated out. Samples of volume
10-6 m3 were taken, the activities being 302, 346, 328, and 340 counts per second,
respectively. It was clear that equilibrium had been achieved before 1 h and it was assumed
that complete mixing had taken place in that time. The average of the last three activities
was 338 counts per second. The activity had decreased by a factor of 338/30200. The
total volume finally occupied by the labeled water was therefore
5x l0-6m3 x
30200
= 4.47 x 10-2 m3.
338
This is the total volume of the subject's body occupied by water.
3-2-13-f Location of Hemorrhage
Recently radioactive-tracer techniques have been applied to the location of
hemorrhage. It is often difficult to tell whether a hemorrhage is taking place or, if it is, its
location. The isotope 51Cr has been used in various studies of blood because it is taken up by
the red cells. In this new application 51Cr-labeled blood is injected into the patient. With
normal blood circulation the radioactivity is distributed throughout the circulatory system.
If hemorrhage is occurring, the radioactivity will markedly increase at some region of the
body, and the rate at which the activity increases is an indication of the volume of blood
being lost. This is a simple and very effective way of dealing with a difficult problem.
3-2-13-g Radiocardiography
A routine method of investigating heart conditions is the insertion of a catheter into
the bloodstream, from where it is worked into the heart. This is a skilled operation, which is
time consuming and is not without its attendant risks. Radiocardiography is a much simpler
procedure, which gives the same information almost routinely, and with no risk whatsoever.
It also gives information about pulmonary conditions.
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A tracer element 137Ba with a half-life of 127 s is used. Ten mill curies are injected
rapidly into the subclavian vein and enter the right ventricle almost immediately. A counter
directed from above at the heart detects the presence of the tracer. There is a dip in the
recording as the tracer is pumped out to the lungs and a rise when it returns to the heart. A
counter at the back, collimated to pick up radiation from the aorta, follows the flow from
the heat. If the flow through other parts of the body is of interest, further counters may
be located in these regions. An e.c.g. trace is normally taken at the same time.
If the heart and lung functions are normal, the recording obtained from the counters
will have a typical form. Blockage or malfunction will lead to a nonstandard pattern, its
features being interpretable in terms of various known conditions. The diagnosis of atrialseptal defect, of ventricular-septal defect, and of congenital, pathological, cardiopulmonary
conditions can be rapidly and easily established.
3-2-13-h Radiotherapy
Radioactive isotopes are also used to destroy unwanted cells. The particles and
radiation emitted produce two main effects on the cells. They can supply energy to a
molecule, resulting in the ejection of an electron. Since the outermost electrons are the
most loosely bound these are the ones most frequently ejected. These are also the
electrons, which take part in chemical bonding, and the loss of one or more electrons can
result in the breaking-up of the molecule into its component parts. Cells may consequently
be destroyed if these molecules play a vital role in their function.
Just as important is the fact that all biological material contains water and
irradiation of the water produces products, which react with the biological material.
Although a water molecule is normally split up into H+ and OH- ions, it can also he split up
into the electrically neutral groups H and OH, which are called free radicals. These are very
chemically reactive. The OH is a powerful oxidizing agent, attracting electrons strongly in
order to turn itself into the stable OH- ion. In doing so it breaks chemical bonds and
produces in consequence biological effects.
Radiotherapy is possible only if the unwanted cells can be destroyed by a dose of
radiation does not permanently damage the surrounding healthy tissue. In general, cells to
be destroyed, such as tumor cells, must be more sensitive to radiation than the healthy
tissue.
Tubes containing radium, or some similar isotope, can be implanted around the
offending volume and left there for a carefully calculated time. The surrounding tissue will
generally receive an intense dose of radiation, and radiation sickness may be produced.
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Since radium is a long-lived isotope, it must be removed after the prescribed time. To avoid
an unnecessary operation, radon or a gold isotope may be used instead, The half-lives are
only of the order of three days and the tubes are not removed.
Even better: if the organ to be treated concentrates a specific radioactive isotope, it
can be ingested or similarly introduced into the patient. Thus a suitable dose of 131I is given
for the treatment of hyperthyroidism, and 32P which is taken up by bone marrow, is used for
the treatment of polycythemia.
PROBLEMS
3-2-1 Eight decays and 6 decays are necessary' before an atom of 238U92 achieves
stability. What are the atomic number, atomic mass number, and chemical name of the final
atom?
3-2-2 A solution containing a radioactive isotope, which emits -particles with a half-life of
12.26 days, surrounds a Geiger counter, which records 480 counts per minute. What
counting rate will be obtained 49.04 days later?
