Unit 21: Nuclear Physics — Long Questions

ATOMIC NUCLEUS

At the centre of each and every atom there is an infinitesimally small nucleus. The entire positive charge of the atom and about 99.9 percent of its mass is concentrated in the nucleus. The nucleus is so small that the radius of the atom is 10⁵ times the radius of the nucleus.

Nucleons

A nucleus consists of protons and neutrons. A proton has a positive charge equal to 1.6 x 10^-19 C and its mass is 1.673 x 10^-27 kg. A neutron has no charge on it, but its mass is 1.675 x 10^-27 kg. The mass of a neutron is almost equal to mass of proton.

Unified Mass Scale (U)

Mass of atomic particles is generally expressed in unified mass scale (U) instead of kilogram. By definition: '1U is exactly one twelveth (1/12) the mass of carbon atom (1u = 1.6606 x 10^-27 kg)'.

In this unit the mass of proton is 1.007276 U and that of deutron is 1.008665 u while that of an electron is 0.00055 u.

Number of Protons are Equal to Number of Electrons

The charge on a proton is equal to the magnitude of charge on an electron. The charge on proton is positive while that of an electron is negative. An atom on the whole is electrically neutral, therefore, we can conclude that the number of protons inside the nucleus is equal to the number of electrons outside the nucleus.

ATOMIC NUMBER

'The number of protons inside the nucleus is called atomic number or charge number of an atom'.

It is denoted by Z. Thus total charge of any nucleus is 'Ze' where e is the charge on one proton.

Mass Number

The combined number of all the protons and neutrons in a nucleus is known as its mass number and it is denoted by A.

The number of neutrons present in a nucleus is given by
N = (A - Z) ...... (1)

Determination of Protons and Neutrons in an Element

We consider different elements of the periodic table. Hydrogen atom is the simplest of all the atoms. Its nucleus is composed of only one proton i.e., for hydrogen.
A = 1 and Z = 1

Therefore, hydrogen is represented by ¹₁ H. (²₁ H) = ¹₁ H

Next in the periodic table (after hydrogen element) is the helium element. Its nucleus contains (composed of) two protons and two neutrons i.e., for helium.
A = 4 and Z = 2

Therefore, helium is represented by ⁴₂ He.

We now take the example of uranium, a heavy element of periodic table. For uranium:
Z = 92 and A = 235

Therefore, uranium is represented by ²35₉2 U.

In uranium number of protons = 92

Number of neutrons are N = A - Z = 235 - 92 = 143

In this way the number protons and neutrons in atoms can be determined.

ISOTOPES

The nuclei of an element that have the same charge number but different mass number are called isotopes of the element.

In an isotope of an element, the number of protons is the same, but the number of neutrons is different.

Isotopes of Helium

Helium has two isotopes. These are symbolically represented as ³₂ He and ⁴₂ He.

As the charge number of helium is 2, therefore, there are two protons in the helium nucleus.

The number of neutrons in first isotopes, ³₂ He is:
N = A - Z = 3 - 2 = 1

The number of neutrons in 2nd isotopes, ⁴₂ He is:
N = A - Z = 4 - 2 = 2

Isotopes of Hydrogen

Hydrogen has three isotopes represented by ¹₁ H, ²₁ H, ³₁ H. First isotope is called ordinary hydrogen or protium. It has only one proton in the nucleus. The second isotope of hydrogen is called deuterium. It has only one proton and one neutron in its nucleus. Its nucleus is called deuteron. The third isotope of hydrogen is called tritium.

It has two neutrons and one proton in its nucleus.

The isotopes of hydrogen are shown below:

Properties of Isotopes

The chemical properties of all the isotopes of an element are alike, as the chemical properties of an element depend only upon the number of electrons around the nucleus, that is upon the charge number Z, which for all the isotopes of an element is the same. It is, therefore, not possible to separate the isotopes of an element by chemical methods. Physical methods are, therefore, successful for this purpose.

MASS SPECTROGRAPH

A simple mass spectrograph is shown in figure.

(1) Ion Source

In figure 'S' is the ion source. This source ionizes the atoms or moleculesof the element under investigation, in the form of vapours. One electron is removed from the particle (atom) making ions with net positive charge +e.

(2) Working

These ions are allowed to escape from the source through slits S₁ and S₂ by applying a potential difference v.

The ions pass through S₂

The K.E of the single charged ion at the slit S₂ will be given by:
1/2 mv² = Ve ...... (i)

The ions are then subjected to a perpendicular and uniform magnetic field B in a vacuum chamber, where they are deflected in semicircular paths towards a detector. The detector records the number of ions arriving per second.

(3) Identification of Isotopes

The centripetal force applied by the magnetic field is given by:
Bev = mv²/r

=> m = Ber/v ...... (i)

From eq. (1)
1/2 mv² = Ve
v² = 2Ve/m
v = sqrt(2Ve/m)

Putting this value in eq. (i), we get:
m = Ber/sqrt(2Ve/m)

Squaring m² = B² e² r²/(2Ve/m)
m² = B² e² r² x m/(2Ve)

m = (er/2V) B² ...... (ii)

r² = 2Vm/(eB²)

r = sqrt(2Vm/eB²)

r = sqrt(2V/eB²) sqrt(m)

sqrt(2V/eB²) = Constant

therefore: r proportional to sqrt(m)

Since isotopes have different masses, so they have different radii. In this way we identify the isotopes.

