Download Nucleus and Radioactivity

Nucleus and Radioactivity
The Nucleus
The first step forward from Dalton's indivisible atom was the discovery of the electron. Its
charge and mass were determined by Millikan and J.J.Thomson. It was also known that all atoms
other then those of hydrogen had more than one electron. Thomson suggested that the atom was a
sphere of positive charge and mass uniformly distributed with electrons embedded in it like plums in a
plum pudding. This model however, failed to explain the coexistence of positive and negative charges
in the same space.
Rutherford and his co-workers projected high speed particles at atoms under investigation and
measured deflections of the projectiles due to their interaction with the target atoms. From these
measurements conclusions were drawn.
Geiger and Marsden’s experiment
Since particle accelerators were yet to be developed, naturally occurring high energy particles
were used as projectiles. Alpha particles are spontaneously emitted by certain heavy elements.
These particles have speeds of the order of 107 m/s and energies of about 8 MeV. These were made
incident on thin films of metals of high atomic weight, such as gold.
A fine beam of alpha particles from a radon tube in a lead block was allowed to impinge on a
thin gold foil placed behind which was a fluorescent screen kept at the focal plane of a microscope.
The arrangement was enclosed in an evacuated container. Scintillations were produced at each point
of impact of alpha particles with the fluorescent screen.
It was found that a great number of particles struck the screen in the direction indicated by the
arrow A. When the screen was displaced to positions such as B and even C, it still received alpha
particles though much fewer in number.
This indicated that only a small percentage of the incident particles came under the influence
of very strong repulsive forces and therefore suffered large deflections. Rutherford found that the
percentage of alpha particles deflected through an angle
was directly proportional to cosec4( /2).
The results of the alpha particle scattering experiment were completely inexplicable in terms of
the existing atom model. If positive charge is distributed throughout the sphere then the charge
density is low and the field strength E at a point inside the sphere distant r from the centre would be
directly proportional to r as shown below.
Let
a = radius of atom
Q = charge on atom
The electric field E is therefore directly proportional to x.
At points very close to the centre of the atom, since the whole positive charge of the atom does
not repel, the electric field strength would be too weak to cause a large deflection of the alpha
particle.
The entire charge on the atom would repel only for distances greater than the atomic radius.
But for distances as large as this the force of electrical repulsion could not be so high as to deviate
the alpha particle through obtuse angles. Hence the large deviations observed in the experiment
cannot be explained based on uniform charge distribution in the atom. Calculations based on this
principle to find the number of alpha particles deflected through any angle produced results which
did not agree with experimental findings.
To account for this discrepency Rutherford concluded that the positive charge was not
distributed over the sphere of diameter in the range of 10 -10 m, which was the atomic diameter. It was
concentrated in a much smaller volume which he called a nucleus. When an alpha particle
approaches the nucleus, the entire concentrated positive charge of the atom exerts a large force of
repulsion on it even when distances are much smaller than the atomic radius. Thus large deflections
are possible.
Assuming that the repulsive force on the alpha particle was governed by an inverse square
law, the calculated percentage of alpha particles deflected through a given angle agreed with the
observed value only if the inverse square law was applicable for distances of approach right down to
values of 10 -14 m, i.e. 1/10,000 of the atomic radius.
The Rutherford model of the atom therefore contains the positive charge in a nucleus whose
diameter could not be greater than 10-4 times that of the atom. Since the electron was already known
to be a very light particle, the mass of the atom was also concentrated at the nucleus. To explain the
coexistence of positive and negative charges within the atom it was postulated that electrons orbit
around this nucleus at such speed that the electrostatic attraction of the nucleus on the electron is
offset by the centrifugal force on the orbiting electron.
Size of nucleus
Similar experiments conducted on a large number of nuclei of various elements showed that the
nucleus is no larger than 1/20,000 to 1/200,000 of the size of the atom. Since atomic diameters are of
the order of 10-10 m, the diameter of the nucleus is of approximate value 10-14m.
Composition of nucleus
The basic fundamental particles contained in the nucleus are protons and neutrons In
a neutral atom the number of orbiting electrons is equal to the number of protons in the
nucleus which is called the atomic number Z. The number of neutrons N is called the
neutron number.
The sum of the atomic number and the neutron number is called the mass number or
nucleon number A
A=Z+N
Chemical properties of an element are dependent on the number of orbiting electrons
which in turn depend on the atomic number Z. Hence atoms having the same number
of protons are deemed to be of the same element. The neutron number does not
determine the chemical properties. Atoms having the same atomic number but different
neutron numbers are called isotopes.
Mass spectrograph
A device that detects the presence of isotopes and determines the mass of the
isotope from the known mass of the common or stable isotope is called a mass
spectrograph.
Singly ionized atoms from a source are narrowed to a fine beam by means of the two
slits S1 and S2 and enter into the region between S2 and S3. An electric field E and a
magnetic field B are maintained perpendicular to each other and to the beam of ions so
that the deflections of the beam caused by these two fields are in opposite directions
as given by Fleming's Left Hand Rule. The electric field E exerts a force EQ on each
ion regardless of its velocity while the force BQv due to the magnetic field B is directly
proportional to the velocity of the ion. Only ions of a unique velocity given by
EQ = BQv
i.e. v = E/ B
will be undeviated in this region which is called the velocity selector.
These ions enter through the slit S3 into the main body of the spectrograph where
a uniform magnetic field B' acting perpendicular to the ion path makes the ions
experience a Lorentz force of magnitude Bqv sin 90o, in a direction which alters so as
to remain always perpendicular with the velocity. This force constrains the ions to
move in a semicircle and strike the fluorescent screen at a point say P.
where v is the velocity of every ion entering the region of magnetic field B' through the
velocity selector and is given by
Since the strengths of the magnetic fields B and B' and the electric field E are
constants and since every ion entering the spectrograph contains the same amount of
charge q, therefore,
where k is a constant.
