Radioactive Decay:
Radioactive decay is the process in which an unstable atomic nucleus spontaneously
loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in
an atom of one type, called the parent nuclide transforming to an atom of a different type, named
the daughter nuclide. For example: a carbon-14 atom (the "parent") emits radiation and
transforms to a nitrogen-14 atom (the "daughter"). This is a random process on the atomic level,
in that it is impossible to predict when a given atom will decay, but given a large number of
similar atoms the decay rate, on average, is predictable.
The SI unit of radioactive decay is the becquerel (Bq). One Bq is defined as one
transformation (or decay) per second. Since any reasonably-sized sample of radioactive material
contains many atoms, a Bq is a tiny measure of activity; amounts on the order of TBq
(terabecquerel) or GBq (gigabecquerel) are commonly used. Another unit of radioactivity is the
curie, Ci, which was originally defined as the activity of one gram of pure radium, isotope Ra226. At present it is equal, by definition, to the activity of any radionuclide decaying with a
disintegration rate of 3.7 × 1010 Bq. T he use of Ci is presently discouraged by the SI.
The neutrons and protons that constitute nuc lei, as well as other particles that may
approach them, are governed b y several interactions. The strong nuclear force, not observed at
the familiar macroscopic scale, is the most powerful force over subatomic distances. The
electrostatic force is almost always significant, and in the case of beta decay, the weak nuclear
force is also involved.
The interplay of these forces produces a number of different phenomena in which energy
may be released by rearrangement of particles. Some configurations of the particles in a nucleus
have the property that, should they shift ever so slight ly, the particles could rearrange into a
lower-energy arrangement and release some energy. One might draw an analogy with a
snowfield o n a mountain: while friction between the ice crystals may be supporting the snow's
weight, the system is inherently unstable with regard to a state of lower potential energy. A
disturbance would thus facilitate the path to a state of greater entropy: the system will move
towards the ground state, producing heat, and the total energy will be distributable over a larger
number of quantum states. Thus, a n avalanche results. The total energy does not change in this
process, but because of the law of entropy, avalanches only happen in one direction and that is
towards the "ground state" –the state with the largest number of ways in which the available
energy could be distributed.
Such a collapse (a decay event) requires a specific activation energy. For a snow
avalanche, this energy comes as a disturbance from outside the system, although such
disturbances can be arbitrarily small. In the case of an excited atomic nucleus, the arbitrarily
small disturbance comes from quantum vacuum fluctuations. A nucleus (or any excited system in
quantum mechanics) is unstable, and can thus spontaneously stabilize to a less-excited system.
The resulting transformation alters the structure of the nucleus and results in the emission of
either a photon or a high-velocity particle which has mass (such as an electron, alpha particle, or
other type).
Spontaneous Emission:
Types of decay
Alpha particles may be completely stopped by a sheet of paper, beta particles by
aluminum shielding. Gamma rays can only be reduced by much more substantial barriers, such
as a very thick layer of lead.
As for types of radioactive radiation, it was found that an electric or magnetic field could
split such emissions into three types of beams. For lack of better terms, the rays were given the
alphabetic names alpha, beta and gamma, still in use today. While alpha decay was seen only in
heavier elements (atomic number 52 and greater), the other two types of decay were seen in all
of the elements.
In analyzing the nature of the decay products, it was obvious from the direction of
electromagnetic forces that alpha rays carried a positive charge, beta rays carried a negative
charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that alpha
particles were much more massive than beta particles. Passing alpha particles through a very thin
glass window and trapping them in a discharge tube allowed researchers to study the emission
spectrum of the resulting gas, and ultimately prove that alpha particles are helium nuclei. Other
experiments showed the similarity between beta radiation and cathode rays; they are both
streams of electrons, and between gamma radiation and X-rays, which are both high energy
electromagnetic radiation.
Although alpha, beta, and gamma are most common, other types of decay were
eventually discovered. Shortly after discovery of the neutron in 1932, it was discovered by
Enrico Fermi that certain rare decay reactions yield neutrons as a decay particle. Isolated proton
emission was eventually observed in some elements. Shortly after the discovery of the positron
in cosmic ray products, it was realized that the same process that operates in classical beta decay
can also produce positrons (positron emission), analogously to negative electrons. Each of the
two types of beta decay acts to move a nucleus toward a ratio o f neutrons and protons which has
the least energy for the combination. Finally, in a phenomenon called cluster decay, specific
combinations of neutrons and protons other than alpha particles were spontaneously emitted
from atoms on occasion.