Abundance of Masses (Ions)

As m = (er²/2V) B²

The above equation shows that mass of each ion reaching the detector is proportional to B². By adjusting the value of B and keeping the term in parentheses (bracket) constant, ions of different mass are allowed to enter the detector.

Then a graph of detector output is plotted as a function of B². This graph gives information what masses are present and the abundance of each mass.

Figure shows a record obtained for naturally occurring neon gas showing three isotopes whose atomic mass number are 20, 21 and 22. The larger the peak, the more abundant is the isotope. Thus most abundant isotope of neon is neon-20.

MASS DEFECT AND BINDING ENERGY

(i) Mass Defect

It is usually assumed that the whole is always equal to the sum of its parts. This is not so in the nucleus. The results of experiments on the masses of different nuclei show that the mass of the nucleus is always less than the total mass of all the protons and neutrons making up the nucleus. In the nucleus the missing mass is called the mass defect 'm' given by

Δm = Zm_p + (A-Z)m_n - m_nucleus ...... (1)

where
Δm = Mass defect
Z = Total number of protons in the nucleus
m_p = Mass of a proton

therefore: Zm_p = Total mass of all proton
A - Z = Total number of neutrons
m_n = Mass of a neutron
(A-Z)m_n = Total mass of all neutron
m_nucleus = Experimentally measured mass of entire nucleus

Thus we can defined mass defect as:

Definition 'Mass defect is the difference in mass between the sum of the masses of its constituents and the mass of the nucleus itself'.

(ii) Binding Energy:

The missing mass is converted to energy in the formation of the nucleus. This energy is found from Einstein's relation:

E = (Δm)c² ...... (2)

and is called Binding energy (B.E) of the nucleus.

Putting eq. (1) in (2), we get Binding energy:

B.E = (Δm)c² = (Zm_p+(A-Z)m_n-m_nucleus) c²

or

B.E = Zm_p c² + (A-Z)m_n c² - mc² ...... (3)

Mass Defect Per Nucleon

Experiments have shown that mass defect exist in elements. The figure, shows a graph between the mass defect per nucleon and charge number Z for different elements. The value of mass defect per nucleon is given by formula:

Δm/A = [Zm_p+(A-Z)m_n - m]/A

The following diagram is a graph between binding energy per nucleon and mass number of different elements.

This graph shows that the binding energy per nucleon increases with the mass number till it reaches a maximum value of 8.8 Mev at mass number 58 and then it gradually decreases to a value of 7.6 Mev at mass number 238.

Note

(1) The binding energy per nucleon is maximum for iron this shows that of all the elements iron is most stable element.

(2) Mass defect for hydrogen is zero.

(3) When heavy elements breaks into lighter elements or the lighter elements are fused to form heaver element then a large amount of energy can be obtained.

RADIOACTIVITY

It has been observed that those elements whose charge number Z is greater than 82 are unstable. Some invisible radiations that can affect the photographic plates are emitted out of these elements. Such elements are called radioactive elements and the phenomenon is called radioactivity.

The radiations coming out of the elements are alpha (α), beta (β) and gamma (γ) radiations.

Discovery of Radioactive Elements

Radioactivity was discovered by Henri Becquerel in 1896. He found that an ore containing uranium (Z = 92) emits an invisible radiation that can penetrate through a black paper wrapping a photographic plate and affects the plate. After Becquerel's discovery Marie Curie and Pierre Currie discovered two new radioactive elements polonium and radium.

Experiment

The analysis of the radiations emitted from a radioactive material can be studied by simple experiment.

The radioactive material is placed at the centre of a block of lead by drilling a hole in the block.

Radiations enter the chamber after passing through two parallel plates. These radiations fall on three different points on photographic film. From this experiment it can be concluded that radiations emitted from radioactive element are not alike.

Types of Radiations

Radioactive radiations are of three types:
(i) α-particle (ii) β-particles (iii) γ-rays

(i) α-particles

The radiations that bend towards the negative plate are positively charged particles. These are called α-particles.

α-particles are helium nuclei. The charge on them is +Ze while their mass is 4u. i.e., every α-particle has two protons and two neutrons in it.

(ii) β-particles

The radiations that bend towards the positive plate are negatively charged particles. These are called β-particles.

β-particles are infact fast moving electrons which come out of the nucleus of radioactive element.

(iii) γ-rays

The radiations that go straight without bending have no charge on them. These are called γ-rays.

γ-rays are electromagnetic waves like X-rays. The wavelength of these rays is much shorter as compared to wavelength of X-rays.

NUCLEAR TRANSMUTATION

Radioactive is purely a nuclear phenomenon. This is not effected by any physical or chemical reaction. Whenever any particle (radiation) is emitted from a nucleus it always changes into nucleus of another element. Therefore, the element changes into new element. The phenomenon is called radioactive decay or nuclear transmutation.

(1) Daughter Element

The element formed due to this change is called daughter element.

(2) Parent Element

The original element is called parent element. During the nuclear changes the laws of conservation of mass, energy, momentum and charge are applicable.

During nuclear decay α-particles, β-particles and γ-rays are emitted. These are called α, β and γ decays.