Thus the radius r of the curved path described by the ion is directly proportional
to the mass of the ion. Thus, if ions of masses m and m' strike the screen at points P
and P'
then,
Since S3P' and S3P are measurable and m is known, m' can be determined
Density of the Nucleus
The various scattering experiments performed indicate the approximate radius of nuclei of
different elements. The radius r is found to depend on the mass which in turn depends on the
mass number A. It is found that the radius is approximately given by
r = ro x A 1/3
where ro is the same constant for nucleii of all elements.
The volume V, being proportional to r3 is given
But V is the volume and A the mass number of the nucleus. This shows that the density of all
nuclei is more or less constant.
Angular Momentum
The particles in the nucleus are in motion and therefore the nucleus has an angular
momentum associated with it. This angular momentum is quantized just as the angular
momentum of the electrons is quantized.
Magnetic Moment
The spin of the nucleus constitutes circulating charge. Since a circular loop of current
is equivalent to a magnet, the nucleus has a magnetic moment.
Forces within the nucleus
Other than the electrostatic repulsion between protons, there exists an attractive
force between nucleons. This is called strong interaction and is unique to the nucleus.
It acts on charged particles as well as on uncharged ones. Its range is far smaller than
that of the electrostatic repulsion. But within this range its effect is much greater than
that of the electrostatic force. This force binds a nucleon with other nucleons in its
immediate vicinity unlike the electrical force with which a proton repels all other protons
in the nucleus. The strong interaction force attains saturation within a closed group of
nucleons. This force appears to favour the binding of pairs of particles such as two
protons with opposite spin or two neutrons with opposite spin and of pairs of pairs i.e. a
pair of protons with a pair of neutrons. Thus the alpha particle which is a helium
nucleus (2He4) has a very stable nuclear structure.
The graph above shows that there is a narrow band of stability for pairs of values of
neutron no. n and proton no. Z. Firstly, this does not imply that every pair of values of n
and Z lying within this band represents a stable nucleus. Only certain pairs of values of
n and Z yields stable nuclei. Some of these possible values are indicated by the dots in
the figure. However, beyond the limits of this band no stable nucleus is possible at all.
For light nuclei N=Z yields stability. Equal numbers of protons and neutrons provide
nuclear stability as the strong force favours pairs. For nuclei containing larger numbers
of protons, this is not the case. The binding force decreasing more rapidly with
increase of distance cannot be equal to the repulsive Coulombian repulsive force
which decreases at an inverse square rate. Hence stability favours those nuclei having
smaller electrical repulsive forces. This is true of nuclei having fewer protons than
neutrons. The highest neutron proton for stability is 1.6.
No nucleus having mass number greater than 209 is stable. No nucleus of proton
number greater than 82 is stable. If the number of protons is too high then electrical
repulsion becomes too high for stability and if the number of neutrons is too high then
not enough of them are paired with protons to yield stability. Such nucleii do however
exist in nature but their life spans are limited. With the passage of time more and more
of these nucleii are naturally disintegrating by a process called radioactivity. The
heaviest naturally ocurring element is Uranium (Z=92). Nucleii of elements with higher
atomic number are so highly unstable that they disintegrate immediately on production.
These are called transuranic elements. They are not to be found in nature but can be
produced in the laboratory for scientific useage.
If similarly charged drops of mercury are brought together against their mutual
electrical repulsion then an external agent would have to do work to combine them into
one large mercury globule which would therefore have much higher electric potential
energy than the separate small droplets did. But as soon as the external forces holding
the globule together are removed, the globule would fly apart into charged droplets
reducing their potential energy.This is exactly what should be happening to the protons
in the nucleus except for the fact that when they are pushed close enough together by
the external agent, the very strong attractive forces - the strong interaction - takes over
control and pulls all the particles even closer together binding them into a stable
nucleus. Till the particles come within range of the strong interaction, the external
agent would do work and the system's potential energy would increase by a certain
amount. But once within range of the strong force, the system's force now does a much
greater amount of work and the system loses this much greater amount of energy than
it had previously gained. Thus the formation of a nucleus involves a substantial net
loss of energy of the system. That is to say that a system of nucleons apart from each
other has more potential energy than a formed nucleus. This accounts for the stability
of the nucleus.
Thus if the nucleus is to be separated into its constituent particles then this
difference in energy has to be supplied to it. This is called the binding energy of the
nucleus.
The binding energy per nucleon is the total energy required to separate all the
nucleons from each other divided by the number of nucleons. Those elements which
have a high binding energy per nucleon have also a high nuclear stability. Thus binding
energy per nucleon is a measure of nuclear stability.
The graph below shows the variation of binding energy per nucleon with respect
to the mass number of the element. It shows that other than for nuclei lighter than
carbon12, the binding energy per nucleon is fairly constant and in the range of 8 MeV.
The peak of the curve is at mass number 56 which is iron. Iron has therefore nuclei of
greatest stability. Among the lighter nuclei, helium and carbon12 show great stability.
Mass Defect
In all atoms of stable nuclei whether heavy or light, whether metal or non metal, whether solid or
liquid or gaseous, the mass of the nucleus is always less than the total mass of its constituent
particles. The difference between the nucleon mass and the nuclear mass is called the mass defect.
This mass defect is a measure of the binding energy of the nucleus. The greater is the excess of the
nucleon mass over the mass of the nucleus, the more stable the nucleus and the more the energy
required to break it up into parts.
The a.m.u.
The atomic mass unit (amu) is a conveniently small unit for measuring masses of subatomic particles.