Still other types of radioactive decay were found which emit previously seen particles,
but by different mechanisms. An example is internal conversion, which results in electron and
sometimes high energy photon emission, even though it involves neither beta nor gamma decay.
Isomeric Transition:
Isomeric transition commonly occurs immediately after particle emission; however, the nucleus may
remain in an excited state for a measurable period of time before dropping to the ground state at its
own characteristic rate. A nucleus that remains in such an excited state is known as a nuclear isomer
because it differs in energy and behavior from other nuclei with the same atomic number and mass
number. The decay of an excited nuclear isomer to a lower energy level is called an isomeric
transition
Gamma Ray Emission:
When a radioactive nucleus emits γ−rays, only the energy level of the nucleus changes
and the atomic number and mass number remain the same. During α or β− decay, the daughter
nucleus is mostly in the excited state. It comes to ground state with the emission of γ−rays.
Example : During the radioactive disintegration of radium (88Ra226) into radon (86Rn222), gamma
ray of energy 0.187 MeV is emitted, when radon returns from the excited state to the ground
state
α – decay :
When a nucleus undergoes alpha-decay, it transforms to a different nucleus by emitting an
alpha-particle (a helium nucleus, 2He4). For example, when 92U 238 undergoes alpha-decay, it
transforms to 90 Th 234
238
→ 90 Th 234 + 2He4
92U
In this process, it is observed that since 4 2He contains two protons and two neutrons, the mass
number and the atomic number of the daughter nucleus decreases by four and two, respectively.
Thus, the transformation of a nucleus Z X A into a nucleus Z-2 YA-4 can be expressed as
Z
X A → Z-2 YA-4 + 2He4
β - Decay :
When a radioactive nucleus disintegrates by emitting a β−particle, the atomic number
increases by one and the mass number remains the same. β− decay can be expressed as
zX
A
→ Z+1YA + −1e0
Example : Thorium (90Th234) is converted to protoactinium (91Pa234) due to β−decay
234
90Th
→ 91Pa234 + −1e0
At a time, either α or β−particle is emitted. Both α and β particles are not emitted during a single
decay.
Positron decay:
Positron emission involves the conversion of a proton in the nucleus into a neutron plus
an ejected positron,
or +. A positron has the same mass as an electron, but the opposite
charge. The result of positron emission is a decrease in the atomic number of the product, but no
change in the mass number.
40
19K
→18 Ar 40 +1e0
+
Electron capture:
Electron capture is a process in which the nucleus captures an inner-shell electron,
thereby converting a proton into a neutron. The mass number of the product nucleus is
unchanged, but the atomic number decreases by 1.
80 Hg
117
+-1 e 0 → 79 Au 197
+
Principles of Nuclear Physics:
The atomic nucleus was discovered by Earnest Rutherford in 1911. Rutherford’s
experiment on scattering of alpha particles proved that the mass of the atom and the positive
charge is concentrated in a very small central core called nucleus. The dimension of nucleus is
much smaller than the overall dimension of the atom. The nucleus is surrounded by orbiting
electrons.
Nucleus
The nucleus consists of the elementary particles, protons and neutrons which are known as
nucleons. A proton has positive charge of the same magnitude as that of electron and its rest
mass is about 1836 times the mass of an electron. A neutron is electrically neutral, whose mass is
almost equal to the mass of the proton. The nucleons inside the nucleus are held together by
strong attractive forces called nuclear forces.
A nucleus of an element is represented as ZXA, where X is the chemical symbol of the element. Z
represents the atomic number which is equal to the number of protons and A, the mass number
which is equal to the total number of protons and neutrons. The number of neutrons is
represented as N which is equal to A−Z. For example, the chlorine nucleus is represented as
35
17Cl . It contains 17 protons and 18 neutrons.
Classification of nuclei
(i) Isotopes
Isotopes are atoms of the same element having the same atomic number Z but different
mass number A. The nuclei 1H1, 1H2 and 1H3 are the isotopes of hydrogen. In other words
isotopes of an element contain the same number of protons but different number of neutrons. As
the atoms of isotopes have identical electronic structure, they have identical chemical properties
and placed in the same location in the periodic table.
