GENERAL PROPERTIES OF NUCLEI�By�Dr.L.Raja Mohan Reddy�Lecturer in Physics �GDC, Rajampeta

COMMOSSIONERATE OF COLLEGIATE EDUCATION

Nuclear Models

Nuclear models are the models to explain the properties and behaviour of the nucleus.

Liquid drop Model:-

Liquid drop model was proposed by Neil’s Bohr in the year of 1937. According to this model

• The nucleus is similar to a small electrically charged Liquid drop. i.e), the nucleus takes a spherical shape for its stability
• The nucleons move with this spherical enclosure like molecules in a liquid drop.
• The nucleons deep inside the nucleus are attracted from all sides by neighbouring nucleons. In this way the binding energy of nucleons of the surface of the nucleus is smaller than the binding energy for the nucleons inside the nucleus.

Assumptions of Liquid drop Model :-

• The material of the nucleus is incompressible.
• The density of all nuclei is same.
• The force in the nucleus consists of Coulomb forces between protons and powerful attractive nuclear forces.

Analogies between liquid drop Model and nucleus:-

• The nucleus is spherical in shape just as a liquid drop is spherical.
• The Surface tension force acts on the surface of the liquid drop similarly, a potential barrier at the surface of the nucleus.
• The density of liquid drop is independent of the volume; similarly density of nucleus is independent of its volume.
• There will be intermolecular force in the liquid drop, where as in nucleus there will be nuclear force.
• When a liquid drop allowed to oscillating it breaks up into two small drops, similarly due to nuclear fission nucleus breaks into two smaller nucleus.
• The molecules in liquid drop interact over short range and so I strue for nucleons in nucleus.

Merits:

• The calculation of atomic mass, binding energy can be done with good accuracy.
• It has been successfully applied in describing nuclear reaction and explaining nuclear fission.

De-Merits

• This model fails to explain other properties like magic numbers.

Shell Model:-

The Shell model assumes that structure of nucleus similar to electron shell in an atom. ⮚ An electrons are grouped in an atom, similarly protons and neutrons are grouped in nucleus. ⮚ The nuclei containing protons and neutrons number 2, 8, 20, 28, 50, 82, 126 etc, known as magic numbers. ⮚ The nuclei for which Z (Protons), A-Z (neutrons) are more stable than their neighbours.

Eg: 2, (₂He⁴) Z=2, A-Z=4

8, (O¹⁶) Z = 8, A-Z = 8 )

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⮚The nuclei for which Z or A-Z is Magic numbers are especially stable.

ex: ₂₈Ni⁶² (Z=28, A-Z=34)

₃₈Sr⁸⁸ (Z = 38, A-Z = 50)

• The binding energy curve shows breaks at these nuclei which represents sudden increase on their binding energy in nucleon.
• The Electric quadruple moments of magic number nuclei very low (nearly zero) compared with those other nuclei.
• This Shows that these nuclei have almost spherical charge distribution. Merits: ¨ This model has been successful to explaining for the magic numbers. ¨ It is also explain the observed Angular momentum, Magnetic moments and Electric quadruple moments of nuclei.
• Demerits:
• The Shell model fails to explain and account for large nuclear quadruple moments and spheroidal shapes of many nuclei.

Introduction�

• Geiger and Muller developed a ‘Particle detector’ for measuring ‘ionizing radiation’ in 1928. They named it as ‘Geiger Muller Counter’. Geiger counter is also called as Geiger tube. This instrument is actually used for detecting and measuring ionizing radiation like alpha particles, beta particles, and gamma rays. A Geiger-Müller counter can count individual particles at rates up to about 10,000 per second and is used widely in medicine and in prospecting for radioactive ores.

Geiger Muller Counter:

Principle

• When an ionizing particle passes through the gas in an ionizing chamber, it produces a few ions. If the applied potential difference is strong enough, these ions will produce a secondary ion avalanche whose total effect will be proportional to the energy associated with the primary ionizing event.
• If the applied potential difference is very high, the secondary ionization phenomenon becomes so dominant that the primary ionizing event loses its importance.A high energy particle entering through the mica window will cause one or more of the argon atoms to ionize. The electrons and ions of argon thus produced cause other argon atoms to ionize in a cascade effect. The result of this one event is sudden, massive electrical discharge that causes a current pulse. The current through R produces a voltage pulse of the order of 10μV. An electron pulse amplifier accepts the small pulse voltage and amplifies them to about 5 to 50 V. The amplified output is then applied to a counter. As each incoming particle produces a pulse, the number of incoming particles can be counted.