1 amu = 1/12 of the mass of a carbon 12 atom
mass of 6.023 x 1023 atoms of C12 = 12 x 10-3 kg
It is known that mass is a form of energy ,i.e. when a mass m disappears in its place there appears
energy of the amount
E = mc2 (Einstein's relation)
where c (= 3 x 108 ms-1) is the speed of light in vacuum.
Therefore, energy equivalent of a mass of 1 amu =
Since, 1 electron volt of energy = 1.6 x 10-19 joule,
The binding energy of a nucleus is therefore its mass defect in amu multiplied by 931 MeV/amu.
Energy Levels
The internal motion of the nucleons within the nucleus corresponds to energy levels. Each
nucleus has a state of lowest energy (ground state) and several permitted excited states. In ordinary
condition, or in the process of a chemical or a physical change the nucleus remains in its ground
state. It may be placed in an excited state either by the release of a radioactive particle ( or ), or by
the bombardment by high energy particles. It then stabilizes by the release of a gamma photon of
characteristic frequency.
Since gamma rays are of wavelengths of the order of 10 -12 m and lower, the excitation
energies of the nucleus are of the order of Mega electron volts as shown below:
Nuclear excitation energies are therefore a million times as high as excitation energies of electrons in
orbits which are of the order of electron volts.
Numericals
1. In mass spectrograph ions of the same charge and velocity with mass numbers 35 and 37 enter a
uniform magnetic field. The radius of circular path for ions of mass number 35 is found to be
0.45 m. Calculate the radius of the path due to the ions of mass number 37.
[0.48
m]
2. Find the binding energy per nucleon of [a] carbon-12 and [b] carbon-14 given that neutron mass =
1.00898 u, proton mass = 1.00759 u, C12 mass = 12.000000, C14 mass = 14.003242 u and 1u
=931 MeV. Which isotope of carbon is expected to be less abundant in nature and why?
[7.71 u and 7.59 u]
Radioactivity
As indicated in the graph of neutron number vs. proton number for stable nuclei, no nucleus of
atomic number greater than 82 is stable, whatever be the neutron number. These nuclei release
energy spontaneously either in the form of high speed particles called alpha particles or beta
particles, or in the form of photons of high frequency electromagnetic radiation called gamma
radiation. This spontaneous release of energy from the nucleus is called radioactivity. Only unstable
nuclei are radioactive. For elements of atomic number higher than 82, all isotopes are unstable and
therefore radioactive. For elements of atomic number less than 82 the commonly available isotope is
stable but certain rare isotopes may be radioactive as they are unstable e.g. carbon14.
If an isotope X of an element is radioactive (i.e. unstable), the nucleus of every one of its
atoms will release energy in the form of a particular type of radioactive radiation which will be the
same for all the nuclei, but will not happen at the same instant of time. There is no particular order in
which nuclei release energy. One nucleus may release energy at a certain time while another one in
close proximity may release energy a million years later. Hence the process is completely random in
terms of the time of release of energy by a particular nucleus. While we can make no concrete
predictions about a particular nucleus, we can accurately predict the behaviour of a radioactive
sample containing a large number of nuclei over a large period of time.
The number of disintegrations(nuclear energy releases) per second from the different atoms of
a particular radioactive isotope is found to depend on the total number of such nuclei present in the
sample. Thus from samples which are massive there are a large number of energy releases per unit
time. Hence the number of nuclei left undisintegrated becomes steadily smaller. This in turn reduces
the number of disintegrations in the next unit of time. The number of disintegrations per unit time is
called the activity of the source. The activity of any source therefore diminishes with the passage of
time.
The activity of the source is however quite independent of physical conditions such as
temperature, pressure, surface area, surrounding medium, etc, and of chemical conditions such as
whether the source is in chemical combination with other elements or is free in nature.
Property
Alpha
Beta
Gamma
Charge
+ 3.2 x 10-19 C
+ 1.6 x 10-19C
0
Mass
approximately 4 amu i.e. equal to that Rest mass equal to that Rest mass = 0
of a helium nucleus
of electron i.e. 1/1836
of mass of proton
Velocity
Up to a maximum of 10% of the
speed of light
Speed just after emission is
characteristic of the source
Up to a maximum of
99% of the speed of
light
3.0 x 108ms-1 in
vacuum
Speeds are not
characteristic of the
source
Energy
1/2 x mv2
Up to a maximum of 8 MeV
1/2 x mv2
Up to a maximum of 1
MeV
=hxf
of the order of
MeV
Ionization of air
Very high
1/100 as high as
1/100 as high
as
Penetration of
matter
Least. Stopped by a postcard. Range
in air at normal pressure is a few
More than alpha.
Maximum.
Stopped by lead sheets Stopped by lead
centimetre due to loss of energy by
high rate of ionization
blocks.
Fluorescence on Maximum
ZnS etc.
Less
Least
Deflection in
electric field
Towards negative plate
Towards positive plate
(if beta negative)
Undeviated
Deflection in
magnetic field
Deviated as per Fleming's left hand
rule
Deviated as per
Undeviated
Fleming's left hand rule
Effect on photographic plates
Plates are exposed.
Plates are exposed
Plates are
exposed
Alpha emission
Alpha
particles
are
fast
moving
helium
nuclei
(2He4)
Alpha emission reduces atomic number of the parent nucleus by 2 units and mass number by 4 units
to form the daughter nucleus.
A
ZX
= 2He4 + Z-2YA-4 + Energy
Mass is not conserved in this process. The mass of the nucleus X is higher than the sum of the
masses of the nucleus Y and the emitted alpha particle. This excess of mass is converted into energy
(E=mc2). The principle of conservation of energy is still valid for this change.
This disintegration energy is equal to the sum of the kinetic energies of the daughter nucleus Y
and the alpha particle in accordance with the laws of conservation of energy and momentum. The
nucleus Y being much heavier than helium acquires the lower velocity. Hence the kinetic energy of
the alpha particle is almost equal to the energy of the disintegration. Thus alpha particles from a
particular source are of a characteristic constant velocity at the instant of emission.