(ii) Isobars
Isobars are atoms of different elements having the same mass number A, but different
atomic number Z. The nuclei 8O16 and 7N16 represent two isobars. Since isobars are atoms of
different elements, they have different physical and chemical properties.
(iii) Isotones
Isotones are atoms of different elements having the same number of neutrons. 6C14 and 8O16 are
some examples of isotones.
General properties of nucleus
Nuclear size:
According to Rutherford’s α−particle scattering experiment, the distance of the closest approach
of α − particle to the nucleus was taken as a measure of nuclear radius, which is approximately
10−15m. If the nucleus is assumed to be spherical, an empirical relation is found to hold good
between the radius of the nucleus R and its mass number A.It is given by
R ∝ A1/3
R = roA1/3
where ro is the constant of proportionality and is equal to 1.3 F(1 Fermi, F = 10−15 m)
Nuclear density:
The nuclear density ρN can be calculated from the mass and size of the nucleus.
ρN =Nuclear mass/Nuclear volume
Nuclear mass = AmN where, A = mass number and mN = mass of one nucleon and
is approximately equal to 1.67 × 10−27 kg
Nuclear volume =4/3 πR3 =4/3 π (ro A1/3)3
ρN = AmN /4/3 π (ro A1/3)3= mN /4/3 π ro3
Substituting the known values, the nuclear density is calculated as 1.816 × 1017 kg m−3 which is
almost a constant for all the nuclei irrespective of its size.The high value of the nuclear density
shows that the nuclear matter is in an extremely compressed state.
Nuclear charge
The charge of a nucleus is due to the protons present in it. Each proton has a positive charge
equal to 1.6 × 10−19 C.
∴ The nuclear charge = Ze, where Z is the atomic number.
Atomic mass unit:
It is convenient to express the mass of a nucleus in atomic mass unit (amu), though the unit of
mass is kg. One atomic mass unit is considered as one twelfth of the mass of carbon atom 6C12.
Carbon of atomic number 6 and mass number 12 has mass equal to 12 amu.
1 amu = 1.66 × 10−27 kg
The mass of a proton, mp = 1.007276 amu
This is equal to the difference in mass of the hydrogen atom which is 1.007825 amu and the
mass of electron.
The mass of a neutron, mn = 1.008665 amu
The energy equivalence of one amu can be calculated in electron-volt
Einstein’s mass energy relation is, E = mc2
Here, m = 1 amu = 1.66 × 10−27 kg ,c = 3 × 108 ms−1
∴ E = 1.66 × 10−27 × (3 × 108)2 J
One electron-volt (eV) is defined as the energy of an electron when
it is accelerated through a potential difference of 1 volt.
1 eV = 1.6 × 10−19 coulomb × 1 volt
1 eV = 1.6 × 10−19 joule
× 10−27 × (3 × 108)2 ] /1.6 × 10−19 = 931 × 106 eV
= 931 million electronvolt = 931 MeV
Thus, energy equivalent of 1 amu = 931 MeV
Hence E = [1.66
Nuclear mass:
As the nucleus contains protons and neutrons, the mass of the nucleus is assumed to be the mass
of its constituents.
Assumed nuclear mass = ZmP + Nmn,
where mp and mn are the mass of a proton and a neutron respectively. However, from the
measurement of mass by mass spectrometers, it is found that the mass of a stable nucleus (m) is
less than the total mass of the nucleons.i.e mass of a nucleus, m < (Zmp + Nmn)
Zmp + NmN – m = Δm
where Δm is the mass defect
Thus, the difference in the total mass of the nucleons and the actual mass of the nucleus is known
as the mass defect.
Binding energy
When the protons and neutrons combine to form a nucleus, the mass that disappears (mass
defect, Δm) is converted into an equivalent amount of energy (Δmc2). This energy is called the
binding energy of the nucleus.
∴ Binding energy = [ZmP + Nmn – m] c2 = Δm c2
The binding energy of a nucleus determines its stability against disintegration. In other words, if
the binding energy is large, the nucleus is stable and vice versa.
The binding energy per nucleon is
BE/A=Binding energy of the nucleus/Total number of nucleons.