3-2-3 Radium 226 has a half-life of 1620 years. What is the mass of a sample, which
undergoes 20000 disintegrations per second?
3-2-4 A fixed quantity of a radioactive isotope is delivered to a hospital at the same time
every week. One day a doctor finds an unopened bottle of the isotope with no label
attached. He places it in front of a Geiger counter and records 4200 counts per second.
When he substitutes a bottle, which has just arrived, he records 47500 counts per second.
If the isotope has a half-life of 8 days, how long has the unlabeled bottle been in the
hospital?
3-2-5 Radioactive 24Na, which has a half-life of 15 h, is sent from the A.E.R.E. Laboratories
at Harwell to a London hospital. What should be its activity when it leaves Harwell if the
activity is the 10 mCi (milli)-when it is used in the hospital 3 h later?
3-2-6A curie was originally defined as the activity of the amount of radon in equilibrium
with 1 g of radium 226. If the half-life of the radium is 1620 years, how much
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disintegration per second does this represent?
3-2-7 A counter detecting the -particles from a radioactive source takes the following
readings:
t (mm)
0 35 60 120 240 360 480 600
(counts/mill)
154 148 140 128 109 92 81 72
When the source is removed, the counter records an average counting rate of 30 per
minute. What is the half-life of the radioactive source?
3-2-8 What are the masses of 1 Ci of
3.90 years, 2.55 mm, and 3.00x l0-6s?
227
Th,
32
P and
212
Po if the respective half-lives are
3-2-9 The linear absorption coefficients for 0.710A X-rays in aluminum, nickel, and lead
are14.3 cm-1,
42l.9cm-1, and 1593 cm-1, respectively. What thickness of each absorber is
necessary to reduce the intensity of a beam of 0.71-0A. X-rays to one-tenth of its incident
value?
3-2-10 The copper Ka-line and K line have wavelengths of 1.54 0A and 1.39 0A, respectively.
The corresponding linear absorption coefficients in nickel are 439 cm-1 and 2546 cm-1. What
thickness of nickel is necessary to reduce the intensity of the K-radiation in a beam to 0.1 %
of its incident value, and what is the percentage transmission of K-radiation through this
thickness of nickel?
3-2-11 Copper KX radiation of wavelength 1.5405 0A undergoes Compton
scattering in a carbon block. What is the wavelength of X-radiation scattered at 900 to the
incident direction, and what is the energy of recoil of the electron?
3-2-12 If 34 eV is necessary to produce an ion-pair in standard air, how many ion-pairs would
be produced in air by the complete absorption of 1R of X-radiation?
3-2-13 The maximum permissible dosage for scientific workers using X-radiation is 6.25
millirads per hour. What is the safe working distance from a shielded source of cobalt 60,
which produces a dose rate of 0.256 rad per hour at a distance of 1 m?
3-2-14 A certain individual receives a whole-body dose of 8 rem of  radiation, whereas
another individual receives a dose of 700 mrad of particles by inhaling a radioactive
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material. Which individual will probably suffer the greater biological damage? QF of
particles= 20.
3-2-15 An accelerator produces a beam of energetic electrons. The beam emerges from the
vacuum region of the accelerator through a thin window. Just outside the window the
electrons have an energy of 5 MeV. The beam is distributed uniformly over an area of 1 cm2
and the beam current is 10 nA (=10-8 A)., A worker in the laboratory accidentally walks close
to the beam, exposing his arm to the beam near the window for 1s. the range of 5-MeV
electrons in tissue is 2.2 cm. What radiation dose (in rad) does the exposed tissue receive?
3-2-16 A burial site yields a wooden artifact which gives 11.6 counts per minute per gram of
carbon present. The corresponding count from wood from living trees is 15.3. When was the
artifact made? The half-life of 14C is 5600 years.
3-2-17In a sample of rock the ratio of 238U to 206Pb is 1:0.75 by weight. Estimate the age of
the rock. The half-life of 238U is 4.5 x l0-9 years.
3-2-18 A patient is injected with 5 x l0-6 m3 of blood labeled with 51Cr, the activity being
60000 counts per minute. The activity of similar-sized samples of blood withdrawn from the
patient at intervals stabilizes at a value of 827 counts per minute. What is the total volume
of blood in the patient's body?
3-2-19 A patient is fed a radioactive isotope, which has an activity of 1 Ci. The activity of
the feces measured 36 h later is 0.25 Ci. How much of the isotope has been taken up by
the patient's body if the half-life of the isotope is 15 days?
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