X being a heavy nucleus must have had more neutrons than protons. Alpha release reduces
both neutron number and proton number by two units each. Two neutrons is a smaller percentage of
the neutrons present than of the protons present. Thus the daughter nucleus is left with a higher
percentage of the original number of neutron and a lower percentage of the original number of
protons. The neutron-proton ratio of the daughter nucleus is therefore higher than that of the mother
nucleus.
Beta emission
Beta particles are fast moving electrons. Some beta particles are positrons (i.e. + 1e0)
Beta emission does not change the mass number. Emission of beta negative increases the atomic
number by 1 unit. In case of the comparatively rare emission of the beta positive, the atomic number
decreases by 1 unit.
A
A
0
ZX = Z + 1Y + -1e + energy
Beta particles are not orbiting electrons as these have energies of the order of electron volts
while beta particles have energies of the order of 105 electron volts. Beta particles are produced in
the nucleus. A neutron changes into a proton and an electron which is immediately emitted. The
mass of a neutron is greater than that of a proton. The excess in mass is converted into energy
(E=mc2).
0n
1
= 1H1 + -1e0 + energy
In the case of beta positive,
1
1H
= 0n1 + +1e0 - energy
Stability therefore favours the emission of beta negative particles
In the process of beta emission a third particle called a neutrino or an antineutrino is also
produced. This particle has zero rest mass. However energy may be distributed in a variety of ways
between the three particles produced. This is why beta particles from a particular source can have a
variety of speeds.
Beta negative emission involves the conversion of a neutron into a proton. It therefore reduces
the neutron-proton ratio.
Gamma emission
Gamma radiation consists of photons of electromagnetic radiation of high frequency. When
alpha emission or beta emission leaves the daughter nucleus in a higher permitted energy level, the
nucleus stabilizes to the ground state by the emission of one or more gamma photons. Thus gamma
rays of different but characteristic frequencies are emitted by a particular isotope, as the energies are
quantized.
Gamma emission does not change the mass number nor the atomic number of the nucleus.
Radioactive Series
Alpha or beta emission leaves behind a daughter nucleus of a different element since its
atomic number is different. In case this nucleus also has an atomic number higher than 82, it is
unstable and will stabilize by alpha emission or beta emission which may be followed by gamma
emission to form yet another element. Thus starting with any radioactive nucleus, a whole series of
nuclear transformations may be set up. The series ends only when the daughter nucleus that results
has an atomic number 82. Such a series is called a radioactive series.
In such a series of radioactive elements there are emissions of alpha particles and of beta
particles. Of these radioactive emissions, only the alpha emission changes the mass number of the
daughter nucleus. Thus, if a radioactive transformation of the nucleus changes the mass number at
all, it changes the same by 4 units at a time. Hence if any one element in the chain has a mass
number which is a multiple of four, then the mass number of every element in the series is a multiple
of four. This series is called the 4n series (n is a natural number). There are three more series called
the (4n+1) series, the (4n+2) series and the (4n+3) series. Of these series, the last one starts with
Uranium 235, a rare isotope of uranium. The 4n series beghins with Thorium 232. The (4n+1) series
is an artificially induced series commencing with neptunium Np237 which is not found in nature but is
produced in reactors. This series ends with bismuth 209.
The more common Uranium series is shown diagrammatically below.
The graph shows the U238 series in terms of neutron number and proton number (i.e. atomic
number). Note that in this series there are isotopes of several elements such uranium (U 238 and U234),
Polonium (Po218, Po214 and Po210) etc.
Note also that in this series Bi 214 shows branching. That is, some nuclei of this isotope emit
alpha particles and change into Tl210 and then Tl 210 emits a beta particle and becomes Pb210. Other
nuclei of the same isotope Bi214 emit beta particles and change to Po214 and then Po214 emits an
alpha particle and becomes Pb210.
Other than Bi214, if one nucleus of a particular isotope is alpha emissive then every nucleus of
that isotope is alpha emissive. Thus every nucleus undergoes the same change converting into
identical daughter nuclei. But it is not fully understood why there may be a long interval of time
between identical nuclei disintegrating in identical manner.
One nucleus cannot simultaneously emit more than one particle.
Activity of a radioactive substance
The number of radioactive particles or photons emitted per unit time is called the rate of emission, or
the activity. As already stated, the rate of emission depends only on the number of atoms of that
particular isotope present in the radioactive deposit. This dependence is found to be linear. That is,
the activity is found to be directly proportional to the number of nuclei present.
where N and t are variables, N being a function of time, and Noand are constants. is called
the decay constant of that isotope. The number of nuclei present decreases exponentially with time.
In a particular time t = T, let half the original number No of the nuclei disintegrate. i.e. at t = T, N=No/2
Substituting these values of the variables N and t, we have
Since is a characteristic constant for a particular isotope of the radioactive element, it follows
that this time T is also a characteristic constant for this isotope. This characteristic constant is called
the half life of the isotope. The half life is a convenient index of how rapidly the exponential fall
occurs.
The half life of a radioactive isotope is the characteristic constant time in which half of any
given number of nuclei of that isotope will disintegrate in identical manner.
Thus if in time T, half of N number of atoms disintegrate then N/2 remain undisintegrated, so
that in the next span of time T only half of N/2,i.e. N/4 atoms disintegrate. Note that in equal spans of
time T it is not equal numbers of atoms disintegrating, but equal fractions of the existing number of
atoms disintegrating. As time passes, the number of atoms left becomes smaller. Accordingly the
number of atoms disintegrating in the same span of time (T) becomes smaller.
A graph of the existing no. of atoms with respect to time is shown below.
Since the activity
is proportional to this number N, a graph of activity vs. time would be of the
same shape.