It is found that the binding energy per nucleon varies from element to element.
A graph is plotted with the mass number A of the nucleus along the X−axis and binding energy
per nucleon along the Y-axis
Explanation of binding energy curve
(i) The binding energy per nucleon increases sharply with mass number A upto 20. It increases
slowly after A = 20. For A<20, there exists recurrence of peaks corresponding to those nuclei,
whose mass numbers are multiples of four and they contain not only equal but also even number
of protons and neutrons. Example: 2He4, 4Be8, 6C12, 8O16, and 10Ne20. The curve becomes almost
flat for mass number between 40 and 120. Beyond 120, it decreases slowly as A increases.
(ii) The binding energy per nucleon reaches a maximum of 8.8 MeV at A=56, corresponding to
the iron nucleus (26Fe56). Hence,iron nucleus is the most stable.
(iii) The average binding energy per nucleon is about 8.5 MeV for nuclei having mass number
ranging between 40 and 120. These elements are comparatively more stable and non radioactive.
(iv) For higher mass numbers the curve drops slowly and the BE/A is about 7.6 MeV for
uranium. Hence, they are unstable and radioactive.
(v) The lesser amount of binding energy for lighter and heavier nuclei explains nuclear fusion
and fission respectively. A large amount of energy will be liberated if lighter nuclei are fused to
form heavier one (fusion) or if heavier nuclei are split into lighter ones (fission).
Nuclear force:
The nucleus of an atom consists of positively charged protons and uncharged neutrons.
According to Coulomb’s law, protons must repel each other with a very large force, because they
are close to each other and hence the nucleus must be broken into pieces. But this does not
happen. It means that, there is some other force in the nucleus which overcomes the electrostatic
repulsion between positively charged protons and binds the protons and neutrons inside the
nucleus. This force is called nuclear force.
(i)
(ii)
(iii)
(iv)
Nuclear force is charge independent. It is the same for all the three types of pairs of
nucleons (n−n), (p−p) and (n−p). This shows that nuclear force is not electrostatic in
nature.
Nuclear force is the strongest known force in nature.
Nuclear force is not a gravitational force. Nuclear force is about 1040 times stronger
than the gravitational force.
Nuclear force is a short range force. It is very strong between two nucleons which are
less than 10−15 m apart and is almost negligible at a distance greater than this. On the
other hand electrostatic, magnetic and gravitational forces are long range forces that
can be felt easily.
Yukawa suggested that the nuclear force existing between any two nucleons may be due to the
continuous exchange of particles called mesons, just as photons, the exchange particle in
electromagnetic interactions. However, the present view is that the nuclear force that binds the
protons and neutrons is not a fundamental force of nature but it is secondary.
Natural Radioactivity:
Natural radioactivity: We have seen that the naturally occurring elements like uranium,
polonium, radium etc. are constantly undergoing a spontaneous change (i.e. change by itself) and
as a result of this they are emitting alpha sym, beta sym- and gamma -rays and thus change into
other elements. This spontaneous change is called natural radio-activity. In natural radioactivity
onl7y a single nucleus is involved It is always found in heavier elements in the periodic table.
(i) Capture reactions: In these reactions the bombarding particle is captured or absorbed by the
target with the emission of gamma -rays. For example:
85
Rb + 1n0-----86R37 + γ
12
C 6 + 1 H 1 - 13 N 7 + γ
238
U 92 + 1 n 0 --- 239 U 92 + γ
Decay Series: (Radioactive Series)
Atoms of heavy elements like uranium, thorium, polonium and radium etc., are
constantly breaking up into fresh radioactive atoms with the emission of α, β and γ rays from
their nuclei. In the process the original (parent) atom disappears and gives rise to new (daughter)
atom. These new atoms are also, in general, radioactive and hence spontaneously break up in
their turn, thereby leading to a long chain of different radioactive elements in the form of a series
until an inactive (usually lead) element is reached. The series of elements thus obtained by the
successive disintegration of the new atoms is known as radioactive disintegration series and the
spontaneous breaking up of the nucleus is known as radioactive disintegration.
All the naturally occurring radioactive elements belong to one of the following three
series:
i. Uranium series / (4n+2) series ii. Thorium series/ (4n) series iii. Actinium Series /(4n+3)series
These series have been named after the name of the element at or near the head of the respective
series .All these three series which are also called natural radioactive series end with a stable
isotope of lead.