α-decay

When an α-particle is emitted out of nucleus then the nucleus loses ⁴₂ He i.e., the mass number of nucleus is decreased by 4 and charge number by 2.

^A_Z X -----> ^A-4_Z-2 Y + ⁴₂ He

where X represents the parent element

and Y represents the daughter element

Example Let us take the example of ²26₈8 Ra.

When α-particle is emitted from radium 226 then it converts into radon gas ²22₈6 Rn. This change is represented as

²26₈8 Ra -----> ²22₈6 Rn + ⁴₂ He

β-decay

When a β-particle is emitted out of nucleus then the nucleus loses ⁰_-1 e i.e., the mass number of nucleus is not changed but charge number is increased by one.

The emission of β-particle is represented as:

^A_Z X -----> ^A_Z+1 Y + ⁰_-1 e

Example Let us take the example of thorium ²32₉0 Th.

When a β-particle is emitted from thorium 232 then it converts into Protactinium ²31₉1 Pa. This change is represented as

²32₉0 Th -----> ²31₉1 Pa + ⁰_-1 e

γ-decay

When a γ-ray is emitted out of nucleus then the mass number and charge number of nucleus does not under to any change. It is the fact γ-radiation is simply a photon that is either mass nor charge.

Like atom nucleus is also sometime excited to a higher state. The excited state of the nucleus is unstable state, in combing back to ground state γ-radiation is emitted.

The emission of γ-particle is represented as:

^A_Z X* -----> ^A_Z X + γ-radiation

Here, ^A_Z X* represents an excited nucleus and ^A_Z X represents a nucleus in ground state.

HALF LIFE

Definition

'The half-life of radioactive element is that period in which half of the atoms decay'.

Explanation

Whenever an α or β particle is emitted from a radioactive element it changes into some other element. This radioactive decay process is quite random this means that we cannot foretell about decay of any particular atom. It could decay immediately or it may remain unchanged for millions of year. Thus we cannot say anything about the life of any particular atom of a radioactive element.

Example Suppose we have 100,000 atoms under consideration and wait till such time that half of these i.e., 50,000 decay into their daughter element. This time is called the half-life T₁/₂ of this element. If the half-life of said element is one day then after one day only 25,000 atoms will remain behind and after two days 12,500 atoms will remain behind. That is with the passage of every one day, the number of atoms remaining behind becomes half.

Conclusions

From above example we can deduce two conclusions:

(1) No radioactive element can completely decay. It is due to the reason that in any half period only half of the nuclei decay and in this way infinite time is required for all the atoms decay.

(2) The number of atoms decaying in a particular period is proportional to the number of atoms present in the beginning of the period. If the number of atoms to start with is large then a large number of atoms will decay in this period and if number of atoms present in the beginning is small then less atom will decay.

Results in Terms of Equation

These results can be represented with an equation. If at any particular time the number of radioactive atoms be N, then in an interval Δt, the number of decaying atom, ΔN is proportional to the time interval Δt and the number of atoms N i.e.,

ΔN ∝ -N
ΔN ∝ Δt

Combining, we get

ΔN ∝ -NΔt
ΔN = -Constant NΔt
ΔN = -λNΔt ...... (1)

where λ is the constant of proportionality, called the decay constant. The negative sign indicates the decrease in the number of atom N.

Decay Constant

Equation 1 shows that if the decay constant of any element is large then in a particular interval of more of its atoms will decay and if the decay constant λ is small then in that very interval less number of atoms will decay.

Eq. (1) can be written as:

λ = -ΔN/N/Δt

Definition

'The ratio of the fraction of decaying atoms per unit time is called decay constant'.

Unit

SI unit of decay constant is s^-1.

Decay Curve

We know that every radioactive decay at a particular rate with time. If we draw a graph between number of atoms in the sample of radioactive element present at different times and the time then a curve as shown in figure is obtained. This graph shows that in the beginning the number of atoms present in the sample of the radioactive element was N₀, with the passage of time the number of these atoms decreased due to their decay. This graph is called decay curve.

After one half life the remaining no. of atoms = N₀/2 = 1/2 (N₀)

After 2nd half life the remaining no. of atoms = 1/2 (1/2 N₀) = (1/2)² N₀

After 3rd half life the remaining no. of atoms = 1/2 × (1/2)² N₀ = (1/2)³ N₀

Similarly;

After nth half life the remaining no. of atoms = (1/2)ⁿ N₀

The graph shown in figure is general for all the radioactive elements.

Estimation of Half Life

But different elements have different values of half life. For example, half life of uranium 238 is 4.5 x 10⁹ years while the half life of radium -226 is 1620 years.

Some elements have very small value of half life, for example, half life of radon is 3.8 days and that of uranium -239 is 23.5 minutes. This shows that the estimation of amount of a radioactive element can be made by the help of its half life (or by knowing its decay constant λ).

Relationship between λ and T₁/₂

The following relation exist between the decay constant λ and the half life T₁/₂:

λ × T₁/₂ = 0.693

INTERACTION OF α-PARTICLES WITH MATTER

(1) An α-particle travels a well defined distance in a medium before coming to rest. This distance is called range of the particle. As the particle passes through a solid, a liquid or gas, it loses energy due to excitation and ionization of atoms and molecules in the matter. The ionization may be due to direct elastic collisions or through electrostatic attraction of α-particle with matter ionization this the main interaction with matter to detect the particle or to measure its energy. The range depends on:

(i) the charge, mass and energy of the particle

(ii) the density of the medium and ionization potentials of the atoms of the medium.