Since the mass m of the deposit is proportional to the number of atoms present, a graph of
mass vs. time will also be of the same shape.
If in a given time t1, the number of atoms (or the activity, or the mass) drops to 1/2n of its
original value, then, substituting these values for the variables N and t in the decay equation, we
have,
In every T units of time the activity drops to half the existing value.
Therefore, in time t1, if the activity (or the number of atoms, or the mass) drops to 1/2n of its original
value, then t1 is n number of half lives which are all equal.
But since alpha particles and beta particles are far too small to be visible, how do we find out
how many of them are being emitted in a given time? It is true that the eye cannot detect radioactive
radiations but there are gadgets that can. One such device is the Geiger Muller Tube. Yet another is
the solid state detector. A third device which can be used to either detect ionizing radiations or to
study their tracks is the Wilson Cloud Chamber.
Geiger Muller Tube
This device detects ionizing radiations that are able to enter through the thin mica window. The
inner metal lining of the cylinder is earthed. The thin axial wire is maintained at a potential of around
400 V positive with respect to the metal lining. In the event of the entry of an ionizing particle, argon
undergoes ionization. The electrons thus produced accelerate at a high and non uniform rate towards
the axial wire. The closer their approach to the wire, the greater is the acceleration in this stronger
field. As these electrons approach the wire they ionize repeatedly by collision. The positive ions
accelerate at a low and decreasing rate towards the areas of weaker electric field outward from the
wire. These ions do not have enough energy to ionize argon or bromine by collision. Successive
ionizations are therefore caused only by the electrons and they therefore occur closer and closer to
the wire and the electrons thus produced are all swept to the wire thereby triggering a discharge
through the extrernal circuit while the heavy positive ions are still in the process of moving outwards.
Metals however have very low ionization energies and thus may release electrons when the positive
ions reach the cathode. This would make the entire process start afresh thus preventing the detection
of the entry of the next ionizing particle through the mica window. To prevent such an occurrence, the
discharge needs to be quenched. This is the function of the trace of bromine vapour present in the
tube.
Thus the entry of each ionizing radiation triggers off a single pulse of discharge and the
counter attached to the tube indicates the rate of entry. This in turn indicates the number of atoms
present in the radioactive deposit.
In order to determine whether the deposit is alpha emissive or beta emissive or gamma
emissive, the mica window may be covered with a sheet of aluminium, which will eliminate alpha
particles, or a sheet of lead which will eliminate both alpha and beta particles.
Solid State Detector
This is a pn junction in reverse bias. The majority carriers would not carry current in this setting
but the minority carriers would. The ionization produced by a radioactive radiation creates more
electron hole pairs which move under the influence of the applied potential difference setting up a
discharge pulse. This detector is especially effective for alpha particles.
Wilson Cloud Chamber
This is used generally to study or photograph the tracks of ionizing radiations though it can also be
used as a detector of such radiations.
When the piston is suddenly moved down, the resulting adiabatic expansion causes cooling.
This makes the alcohol vapour condense on dust particles which then settle downwards. The dust
free air is then subjected to a controlled expansion causing super saturation and the air is
simultaneously exposed to radiations from a source. Droplets of liquid immediately condense around
the ions left in the wake of the alpha particle. The tracks become visible under strong illumination.
Alpha tracks are long and straight, and of length characteristic of the source. Compared to high
speed alpha particles, low speed ones cause shorter but thicker tracks, that is per unit length of path
in air they produce more ionization as they take a longer time to cover each unit length of path.
Beta tracks are thinner than alpha tracks due to less ionization. They are also irregular in
shape due to collisions with gas molecules.
Gamma radiation tracks are themselves invisible. These radiations interact with matter to
produce a pair of equally charged prticles - a positron and an electron. This pair of charges together
add up to zero - charge is therefore conserved. The total rest mass of the two particles is created out
of the energy of the gamma ray photon. These particles cause visible tracks by ionization.
Radiation units
The activity of a source is measured in the unit Curie (C). One Curie is the activity of a material
which undergoes 3.7 x 1010disintegrations per second. This is approximately the disintegration rate of
1 gram of radium.
Radiological dose is measured by the charge of either sign produced by the radiation in 1 kg of air. If
this charge produced per kg of air is 258 micro Coulomb then the radiological dose is one Roentgen.
Safety precautions
Exposure to radioactive radiation causes burns and destruction of cells, initiates diseases,
affects functioning of living cells and may even cause genetic changes. The effect of such radiations
is cumulative. Hence it is essential to take adequate safety precautions against overexposure.







All sources must be weak (activity less than 10 micro Curie)
All sources must be sealed in foil and placed in lead lined containers in cupboards remote from
the working area.
Sources must be handled with forceps and held away from the body.
There should be no eating drinking or smoking in the laboratory where such sources are in
use.
Radium sources must be carefully sealed to prevent leakage of alpha active radon gas (see
uranium series graph). Other alpha emissive sources are less dangerous because of the small
range of alpha particles.
A thickness of a few millimetres of lead gives complete protection from beta particles.
Great care should be taken when using gamma sources. These must be as weak as possible
for even lead lined gloves or lead lined suits are not adequate protection.
Uses of radioactive radiations
For practical considerations, radioactive nuclei may be classified into four groups.
Firstly, naturally occurring elements of long half life (of the order of 106 years or more) that have been
present since the formation of the earth. e.g. Uranium 238, Uranium 235, Thorium 232. These
elements are alpha emissive and ultimately disintegrate into lead. Potassium 40 also of very long half
life disintegrates into argon by beta emission. These elements are useful in dating geological
specimens using a method similar to radiocarbon dating described in the following section.
Next, those that are being produced continuously by the disintegration of other elements and are
themselves disintegrating with a smaller half life into other elements so that the production rate
balances the decay rate. e.g. Thorium 230 and Radium of half lives of the order of 103 or 104 years.