Some elements of each series emit α-particles whereas some other elements emit β
particles. Although no one atom can go both ways ,some atoms go either of the two ways and
cause branches in the series .no matter which way the parent goes, the daughter the goes other
way so that even though the series branch , they always come together again.
Uranium series [(4n+2) series] : This series is also called (4n+2)series because the mass
number of the elements of this series are given by this expression in which’ n’ is an integer
whose value decreases by unity when go from one radioactive element to the next one below it.
The mass numbers of the members of this series give a reminder of 2when divided by 4.In this
series 92U238 is the parent element and through the successive disintegrations .It is finally
transformed into a stable isotope of lead, 82 Pb 206.
Thorium series [(4n) series]: This series is also known as 4n series because mass
numbers of the members of this series are divisible by 4.This series starts with 90Th232 as shown
in the following figure by a successive transmutation or disintegration it ends up in a stable
isotope of 82 Pb 206.
Actinium Series [(4n+3) series]: This series is also known as (4n+3) series because the
mass numbers of the members of this series give a remainder of 3 when divided by 4. Actinium
was one time thought to be the starting element of this series, but now it is known that the true
starting element is
which by successive transformations ends up in a stable isotope of lead,
the whole chain of elements is shown in Figure.
Similarities between Radioactive series. There are many points of similarity between three
radioactive series:
i)
ii)
iii)
In all series, a product is formed which disintegrates in a branching process by
emitting either the two substances thus produced are then transformed in such a way
as to give a common product.
In all series, there is an element of atomic number 86 which has the properties of an
inert gas and is called emanation.
The stable end-product in all the three series having an atomic number of 82, is an
isotope of lead i.e.
Neptunium Series
In addition to the three series described above, there is a fourth series which has been obtained
from an artificially-produced radioactive material. The first element in this series is
after
which it has been named and the stable end product is the ordinary bismuth
rather than an
isotope of lead as in the uranium, actinium and thorium series. This series is also known as (4n
+1) series. All the members of this series are either unknown or extremely rare in nature.
It is quite obvious from the study of these series that all the members of a particular series
are characterized by having (4n+q) where q is one of the integers 0,1,2,3 characteristic of a given
series
Half life period:
Since all the radioactive elements have infinite life period, in order to distinguish the
activity of one element with another, half life period and mean life period are introduced. The
half life period of a radioactive element is defined as the time taken for one half of the
radioactive element to undergo disintegration.
From the law of disintegration
N = Noe–λt
Let T½ be the half life period. Then, at t = T½ , N =N0/2
∴N0/2 = Noe–λT½ ; log e 2 = λT½
T½= loge2/ λ = (log10 2 x 2.3026) / λ =0.6931/λ
The half life period is inversely proportional to its decay constant.The concept of half time
period can be understood from Figure.For a radioactive substance, at the end of T½, 50% of the
material remain unchanged. After another T½ i.e., at the end of 2 T½,25% remain unchanged. At
the end of 3 T½, 12.5% remain unchanged and so on.
Type of radiations & their applications:
Types of Radioactive Rays
Rutherford and his co-workers, in 1904, passed the radiations emitted by radioactive
elements through a strong electric field between parallel plates and thus separated them into
three quite different kinds which are:
(i) Alpha (α) rays. The rays which are deflected towards the negative plate are positively
charged and are called alpha (α) rays or alpha particles. These rays consist merely of helium
nuclei.
(ii) Beta (β) rays. The rays which are deflected towards the positive plate are negatively
charged and are called beta (β) rays or beta particles. These rays merely consist of electrons.
(iii) Gamma (γ) rays. These rays which are not deflected at all are neutral and are called
gamma (γ) rays.
Applications of Radioactive Radiations:
(i) Many radiation sources such as cobalt --60 ( - ray emitter) have been used for
industrial radiography i.e. for investigating the interiors of metallic castings for detecting any
flaws or defects.
(iit) Radioactive nuclides emitting alpha sym-or beta sym-particles have deen used for the
production of electric power by thermo-electric conversion. When alpha sym or beta symparticles are absorbed in matter, the energy of the radiation is converted into heat which can be
utilized for production of electric power. Such radio nuclide power generators are particularly
suitable for space vehicles because of their light weight, long life and absolute reliability.