Construction �

• It consists of a hollow metal case enclosed in a thin glass tube. This hollow metal case acts as a cathode.
• A fine tungsten wire is stretched along the axis of the tube and is insulated by ebonite plugs. This fine tungsten wire acts as anode.
• The tube is evacuated and then partially filled with a mixture of 90% argon at 10 cm pressure and 10% ethyl alcohol vapours at 1cm pressure.
• The fine tungsten wire is connected to positive terminal of a high tension battery through a resistance R and the negative terminal is connected to the metal tube.
• The direct current voltage is kept slightly less than that which will cause a discharge between the electrodes.
• At one end of the tube a thin window of mica is arranged to allow the entry of radiation into the tube.

Working�

• The tube is filled with Argon gas, and around voltage of +400 Volts is applied to the thin wire in the middle. When a particle arrives into the tube, it takes an electron from Argon atom. The electron is attracted to the central wire and as it rushes towards the wire, the electron will knock other electrons from Argon atoms, causing an "avalanche". Thus one single incoming particle will cause many electrons to arrive at the wire, creating a pulse which can be amplified and counted. This gives us a very sensitive detector.

Plateau graph �

• There is a threshold below which the tube doesn’t work. This can be several hundred volts. After this, the number of pulses is proportional to the voltage. This region is known as proportional region.
• If the applied voltage is increased further, then a point will be reached after which the count rate remains constant over a certain region. This region is known as plateau region or Geiger region. This region is used for Geiger Muller operation.
• Beyond the plateau region the applied electric field is so high that a continuous discharge takes place in the tube and the count rate increases very rapidly. It does not require any ionization event to happen so that the tube must not be used in this region.

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• The Geiger Muller counter can account for about 500 particles per second. The GM counter will not register those particles that pass through it in the dead time. Dead time refers to the time taken by the tube to recover between counts. It requires about 200 μs for the tube to recover. If lot of particles enter the GM tube at a rapid rate, the tube will not have time to recover and some particles may not be counted.
• The efficiency of the counter is defined as the ration of the observed counts per second to the number of ionizing particles entering the counter per second. Counting efficiency is defined as the ability of counting of the GM counter.

Applications�

• To detect radioactive rocks and minerals in the course of mineral prospecting.
• For Fire responders for making an initial determination of radiation risk.
• For Hazard Management personnel in checking for radiation danger in an emergency situation.
• To check for environmental levels of radioactivity near a nuclear power facility.
• To test for danger amidst a nuclear accident or leakage of radioactive coolant.
• To check for radioactive contamination of clothing and shoes in your workplace.
• Radiation detection in the scrap metal processing business.
• To check possible leakage or exposure to X-rays in a medical facility
• To check for radiation in areas where depleted uranium ammunition shells have been used.
• To check for irradiated gemstones in the jewellery trade.
• To check the levels of iodine 131 in cancer patients undergoing radiation therapy.
• You are in close proximity to a uranium mine and want to test the soil and environment for dangerous levels of radioactivity.
• To test for radioactive contamination of food.
• To check materials in your anthropology or archaeology field.
• To check for radioactivity in metal objects in your home or office that could be made of recycled radioactive materials.

Wilson Cloud Chamber

C.T.R. Wilson designed a cloud chamber which made it possible to see and photograph the tracks of ionising particles. Unlike In the case of other counters, in the case of cloud chamber we can see actually the tracks of ionising particles. In the case of nuclear reactions, a single photograph can show us how many fragments are formed in a reaction, what are their directions before and after the èvent and their ranges also..

Principle : The basic principle of Wilson Cloud chamber is based on the principal that super cooled vapour condenses only on nuclei like dust particles or ions and if the ions are not present, they remain in super saturated vapour state which is most unstable. That is they do not condense. In wilson cloud chamber, ions act as nuclei for condensation of super saturated water vapour.The ions are produced by the passage of high energy particles like a,b and y radiations etc., through the chamber. This formation of the condensation cloud in an ionized air forms the basic principle of cloud chamber.

Construction

There are two types of Wilson cloud chambers, 1) Expansion type Wilson cloud chamber, 2) Diffusion type Wilson cloud chamber. Here let us discuss expansion type Wilson cloud chamber which is shown in fig.

It consists of an air tight cylinder C provided with a movable piston P at the bottom and the top end is covered with a glass plate G. The chamber contains a mixture of alcohol vapour and air. A small amount of water and alcohol is kept in a trough at the lower end of the chamber. The chamber is illuminated by mercury vapour lamp L whose light enters the chamber through the side window. Radiations emitted by the radiactive substance enter into the chamber by the side window as shown in fig. Photographic camera is adjusted on the top side of the chamber.

Working:

The volume of air in the cylinder C is suddenly increased by pulling the piston downwards. Then adiabatic expansion takes place in the chamber. This sudden expansion cause cooling and as a result of cooling the water vapour gets super saturated. At this stage, the ionizing charged particles are allowed into the chamber and they cause ionization of air inside the chamber C. Therefore, negative and positive ions are formed all along the path of these charged particles. These ions act as condensation centres. Hence water vapour inside chamber C which is in super saturated state condenses and forms droplets on the ions along the path of rays. The droplets are clearly visible when chamber is illuminated by light. The tracks can be photographed with the help of camera. Different particles produce different types of tracks as shown in fig.