These are useful for determining the chronology of seciments on the ocean floors.
Thirdly, those produced in nature by the bombardment of stable nuclei by cosmic rays, e.g.
Tritium,Carbon 14 etc.
For example, atmospheric nitrogen bombarded by fast neutrons disintegrates into carbon 12 and
tritium which is radioactive and has a half life of 12.5 years and can therefore be used for dating water
samples.
Finally, those artificially produced by bombardment of stable nuclei by accelerated
particles. Examples of these are cobalt 60, sodium 24, iodine 131 etc. These are produced for a
variety of specific uses as described below:
In agriculture artificially produced isotopes are used in pest control by gamma sterilization and
in the production of crop mutations to obtain high yield.. They are also used to test absorption rate of
fertilizers by radioactive tracers. A small amount of radiophosphorus may be injected into the stem
along with the phosphate fertilizer, this circulates in the plant and its progress may be ascertained by
the use of a counter held externally.
In industry they are used to locate flaws in casting or welding, to locate cracks in dams. They
are also used to test thickness of sheets of rubber plastic or polythene by beta absorption.
In medicine they are used for diagnostic purposes such as the use of radio sodium tracer for
locating constrictions in the circulatory system. Radio iodine is also absorbed selectively by malignant
tumours which are then located by the use of a counter. They are also used for therapeutic purposes.
Gamma rays from cobalt 60 are used to treat cancer.
Radiocarbon dating
Bombardment by slow neutrons causes atmospheric nitrogen to disintegrate into carbon 14 and
hydrogen 1
7
N 14 + 0 n 1 = 6 C 14 + 1 H 1
Carbon 14 is radioactive. By the emission of a beta particle it disintegrates into nitrogen with a half life
of approximately 5600 yr
6
C 14 = 7 N 14 + -1 e 0
Due to the ongoing processes of formation and disintegration, the small percentage of carbon
14 that exists with ordinary carbon 12 has been more or less constant in the atmosphere. Plants
absorb this fixed ratio of radio carbon atoms in the form of carbon dioxide and all living organisms
absorb the same ratio of radio carbon either directly or through plants. All living things have therefore
the same fixed proportion of radio carbon among the normal carbon 12 atoms in chemical
combination in their systems. When the organism dies there is no forther absorption of carbon of
either variety but while the carbon atoms of both types undergo chemical reactions in the process of
decomposition, the carbon 14 atoms also continue to disintegrate by beta emission into nitrogen.
Carbon 12 does not undergo any nuclear change. Thus the ratio of carbon 14 atoms to carbon 12
atoms steadily decreases. Measurement of this ratio from a sample of the remains reveals the time
elapsed since the death of the organism.
Numericals
1. A radioactive source has decayed to 1/128 of its initial activity in 50 days. What is the half life?
[ 7.1 days]
2. Energy from the decay of unstable radioactive isotopes is sometimes used where a continuous
powerful but compact energy source is required. Such isotopes have been used to provide power
for pacemaker batteries and for scientific apparatus used in space vehicles. Given that
Polonium210 has a half life of 140 days and emits alpha particles each of energy 5.3 MeV, find
the mean power output per gram of Polonium 210 during the first half life. (Avogadro’s number is
6 x 1023 molecules per mole). Will the average power production be lower, higher or the same
during the next half life?
[100W]
3. The half-life of polonium is 3 minutes. Starting with a sample of 32 grams of polonium, note down
in a table the amount of polonium left after every three minutes. Plot the decay curve on graph
paper and from it find the amount of polonium left after 13.5 minutes.
[1.5 g]
4. Calculate the velocity of an alpha particle which will have the same kinetic energy as the energy
of a photon of gamma radiation of wave length 4.5 x 10-13 m.
(h = 6.62 x 10-34 J s, mass of alpha = 6.62 x 10-27 kg and c = 3 x 108 m s-1)
[1.15 x 107 ms-1]
Transmutation
Transmutation is the change of the proton number of a nucleus, that is, a nucleus of one
element becomes that of another element by the emission of a particle from the nucleus or the
capture of a particle into the nucleus. Transmutations occur naturally in the process of alpha emission
and beta emission from a radioactive nucleus. Transmutations may also be artificially induced by
bombarding a nucleus with a particle such as deuteron, proton, neutron or electron.
Positively charged particles used for bombardment have to be accelerated to very high
velocities to overcome the electrical repulsion of the nucleus under bombardment. While electrons
are not repelled by the nucleus, the low mass reduces their effectiveness in transmutation reactions.
Neutrons are convenient to use as bombarding particles due to their high mass and lack of charge.
The entry of a bombarding particle into the nucleus excites the nucleus by adding energy to it
and disturbs the existing arrangement of the nucleons. This results in the nucleus stabilizing by the
emission of particles or of gamma rays.
In the event that charged particles are to be used in a transmutation reaction, these have to be
accelerated to very high velocities. This is achieved by the use of particle accelerators such as a
cyclotron.
Cyclotron
This is a device that can accelerate charged particles to energies of the order of 10 MeV. The
device uses a magnetic field to guide and an electric field to accelerate repeatedly a beam of charged
particles. The core of the cyclotron is a hollow copper cylinder cut into two halves along a diameter of
the circular cross section. The two halves, called 'Dees' because of their shape, face each other
along the diametral gap. They are enclosed in a hollow evacuated steel cylinder but electrically
insulated from it.
The whole apparatus is placed between the poles of a powerful electromagnet providing a
magnetic field perpendicular to the plane of the dees. The dees are connected to a high frequency
a.c. source creating a changing electric field across the gap between them. The interior of the dees is
thus subject to the magnetic field but free of the electric field due to the electrical shielding effect of
the metallic dees.