(2) Since α-particle is about 7000 times more massive than a electron so it is not deflected easily from its straight path. (Provided it does not approach to closely to the nucleus of the atom). Thus α-particle continues producing intense ionization along its straight path till it loses all its energy and comes to rest. It then captures two electrons from the medium and become a neutral helium atom.

(3) α-particle radiate energy as X-ray photons when they are slowed by the electric field of the charged particles in a solid material.

(4) α-particles produces florescence or glow on striking some substances like zinc sulphide, sodium iodide or barium platinocyanide coated screens.

Fluorescence

"Fluorescence is the property of absorbing radiant energy of high frequency and reemitting energy of low frequency in the visible region of electromagnetic spectrum".

INTERACTION OF β-PARTICLES WITH MATTER

(1) β-particles loses energy by producing ionization. However its ionizing ability is about 100 times less than that of α-particles. As a result its range is about 100 times more than α-particles. β-particles are more easily deflected by collisions than α-particles. Therefore, path of β-particle is not straight but shows much straggling scattering.

The range of β-particle is measured by effective depth of penetration into the medium not by the length of erratic path. The more dense the medium (material) the shorter its range will be.

(2) β-particle radiate energy as X-rays photons when they are slowed by the electric field of charged particles in a solid material.

INTERACTION OF γ-PARTICLES WITH MATTER

(1) Photons or γ-rays, being uncharged, causes very little ionization they interact matter in three different ways depending on their energy.

(i) A low energies (less than about 0.5 Mev), the γ-rays produce photoelectric effect.

(ii) At intermediate energies, the γ-rays produce compton effect.

(iii) At higher energies (more than 1.02 Mev), γ-rays produce pair production.

(2) In air γ-rays intensity falls off as the inverse square of the distance from the source, in much same manner as light from a lamp. In solids, the intensity decreases exponentially with increasing depth of penetration into the material.

The intensity Io of a beam after passing through distance X in the medium is reduced to intensity I given by the relation

I = Ioe^-μx

where μ is the linear absorption coefficient of the medium. This coefficient depends on the energy of the photon as well as on the properties of the medium.

(3) γ-radiation produce florescence or glow on striking some substances like zinc sulphide, sodium iodide or barium platinocyanide coated screens.

INTERACTION OF NEUTRONS WITH MATTER

Neutrons, being neutral particles, are extremely penetrating particles. To be stopped or slowed down, a neutron must undergo a direct collision with nucleus or atom of comparable size (mass).

Materials such as water or plastics (which contain more low mass nuclei per unit volume) are used to stop neutrons.

Neutrons produce a little indirect ionization when they interact with materials containing hydrogen atoms and knock out protons.

Note If question is asked: Give brief account of interaction of radiation with matter then. You must not repeat the similar point separately rather you can say … α, β and γ produce florescence …

Table The summary of the nature of α, β and γ radiation

Characteristics | α-particles | β-particles | γ-rays
1. Nature | Helium nuclei of charge 2e | Electrons or positrons from the nucleus of change i.e., | E.M. waves from excited nuclei with no charge
2. Typical sources | Radon-222 | Strontium-94 | Cobalt-60
3. Ionization (ion pairs mm in air) | About 10⁴ | About 10² | About 1
4. Range in air | Several centimetres | Several metres | Obeys inverse square law
5. Absorbed by | A paper | 1-5 mm of Al sheet | 1-10 cm of lead sheet
6. Energy spectrum | Emitted with the same energy | Variable energy | Variable energy
7. Speed | ~10⁷ ms^-1 | ~1 x 10⁸ ms^-1 | ~3 x 10⁸ ms^-1

WILSON CLOUD CHAMBER

It is a device which shows the visible path of an ionizing particle.

Principle

It is based upon the principle that supersaturated vapours condense more readily on ions. The number of ions produced depends upon the ionizing power of the particle. If an ionizing particle passes through a region in which aloud droplets are about to form, the droplets will form first along the particle's path, showing the path as a trail of droplets.

Construction

It consists of a cylindrical chamber fitted with a piston at its bottom as shown in figure.

The top of the chamber is made of transparent glass and a camera is fixed to take photographs above the glass top. A black felt pad soaked in alcohol is placed on a metal plate inside the chamber. The air soon becomes saturated with alcohol vapours.

Working

When the piston is moved down quickly, the mixed air (air mixed with vapours) expand adiabatically and so cools down the saturated vapours inside the chamber becomes supersaturated (i.e., they contain more liquid than they can hold). The supersaturated vapours condense in the form of tiny droplets on ions. They look like fog when viewed from the glass top and expansion is done at the time when the ionizing particles enter the chamber, the vapours condense on the ions. This will give a visible trail of droplets along the path followed by ionizing particles. By using a strong light, the camera mounted above the glass top is used to take the photograph of this path.

Clearance of Unwanted Ions

After taking photograph the piston is pushed back to its original position and a potential difference of order 1 KV is applied between top and bottom of chamber which clear away all the unwanted ions from the chamber to make it ready for use.