Heavy, slow and highly ionizing particles (a particles) produce short, densely packed straight line tracks. On the other hand, the light, slow and less ionizing particles (B-particles) produce thin and curved tracks. We know that the ionizing power of y-rays is very low and hence they are never observed in a cloud chamber.

The chamber is cleared off the ions by means of sweeping electric field applied across the chamber. The piston Pis returned to the original position so that the chamber is once again ready to study the track of another ionizing particle.

when the cloud chamber is placed between the poles of strong electromagnet, the ions travel in curved paths. Then from the direction of curvature the positive and negative charged particle can be distinguished from each other, the curvature not only gives the sign of the charge but the momentum of the ionizing particle can be estimated. As a result energy can also be calculated by using formula.

mv2/r = Bqv

mv = momentum = Bqr =p

Energy is given by E = pc

Here c = velocity oF light

Advantages

1. Cloud chamber can be used to study about radioactive radiations, cosmic rays, positrons, neutrinoes and artificial transmutations.

2. By counting drops in cloud track, the specific ionisation can be determined.

3. The tracks of ionising particles can be recorded on a photographic plate using cloud chamber.

4. By applying a magnetic field on the moving particle inside the chamber, its momentum and energy can be determined

5. By seeing the direction of curvature of track in the magnetic field, sign of charge of ionising particle can be determined,

6. The cloud chamber has led to the discovery of many elementary particles like positron, Peti meson etc.

Disadvantages:

1. One is not always sure of the sense of track photographed.

2. If the range of the ionizing particle exceed the dimension of the chamber, the tracks of such "particles cannot be photographed..

3. This can not directly record the track of electrically neutral particle like neutron.

4. There remains a certain amount of uncertainity about the nature of the nuclei.

5. The limitation of the cloud chamber lies in the fact that it needs a

definite time interval to recover after an expansion. Hence it is not possible to have a continuous record of events taking place in the chamber.

Construction:

Solid State Detector :

The solid state detector essentially possess a p-n diode. The diode is formed by depositing a n-type silicon on a p-type silicon as shown in fig. Contact is made with n-type silicon layer by a thin evaporated film of gold. While the other side of p-type silicon is coated with a metallic plating. In order to minimise the current flowing in the detector, when no radiation is striking it, a reverse biased diode is always used..

The positive bias applied to the gold film will push all the positive charge carriers away from the junction and produce a depletion layer as indicated in the figure. The depletion layer contains almost no carriers of either sign.

When an energetic charged particle travels through the depletion layer, its interaction with the electrons in the crystal produces electron - hole pairs. There is an electron - hole pair for every 3.5 eV (in silicon) of energy lost by the charged particle. The electrons and holes are swept away by the applied electric field and registered as a voltage pulse over the resistor R. The number of charge carriers produced in a semiconductor material is approximately 10 times as large as the number of ion pairs produced in a gas ion chamber i.e., the energy extended per pair Is about 3.5 eV in silicon compared to about 30eV for gases. The voltage pulse will therefore be about 10 times larger. Hence this detector has much better energy resolution than other radiation detectors. In solid state detectors the silicon has been used mostly because of its low intrinsic conductivity. This means that the detector can be operated at room temperature without excessive leakage current. For y-ray detection, Germanium detectors are much better than silicon because of the larger density of Germanium.

Working:

Advantages :

1. It is useful for highly penetrating radiations like gamma rays 2. Energy required for the creation of an ion pair, in solids is much smaller as compared to air or gases. 3. If the particle range is less than the junction thickness then the pulse height is proportional to the kinetic energy of the incident particles. 4. High counting rates are possible. 5. The rise time of pulse is very small, which makes them more suitable in coincidence experiments.

6. These donot require any window for allowing the particle to enter.

7. The applied voltage and as well as size and weight of these counters are considerably small.

Elementary particles:

Elementary pasticle is a particle not known to have substructure. If an elementary particle Truly has no structure, then it is one of the basic particles of the universe from which other particles are made.

On the basis of the nature of the force by which a particle interacts with other particles, the elementary particles can be classified into three families. 1) Photons 2) Leptons 3) Hadrons

1) Photons:-The photon family has only one member i.e. The photon. .

Photon interacts only with charged particles and the interaction is electromagnetic.

2) Lepton's:- The Lepton family consists of particles that interact by means of weak nuclear force. O The Lepton's can also exert gravitation and Electromagnetic forces on other particles.

3) 3. Hadron's:- The hadron family contains the particles that interact by means of both the strong and weak nuclear forces. 0 Most of hadrons are short lived. Hadrons are further subdivided into two groups called the mesons and the baryons.