Consider an ion of charge +Q and mass m introduced from an ion source S centrally located in
the gap between the dees, at an instant when the dee D 1 is positive. The ion accelerates to a velocity
say v1 as it enters into the dee D2 in a direction perpendicular to the magnetic field. Thus it describes
a semi-circular path inside the dee. If r1 be the radius of this path, then,
Since the right hand side of the equation is a constant, any change in the speed v of the
particle must change the radius r of its track in the same ratio. Every time the particle crosses the gap
between the dees, as it is accelerated by the electric field to a higher speed, so the radius of the path
increases.
As the ion emerges into the gap, the polarities of the supply reverse making D 1 negative and
thus accelerating the ion to a velocity v2 as it enters into the interior of the dee D1 wherein it again
describes a semi-circular path under the effect of the magnetic field. If r2 be the radius of this path,
But this is the constant angular velocity of the ion inside the dees. Thus the time required to
cover each such semicircular path is a constant as increase of speed caused by the electric field
results in the radius of the path increasing in the same ratio.
The time t required to cover the semi-circular path is given by
The time required thus depends only on the strength of the magnetic field and the specific
charge of the particle under acceleration. The supply frequency is adjusted to such a value that this is
the half time period of the cycle.
The particle thus spirals outwards gaining in speed each time it crosses the gap. A plate P
charged to an electrostatic potential deflects the ion through a gap in the periphery and directs it on to
the target nucleus.
The limitations of this particle accelerator are :
i.
ii.
the introducing of the ion at the right phase of the a.c. cycle is difficult to achieve.
At very high speeds the relativistic mass increase causes an increase in the time required thus
resulting in particle revolutions going out of phase with the a.c. cycle.
Artificial Transmutation
Artificial transmutation reactions are usually named according to the bombarding particle and the
emitted particle. For example, the following disintegration is an n-p reaction:
14 + n1 = C14 + H1
7N
0
6
1
Given below is a d - reaction
16 + H2 = N14 + He4
8O
1
7
2
The following is a p - reaction
7
1
2
4
4
3Li + 1H = He + 2He
It should be clearly understood that there is an essential difference between a nuclear reaction and a
chemical reaction. In the latter case the nucleus remains unchanged while only the peripheral
electrons are shared in a different mode. Thus in this type of reaction the total mass of the reactants
is always equal to the total mass of the products. In case the reaction is exothermic, it is the chemical
energy that is converted into the heat energy released. In case of a nuclear reaction an entirely
different element is produced. The total mass of the reactants exceeds that of the products, the
difference in mass being the source of the energy released.
In each of the following nuclear reactions, the number of nucleons in the reactants and that in
the products are necesarily equal. Thus the total nucleon mass of the reactants and that of the
products are equal. But each nucleus has a mass less than the total mass of its nucleons. The
nuclear masses are not equal on the two sides of the equations.
226 =
222 + He4
88Ra
86Rn
2
14
6C
2
1H
= 7N14 + -1e0
+ 1H3 = 2He4 + 0n1
235
92U
+ 0n1 = 57La148 + 35Br85 30n1
The energy released in the reaction is given by
E = (m1 - m2) x c2
Thus energy released is at the expense of the nuclear mass which must therefore decrease.
The greater the energy released when a nucleus is formed the greater the energy that would have to
be supplied when the nucleus is to be separated into its constituents. That is to say, the greater is the
binding energy of the new nucleus. Such a nuclear reaction is said to be heading towards stability as
a state of lower energy content (higher binding energy) is more stable. Lower nuclear mass implies
higher binding energy since the sum total of these two quantities measured in the same units must
give equal values on both sides of the equation.
As indicated in the sketch graph below, medium weight nuclei have the greatest binding
energy per nucleon, that is, they have the greatest nuclear stability. When the very heavy nuclei
undergo fission into smaller nuclei of medium mass the binding energy increases (nuclear mass
reduces) and the process releases energy. This phenomenon is called nuclear fission.
When the very light nuclei merge together to form medium weight nuclei, the binding energy
increases (nuclear mass reduces) and the process releases energy. This process is called nuclear
fusion.
Nuclear fission
Large nuclei are unstable. Protons at the surface of the nucleus are repelled by a force
proportional to the total number of protons in the nucleus, but attracted towards the interior by a force
proportional to the number of nucleons in its immediate vicinity (which is constant for light or heavy
nuclei). Thus the electrical repulsion sets a maximum limit to the number of protons in a nucleus. The
maximum limit to the number of neutrons is set by the strong force which seeks to bind pairs of
neutrons to pairs of protons. Thus if the neutron excess becomes too large, a neutron spontaneously
changes into a proton. Since very heavy nuclei have too many of both neutrons and protons, they
spontaneously emit tightly bound nuclear sub assemblies (a). This is naturally occurring fission.
Fission may be artificially triggered by bombardment with neutrons. Heavy nuclei break up
under such bombardment into a pair of lighter nuclei () with the release of energy far exceeding the
total kinetic energy of the colliding particles. This excess energy is due to the reduction of nuclear
mass. Furthermore, as the nucleus breaks the fragments fly apart under electrical repulsion and heat
up the environment by collisions with neighbouring particles. The fragments are also in a highly
excited state and its nucleons rearrange into configurations appropriate to medium weight nuclei by
release of gamma radiation. As these medium weight nuclei would have smaller neutron proton
ratios, some neutrons convert to protons by beta emission.
Other neutrons are ejected from the nucleus. These emitted neutrons are of great practical
significance as they bombard other heavy nuclei and the entire process recurs repeatedly. Without
this property of setting up a chain reaction, nuclear fission would be a mere laboratory curiosity but
with this property we are confronted with the problems and the opportunities of our atomic age.
If the chain reaction set up is allowed to proceed unchecked then a vast amount of energy is released
in a small time, that is, it is an atom bomb.
A device that allows the chain reaction to proceed at a controlled rate is a nuclear reactor. Its
most common application is the generation of electrical power. Other practical applications are in the
production of artificial radioactive isotopes for their variety of uses, of high intensity neutron beams for
nuclear research and of transuranic elements (Z>92) such as plutonium. A reactor that produces
transuranic elements is called a fast breeder reactor.
A nuclear reactor operates on an efficiency of approximately 1/3. To generate 1000 Megawatt
of electrical power, the thermal power requirement would thus be 3000 MW.
Energy released per fission is 200 MeV = 200 x 1.6 x 10-13 Joule
Energy required per second is 3000 x 106 Joule
Number of fissions required per second = (3 x 109)/(32 x 10-12)
Since 6.023 x 1023 atoms of U235 weigh 235 x 10-3 kg,
therefore, 3 x 1021/32 atoms weigh
Thus the mass of uranium to be fissioned per second
Thus the mass of uranium to be fissioned per day
To generate the same power from a coal fired plant the coal requirement is approximnately
11,000 tons/day.
Nuclear Reactor
The sketch below shows the essential components of a nuclear reactor in a schematic diagram
Some typical disintegrations occuring in the reactor are
In this reactor, the fuel rods are uranium238 mixed with the fissionable uranium 235 in the ratio
1:140. These are usually alloyed with other metals to maximize heat conductivity and strength and
reduce corrosion. In homogeneous reactors the fuel is uniformly distributed in the form of a salt in a
fluid as a slurry. The control rods are made of a material which readily absorbs neutrons. Commonly
used are cadmium and boron. Their function is to control the reaction rate. By varying the degree of
insertion of these rods the free neutron population can be controlled. They are set so that the rate of
production of neutrons is equal to their rate of absorption and loss by leakage. The reactor is then
said to be 'critical'.
The moderator is a material of low atomic weight which slows down the fast neutrons produced in the
reaction and thus increases the probability of fission. Light nuclei are used so that the neutron
transfers a larger fraction of its kinetic energy in each collision. This is a necessary process as fast
neutrons which are released do not fission but slow neutrons do.
The reflector is a shell completely surrounding the reactor proper. Its function is to reflect the
neutrons back into the reactor. It scatters the neutrons but does not absorb them. It may be made of
the same material as the moderator.
The lead shield is necessary to provent leakage of radioactive radiation.
The coolant is a gas or liquid pumped through the reactor for the purpose of transferring the
generated heat to a boiler or burbine. Common coolants used are carbon dioxide, water, liquid
sodium and helium.
Nuclear fusion
As seen from the graph showing binding energy vs. mass number, when two very light nuclei
fuse to form a single heavier nucleus, the binding energy of the product is higher than the total
binding energy of trhe reactants, that is energy is released in the process. Examples of such energy
releasing fusion reactions are as follows :
1
1
2
0
1H + 1H = 1H + 1e
2
1
3
radiation
1H + 1H = 2He +
3
3
4
1
1
2He + 2He = 2He + 1H + 1H
These reactions known as the proton-proton chain are believed to take place in the interior of
the sun and of other stars primarily composed of hydrogen. The positrons produced annihilate free
electrons in the plasma and gamma radiation is released in the process.
For fusion to occur, the two nuclei must approach each other to within the range of the strong
force (i.e. 2 x 10-15 m approximately). The potential energy of two protons separated by this distance
can be calculated from
W=VxQ
W=
W=
= 1.1 x 10-13 Joule
Though all nuclei do not require to have this amount of energy, for any appreciable fraction of
nuclei to fuse together, the required temperature is of the order of 106 K.
Such temperatures occur in the stars as a result of gravitational contraction releasing
gravitational potential energy. When sufficiently high temperatures are attained fusion reactions are
initiated automatically thereby releasing more energy. The pressure of the resulting radiation prevents
further contraction. Only after most of the hydrogen is converted into helium will there be further
contraction and rise of temperature creating conditions for the formation of heavier nuclei. This is the
mechanism by which most of the nuclei in the universe were synthesized.
As fusion represents an enormous source of energy, intensive efforts are being made to
achieve it on a laboratory scale. The required temperature is achieved in the core of an atomic bomb
utilizing nuclear fission of uranium or plutonium. The problem is the maintainance of this temperature.
All current approaches involve the ue of complicated magnetic fields for confining the plasma. In the
foreseeable future it should be possible to extract energy from fusion reactions at a slow enough rate
to be useful for industrial power production.
Numericals
1. Bombardment of Lithium with protons gives rise to the following reaction :
The atomic masses of Lithium, Hydrogen and Helium are 7.016u, 1.008u and 4.004u respectively.
Find the initial energy of each alpha particle (1 u = 931 MeV)
[7.448 MeV]
2. Calculate in MeV the energy liberated when a helium nucleus is produced (i) by fusing two
neutrons and two protons, and (ii) by fusing two deuterium nuclei, Why is the quantity of energy
different in the two cases? (neutron mass = 1.00898 u: proton mass = 1.00759 u; nuclear
deuterium mass = 2.01419 u; nuclear helium mass = 4.00277 u; 1 u is equivalent to 931 MeV)
[28.27477 u; 23.84291 u ]
3. The energy liberated in the fission of a single uranium 235 atom is 3.2 x 10 -11 J. Calculate the
power production corresponding to the fission of one kg of uranium per day.
(Avogadro number = 6.02 x 1023 per mol).
[950 megawatt]
4. An alpha particle of charge 3.2 X 10-19C and mass 6.6 X 10-27 kg is moving along a circular path of
10.0 cm radius in a magnetic field. Its speed is 1.0 X 106 m s-1.
i.
ii.
How much force is acting on the alpha particle?
Find the direction and the strength of the magnetic field.
[0.21 Wb]