Tracks of Particle

Tracks of α-particles

The tracks of α-particles are thick, straight and continuous due to high ionization by them as shown in figure (a).

Tracks of β-particles

The tracks of β-particles are thin, discontinuous due to less ionization, and showing frequent deflections as shown in figure (b).

Tracks of γ-rays

Gamma rays have no definite tracks along their paths. The length of track depends upon the energy of incident particles.

GEIGER MULLER COUNTER

Geiger-Muller tube is a well known radiation detector.

Principle

The discharge in the tube results from the ionization produced by the incident radiation.

Construction

It consists of a stiff central wire acting as an anode in a hollow metal cylinder. The walls of the cylinder are acting as cathodes. The tube is filled with a suitable mixture of gas at about 0.1 atmospheric pressure. One end of the tube has a thin mica window to allow the entry of α or β-particles and other end is sealed by non-conducting material and it carries connecting pins for the two electrodes. A high potential difference (about 400 v for neon bromine filled tube) but slightly less than that necessary to produce discharge through the gas is maintained between the electrodes.

Working

When a radiation enters the tube through then mica window, the gas inside the tube is ionized. Positive ions and electrons are produced. These electrons and ions are accelerated by the electric field in opposite directions. They produce further ionization by suffering collisions with the atoms of the gas. As a result a cascade (group) of electrons is formed. At this stage a discharge occurs and the gas becomes conducting, causing the current to flow in the external circuit. The voltage drop across the resistance R produces a current pulse of short duration which is amplified and recorded by an electric counter. The counter which also provides the power, is called a scalar.

Quenching Effect

The cascade (group) of electrons produced by the entry of an ionizing particle is counted as single pulse (whatever the energy or size of the pulse may be). The entire pulse takes less than 1 μs. However, positive ions, being very massive than the electrons, take several hundred times longer to reach the outer cathode. During this time, called the dead time (~ 10^-4 s) of the counter, further incoming particles cannot be counted. When positive ions strike the cathode, secondary electrons are emitted from the surface. These electrons will disturb the counting. This is prevented by mixing a small amount of quenching gas with the principal gas.

Self Quenching

The quenching gas must have an ionization potential lower than that of principal gas (inert gas). Thus the ions of quenching gas reach the cathode before principal gas ions. When they reach near the cathode, they capture electrons and become neutral molecules. For example, Bromine gas is added to neon gas. The bromine molecules absorb energy from the ions of secondary electrons and dissociate into bromine atoms. The atoms then readily recombine into molecules again for the next pulse. The gas quenching is called self quenching.

Electronic Quenching

All commercial Geiger tubes are self quenched, it is common practice to use electronic quenching in addition. For this purpose, a large negative voltage is applied to the anode immediately after recording to output pulse.

Drawback of Geiger Counter

Geiger counter is not suitable for fast counting. It is because of its relatively long "dead time" of the order of more than a millisecond which limits the counting rate to a few hundred counts per second. If particles are incident on the tube at faster rate, not all of them will be counted since some will arrive during the dead time.

Uses

Geiger counter can be used to:

(1) Determine the range or penetration power of ionizing particles.

(2) The reduction in the count rate by inserting metal plates of varying thickness between the source and the tube helps to estimate the penetration power of the incident radiation.

(3) It is very small in size than any other detector and operates at low voltage.

(4) This type of detector is used for detecting α or β particles but a specially designed device can be used for γ-rays.

SOLID STATE DETECTOR

If a semi-conductor like p-n junction diode is used for the detection of nuclear radiations (α, β, γ-rays) it is called a solid state detector.

Principle

Its working principle is based upon the reverse bias. The applied reverse-bias enlarges the charge free-region in a p-n junction. In other words, when radiation is allowed to enter the depletion region, electron-hole pairs are produced by the incident radiation.

Construction

Solid state detector is basically a special designed p-n junction as shown in figure. The detector is made from a p-type silicon or germanium. An n-type thin layer is produced by doping the top surface with donor type impurity. The top and bottom surfaces are cooled with a thin layer of gold to make good conducting contact with external circuit. The combined thickness of n-type and gold layer absorbs so less energy of the incident particle that the junction may be supposed to be placed at the front surface. This is known as the surface barrier type detector.

Working

A reverse bias is applied through the two conducting layers of gold. This enlarges the charge free region around the junction called depletion region. Normally, no current flows through the circuit.

When an incident particle enters the detector from n-side, it is absorbed in the depletion region and it produces electron-hole pairs. These mobile charge carriers move towards the respective sides due to applied electric field. It means that electrons move towards the positive side of the electrode and holes towards the negative side. These charges produce potential drop across the junction and a current pulse whose magnitude is proportional to the energy of the incident particle, is created through the external circuit. This current pulse is amplified and registered by a scalar unit (i.e., electronic counter).

The p-n junction again becomes non-conducting when the electrons and holes arrive at the specific ends. It becomes ready to receive the next incident particle for producing electron-hole pairs.

NUCLEAR REACTIONS

When an α-particle is emitted from uranium -226, radon -222 is obtained. The nuclear reaction is represented by

²26₈8Ra → ²22₈6Rn + ⁴₂He

This type of reaction takes place on its own accord. Rutherford first of all expressed his opinion that besides natural radioactive decay processes, other nuclear reactions can also occurs.

A particle x is bombarded on any nucleus X and this process yield a nucleus Y and a light object y as shown below:

X + x → Y + y

Rutherford in 1918 bombarded an α-particle on nitrogen. He observed that as a result of this reaction, oxygen is obtained and a proton is emitted that is:

¹4₇N + ⁴₂He → ¹7₈O + ¹₁H

This reaction indicate that when an α-particle enters the nucleus of ¹4₇N then an excitation is produced in it and as a result of it ¹7₈O and a proton are produced.

Condition for Nuclear Reactions

For nuclear reactions to take place, the following conditions must be satisfied.

(1) Conservation of Mass

Before and after any nuclear reaction the number of protons and neutrons must remain the same because protons and neutrons can neither be destroyed nor they can be created.

Consider the reaction

¹4₇N + ⁴₂He → ¹7₈O + ¹₁H

Number of protons = 7 + 2 = 8 + 1
9 = 9

Number of neutrons = 7 + 2 = 9 + 0
9 = 9

(2) Conservation of Energy

A nuclear reaction can take place only when the total energy of reactants including rest mass energy is equal to the total energy of the products. In this case, we again consider the nuclear reaction.

¹4₇N + ⁴₂He → ¹7₈O + ¹₁H

Mass of reactants is

Mass of ¹4₇N = 14.0031 U
Mass of ⁴₂H = 4.0026 U

Total mass of reactants = 18.0057 U

Mass of product is

Mass of ¹7₈O = 16.9991 U
Mass of ¹₁H = 1.0078 U

Total mass of products = 18.0069 U

Difference between masses = (18.0069 - 18.0057) U
= 0.0012 U

This shows that total mass after reaction is greater than total mass before reaction by 0.0012 U. We know that:

1 u = 931 Mev

∴ 0.0012 u = 0.0012 × 931 = 1.13 Mev

This energy is required to be supplied in order to have the nuclear reaction given above. So an α-particle is emitted by Po-214, whose energy is 7.7 Mev, which is greater than 1.13 Mev, which makes this nuclear reaction possible.

The above conditions are called the before-test of a nuclear reaction which will enable us to know whether reaction will take place or not.

Nuclear Reaction in Reverse Direction

If we accelerate protons, with the help of cyclotron, and increase their velocities and then bombard these high velocity proton on ¹7₈O, the above given reaction will proceed in reverse direction as shown.

¹7₈O + ¹₁H → ¹4₇N + ⁴₂He

Discovery of Neutron

In 1932 James Chadwick discovered neutron. When ⁹₄Be was bombarded with a-particle (emitted from ²10₈4 PO) then ¹2₆C and neutron were obtained. The reaction is:

⁹₄Be + ⁴₂He → ¹2₆C + ¹₀n

As neutron is neutral particle therefore, its identification was difficult. But when neutron were passed through a block of paraffin, fast moving protons were ejected out and these were easily identified.

Figure shows the experimental arrangement of Chadwick's apparatus used for the discovery of neutron.

NUCLEAR FISSION

"Such a reaction in which a heavy nucleus like that of uranium splits up into two nuclei of equal size alongside the emission of energy during the reaction is called fission".

Explanation

Otto Hahn and Fritz Strassman of Germany while working upon nuclear reactions made a wonderful discovery. They observed that when slow moving neutrons are bombarded on ²35₉2U, then as a result of nuclear reaction ¹41₅6Ba, ⁹2₃6Kr and an average of three neutrons are obtained.

It may be remembered that mass of both Krypton and barium is less than that of mass of uranium. This nuclear reaction was different from earlier nuclear reactions by two ways:

(1) As a result of breakage of the nucleus two nuclei of almost equal size are obtained.

(2) A very large amount of energy is given out in this reaction. Fission reaction of (uranium) ²35₉2U can be represented by

²35₉2U + ¹₀n → ¹41₅6Ba + ⁹2₃6Kr + 3¹₀n + Q

where 'Q' is energy given out in this reaction.

By comparing the total energy on the left side of the equation with total energy on the right-side, we find that in the fission of one uranium nucleus about 200 Mev energy is given out.

Fission reaction is shown in figure.

Per Nucleon Energy

Fission reaction can be explained easily with the help of the study of binding energy. We know that binding energy per nucleon is greatest for the middle elements of the periodic table and this binding energy per nucleon is a little less for the light or very heavy elements i.e., the nucleons in the light or very heavy elements are not so rigidly bound. For example the binding energy per nucleon for uranium is about 7.7 Mev and the product of fission reaction of uranium (barium and krypton) have total mass less than the mass of uranium. i.e.,

8.5 - 7.6 = 0.9 Mev per nucleon

thus when a uranium nucleus breaks up (by fission reaction) into barium and krypton then energy at a rate of 0.9 Mev per nucleon is given out. This means that an energy 235 × 0.9 = 211.5 Mev is given out in the fission of one uranium nucleus.

Possible Uranium Reactions

The fission process of uranium does not always produce the same fragments (Ba, Kr). In fact any of the two nuclei present in the upper horizontal part of binding energy could be produced.

Two possible fission reactions of uranium are given below as an example:

²35₉2U + ¹₀n → ¹32₅0Sn + ¹01₄2Mo + 3¹₀n + Q

²35₉2U + ¹₀n → ¹40₅4Xe + ⁹4₃8Sr + 2¹₀n + Q

Hence in uranium fission reaction several products may be produced.

All these products (fragments) are radioactive. Fission reaction is not confined to uranium alone, it is possible in many other heavy elements. However, it has been observed that fission takes place very easily and plutonium are most useful nuclei used for fission purposes.

Fission Chain Reaction

We know that during fission reaction a nucleus of uranium -235 absorbs a neutron and breaks into two nuclei of almost equal masses besides emitting two or three neutrons. By using these neutrons properly fission reaction can be produced in more uranium atoms such that a fission reaction can continuously maintain itself. This process is called fission chain reaction.

There are two types of fission reaction:

(i) Uncontrolled fission chain reaction

(ii) Controlled fission chain reaction

(i) Uncontrolled Fission Chain Reaction OR (Fission Chain Reaction)

Suppose we have a definite amount of ²35₉2U and a slow neutron (originated from any source) produces fission reaction in one atom of uranium. During this fission three neutrons are produced. If conditions are appropriate these neutrons will produce fission in some more atoms of uranium and more neutrons will be emitted. In this way this process will rapidly proceed and in a very small time a large amount of energy along with huge explosion is produced.

The figure represents a (uncontrolled) fission chain reaction.

(ii) Controlled Fission Chain Reaction

It is possible to produce such condition in which only one neutron out of three becomes the cause of further fission reaction. The other neutrons either escape out or are absorbed in any other medium except uranium. In this case the fission chain reaction proceeds with its initial speed.

Let us try to understand this by following figures:

(a) In figure (a) a thin sheet of uranium (²35₉2U) is shown in which fission reaction is in progress. The resulting neutrons scattered in the air and they are unable to produce any fission chain reaction.

(b) In figure (b) a favourable condition for chain reaction is shown. In this case some of the neutrons produced in the first fission reaction produce only one more fission reaction but they do not produce any further fission, therefore, chain reaction is not possible.

(c) In figure (c) a sphere of ²35₉2U is shown. If the sphere is big then most of the neutrons produced due to the fission reaction get absorbed in ²35₉2U before escaping out of the sphere and produce chain reaction.

Critical Mass

Such a mass of uranium in which one neutron out of all the neutron produced in one fission reaction, produces further fission is called critical mass. The volume of this mass is called critical volume.

Mass of Uranium and Critical Mass

(i) If the mass of uranium is much greater than the critical mass, then the chain reaction proceeds at a rapid speed and huge explosion is produced. Atom bomb works at this principle.

(ii) If the mass of uranium is less than critical mass, the chain reaction does not proceed.

(iii) If the mass of uranium is equal to the critical mass, the chain reaction proceeds at its initial speed and in this way we get a source of energy. Energy in an atomic reactor is obtained on this principle.

The chain reaction is not allowed to run wild, as in an atomic bomb but is controlled by a series of rods, usually made of cadmium (that are inserted into the reactor) cadmium is an element that is capable of absorbing a large number of neutrons with out becoming unstable or radioactive. Hence when the cadmium control rods are inserted into the reactor, they absorb neutrons to cut down on the number of neutrons that are available for the fission process. In this way fission reaction is controlled.

NUCLEAR REACTOR

In a nuclear power station the reactor plays the same role (part) as the furnace does in thermal power station. In a furnace, coal or oil is burnt to produce heat, while in reactor fission reaction produces heat. When the fission takes place in the atom of uranium or any other heavy atom, then an energy at the rate of 200 Mev per nucleon is produced. This energy appears in the form of kinetic energy of the fission fragments. These fast moving fragments besides colliding one another also collide with uranium atoms. In this way their K.E is transferred in heat energy. This heat is used to produce steam which rotates the turbine. Turbine rotates the generator which produces electricity.

Principle

The principle of nuclear reactor is based on controlled fission chain reaction.

Main Parts of Nuclear Reactor

(1) Core

It is the main part of nuclear reactor. Here the fuel is kept in the shape of cylindrical tubes. Reactor fuels are of various types.

Uranium was used in the elementary reactors. In this fuel the quantity of ²35₉2 U is increased from 2 to 4 percent. It may be remembered that quantity of ²35₉2 U in naturally occurring uranium is only 0-7 percent. Now a days plutonium -239 and uranium -233 are also used as fuel.

(2) Moderator

The fuel rods are placed in a substance of small atomic weight, such as water, heavy water, carbon or hydrogen, etc. These substances are called moderators. The function of these moderators is to slow down the speed of the neutrons produced during the fission process and to direct them towards the fuel. Heavy water is made of ²₁ H, a heavy isotope of hydrogen instead of ¹₁ H. The neutrons produced in the fission reaction are very fast and energetic and are not suitable for producing fission in reactor fuel like ²35₉2 U or ²39₉4 Pu etc. For this purpose slow neutrons are more useful. To achieve this moderators are used.

(3) Absorbing Rods

There are neutrons absorbing rod which control the number of neutrons which produce nuclear fission reaction. For this purpose cadmium or boron materials are used. These materials have the property of absorbing fast moving neutrons. These control rods are moved in or out of the reactor core to control the neutrons that can initiate further fission reaction. In this way the speed of the chain reaction is kept under control. In case of emergency or for repair purposes control rods are allowed to fall back into the reactor and thus stop the chain reaction and shut down the reactor.

(4) Heat Exchanger

Heat is produced due to fission chain reaction taking place in the core of the reactor. The temperature of the core, therefore, rises to about 1200°C. To produce steam from this heat, it is transported to heat exchanger with the help of hot water, heavy water, or any other liquid under great pressure. In the heat exchanger this heat is used to produce steam from ordinary water. The steam is then used to run the turbine which rotates the generator to produce electricity. The temperature of the steam coming out of the turbine is about 300°C. This is further cooled to convert it into water again. To cool this steam, water from some river or sea is, generally, used.

KANUP

In Karachi Nuclear Power Plant (KANUP), heavy water is being used as a moderator and for transportation of heat also from the reactor core to heat exchanger, heavy water is used. To cool steam coming out of the turbine seawater is being used.

RADIATION EXPOSURE

When a Geiger tube is used in any experiment, it records radiation even when a radioactive source is not there. This is caused by radiation called background radiation. It is partly due to cosmic radiation which comes to us from outer space and partly from naturally occurring radioactive substance in the earth's crust.

Cosmic Rays

The cosmic radiations consists of high energy charged particles and electromagnetic radiation. The atmosphere acts as a shield to absorb some of these radiations as well as ultraviolet rays. In recent past, the depletion of ozone layer in the upper atmosphere has been detected which particularly filters ultraviolet rays reaching us. This may result in increased eye and skin diseases. The depletion of ozone layer is suspected to be caused due to excessive release to some chemicals in the atmosphere such as chlorofluoro carbons (CFC) used in refrigeration, aerosol spray and plastic form industry. Its use is now being replaced by environmentally friendly chemicals.

Building Materials

Many building materials contain small amounts of radioactive isotopes. Radioactive radon gas enters buildings from the ground. It gets trapped inside the building which makes radiation levels much higher from radon inside than outside.

A good ventilation can reduce radon level inside the building. All types of food also contain a little radioactive substance. The most common are potassium-40 and carbon-14 isotopes.

Medical Radiation Exposure

Some radiation in the environment is added by human activities. Medical practices, mostly diagnostic X-ray probably contribute the major portion to it. It is an unfortunate fact that may X-ray exposures such as routine chest X-ray and dental X-ray are made for no strong reason and may do more harm than good.

Every X-ray exposure should have a definite justification that outweighs the risks.

Other Sources

The other sources include radioactive waste from nuclear facilities, hospitals, research and industrial establishments, colour television, luminous watches and tobacco leaves. A smoker not only inhales toxic smoke but also hazardous radiation. Low level background radiation from natural sources is normally considered to be harmless. However, higher levels of exposure are certainly damaging. We cannot avoid exposure to radiation. However, the best advice to avoid unnecessary exposure to any kind of ionizing radiation.

Biological Effects of Radiation

To study the effects of radiation, we need to define some of the units of radiation. The strength of radiation source is indicated by its measured in Becquerel (Bq) and Curie (Ci).

Becquerel (BQ) One disintegration per second is called becquerel.

Curie (C) 3.7 x 10¹0 disintegration per second is called curie.

Absorbed Dose The energy absorbed from ionizing radiations per unit mass of absorbing body is called absorbed dose.

It is expressed as

D = E/m

Gray The unit of absorbed dose is gray (Gy). It is defined as one joule per kilogram i.e.,

1 Gy = 1 Jkg^-1

Rad The old unit of absorbed dose is rad (an acronym for radiation absorbed dose).

1 rad = 0.01 Gy

Biological Effects

It has been experimentally proved that equal dose of different radiations do not produce same biological effects. For the same absorbed dose, α-particles are 20 times more damaging than X-rays. The effect also depends on the part of the body absorbing the radiation. For example, neutrons are particularly more damaging to eyes than other parts of the body. To allow this, the absorbed dose is multiplied by quality factor known as relative biological effectiveness or RBE.

Equivalent Dose De

The equivalent dose (De) of any absorbed radiation is defined as:

"The product of absorbed dose and RBE of the kind of radiation being absorbed".

The equivalent dose can be written as:

De = D x RBE

Seivert

The SI unit of equivalent dose is Seivert (Sv)

where 1 Sv = 1 Gy x RBE

An old unit of equivalent dose is rem

1 rem = 0.01 Sv

General Information about Biological Effects of Radiation

(1) The background radiation to which we are exposed, on average, is 2m Sv per year.

(2) Dose of about 3 Sv cause radiation burns to the skin.

(3) For the workers where nuclear facilities are provided or inside mines a weekly dose of 1m Sv is considered safe.

(4) The damage from α-particle is small unless the source enters the body.

(5) α and β particles can cause redness and sores on the skin.

(6) The low level radiation effects are loss of hair, ulceration, stiffening of the lungs, and a drop in the white blood cells which is followed by a sickness pattern of diarrhea, vomiting and fever known as radiation sickness as shown figure.

(7) High levels dose of radiation may disrupt the blood cells seriously leading to diseases such as anemia and leukasemia.

(8) Chromosome abnormalities or mutation may cause delayed genetic effects such as cancer, eye cataracts and abnormalities in the future generations. These may develop many years after exposure to harmful radiation.