(iti) Radio nuclides have been used as compact sources of heat energy because of which
they find many spac e-related applications. Radio nuclides of promethium--147, polonium--210
and plutonium--238 have been used to heat the propellant gas (hydrogen in low thrust rockets.
(iv) Chemical changes initiated by radiations from radioactive substances is the basis of a
newly developed subject called radiation chemistry which has been applied in the production and
modification of plastics and in the production of irradiated wood-plastic combinations.
(v) Nuclear radiations like gamma sym-rays have been utilized for the preservation of
food. The irration of food-stuff mainly meat, poultry, fish and fuits is achieved by exposure to
gamma sym-rays from cobalt--60 or calcium--137. A dose of 2 to 5 million rays is sufficient to
destroy almost all bacteria in food. This increases the shelf-life of these articles without
refrigeration. Radiations have also been employed for insect disinfestation of wheat and flour.
(vi) Gamma radiations from cobalt--60 are used in hospitals for sterlization of materials
like dressings, hypodermic syringes and surgical sutures.
(vii) Population of insects which causes considerable damage to both plant crops and
livestock can be controlled by irradiating the male members of these insects so that they become
sterile.
(viii) Radiation mutations in plansts have been practised to produce new varieties of these
plants.
(ix) Self-luminous paints for use on instruments and watch dails have been made by
adding a natural alpha sym -emitting radioactive substance to phosphor.
(x) The ionization produced by beta sym -particles has been widely used for the
elimination of static electricity which constitutes a serious fire and explosion hazard in the paper,
textile, rubber and plastic industries.
Production of Radio nuclides:
Cyclotron produced radionuclide:
Cyclotron is a device used to accelerate charged particles to high energies. It was devised
by Lawrence.
Principle:
Cyclotron works on the principle that a charged particle moving normal to a magnetic
field experiences magnetic lorentz force due to which the particle moves in a circular path.
Construction
It consists of a hollow metal cylinder divided into two sections D1 and D2 called Dees,
enclosed in an evacuated chamber (Fig ). The Dees are kept separated and a source of ions is
placed at the centre in the gap between the Dees. They are placed between the pole pieces of a
strong electromagnet. The magnetic field acts perpendicular to the plane of the Dees. The Dees
are connected to a high frequency oscillator.
Working:
When a positive ion of charge q and mass m is emitted from the source, it is accelerated
towards the Dee having a negative potential at that instant of time. Due to the normal magnetic
field, the ion experiences magnetic lorentz force and moves in a circular path. By the time the
ion arrives at the gap between the Dees, the polarity of the Dees gets reversed. Hence the particle
is once again accelerated and moves into the other Dee with a greater velocity along a circle of
greater radius. Thus the particle moves in a spiral path of increasing radius and when it comes
near the edge, it is taken out with the help of a deflector plate (D.P). The particle with high
energy is now allowed to hit the target T. When the particle moves along a circle of radius r with
a velocity v, the magnetic Lorentz force provides the necessary centripetal force.
Bqv =mv2 / r
∴ v/r =Bq/m
The time taken to describe a semi-circle
t = π r /v = π m /Bq
It is clear from equation (3) that the time taken by the ion to describe a semi-circle is independent
of (i) the radius (r) of the path and (ii) the velocity (v) of the particle hence, period of rotation
T = 2t = 2 π m /Bq
So, in a uniform magnetic field, the ion traverses all the circles in exactly the same time. The
frequency of rotation of the particle,
υ = 1/T = Bq/2πm
If the high frequency oscillator is adjusted to produce oscillations of frequency as given in the
last equation , resonance occurs.
Cyclotron is used to accelerate protons, deuterons and α - particles.
Limitations
(i) Maintaining a uniform magnetic field over a large area of the Dees is difficult.
(ii) At high velocities, relativistic variation of mass of the particle upsets the resonance condition.
(iii) At high frequencies, relativistic variation of mass of the electron is appreciable and hence
electrons cannot be accelerated by cyclotron.
Reactor produced radionuclide:
Fission &electron capture reaction:
Radionuclide generator:
Milking process:
Linear accelerator:
Radionuclide used in
medicine and technology: