NUCLEAR PHYSICS

Nucleus:

Nucleus is the central core of an atom. Entire mass of an atom is concentrated in the nucleus. The atomic nucleus was discovered in 1911 by Rutherford. Nucleus consists of protons and neutrons and in general protons and neutrons are called nucleons. Hydrogen nucleus does not contain neutron and has only one proton.

Proton:

The rest mass of proton is 1.007277 amu and charge of proton is +1.6 x 10^–19 coulomb. The rest mass of proton is 1836 times the rest mass of electron.

Neutron:

The rest mass of neutron is 1.008665 amu and charge of neutron is zero. Neutrons are slightly heavier than proton.

Atomic mass unit:

1 atomic mass unit (amu) is 1.66 x 10^-27 kg. The mass of a nucleon is 1.67 x 10^–27 kg.

Atomic mass unit is defined as mass of 1/12^th of carbon-12 atom and the energy equivalent of 1 amu is 931 MeV.

Representation of a nucleus:

The symbolic representation of a nucleus is _zX^A.  Z is the atomic number and the atomic number can be the number of protons or number of electrons. A is the mass number, which consist of the number of protons and neutrons.

Nuclear radius:

The nuclear radius is of the order of 10^–14 m to 10^–15 m. The equation for the atomic radius is given by R = r_o A^1/3, where r_o is a constant and has a value of 1.3 x 10^–15 m.

Nuclear mass:

The nuclear mass is the total mass of protons and neutrons and is also equal to the total mass of the nucleons. Nuclear mass = Zm_p + Nm_n = Am_N where Z is the number of protons and m_p is mass of one protons, N is the number of neutrons and m_n  is mass of one neutron, A is mass number and m_N is mass of one nucleon.

  

Nuclear density:

Nuclear density = nuclear mass / nuclear volume. Nuclear density is independent of mass number A. Nuclear density has value of 1.816 x10¹⁷ kg/m³. Nuclear density is extraordinarily very high and it very large compared to density of lead (1.134 x 10⁴ kg/m³), which is considered to be the highest dense material available.

Isotopes:

Elements having the same atomic number Z and different mass number A are called isotopes. Examples are isotopes of hydrogen, ₁ H ¹, ₁ H ², ₁ H ³ and ₉₂ U ²³⁵, ₉₂ U ²³⁸. Since the number of charge is responsible for the characteristic property of an atom, all isotopes

of an element have the same chemical properties but different physical properties

Isobars:

Elements having the same mass number A and different atomic number Z is called isobars. The nuclei ₈ O ¹⁶, ₇ N ¹⁶ are example of isobars. The isobars are atoms of different elements and have different physical and chemical properties

Isotones:

Elements having the same number of neutrons are called isotones. Examples are isotopes of hydrogen, ₆ C ¹⁴, ₇ N ¹⁵, ₈ O ¹⁶, N = 8 in each case.

Isomers:

Elements having the same atomic number Z and same mass number A but differ from one anther is their nuclear energy states and exhibit differences in their internal structure are called isomers. The elements are distinguished from their different half life time.

Mass defect:

Mass defect is defined as the mass difference between the sum of the masses of the constituents of an atom and its actual mass M. Mass defect Dm = [(Zm_p + Nm_n)– M]

Binding energy:

Binding energy B.E is the energy needed to bind the nucleons in the nucleus and is also the conversion of mass defect into energy to bind the nucleons in the nucleus. Binding energy = Dm C² = [(Zm_p + Nm_n)– M]C²

Nuclear force

Nuclear force is the strongest force that binds the protons and neutrons inside the nucleus. There are three types of nuclear forces namely (p-p) force, (p-n) force and (n-n) force.

  

Ø  Nuclear forces are short-range forces and they are effective only at short range.

Ø  Nuclear forces are charge independent.

Ø  Nuclear forces are the strongest known forces in nature.

Ø  Nuclear forces have saturation property which means nuclear forces are limited in a particular range. As a result each nucleon interacts only with a limited number of nucleons nearest to it.

The liquid drop model:

The liquid drop model was proposed by Neils Bohr. Neils Bohr has observed that there are certain marked similarities between an atomic nucleus and a liquid drop.

Ø  The nucleus is spherical in shape in the stable state just as a liquid is spherical due to symmetrical surface tension forces.

Ø  The force of surface tension sets on the surface of the liquid drop and similarly there is a potential barrier at the surface of the nucleus.

Ø  The density of the liquid drop is independent of its volume and similarly the density of the nucleus is also independent of its volume.

Ø  The intermolecular forces in a liquid are short-range forces. The molecules in a liquid drop interact only with their immediate neighbors. Similarly the nuclear forces are short-range forces. The nucleons interact only with their neighbors and this leads to the saturation in the nuclear forces and constant binding energy per nucleon.

Ø  The molecules evaporate from a liquid drop on raising its temperature. Similarly when energy is given to a nucleus by bombarding it with a nuclear projectile a compound nucleus is formed which emits nuclear radiation.

Ø  When a small drop of liquid is allowed to oscillate it breaks up into two smaller drops of equal size. Similarly when sufficient energy is given to a nucleus by bombarding with a nuclear projectile it breaks into two smaller nuclei.

Shell model:

Shell model is some times referred to as independent particle model. According to this model the protons and neutrons are grouped in shells in the nucleus similar to extra nuclear electrons are grouped in shells in the nucleus. The number of nucleons in each shell is limited by Paula exclusion principle.

Neutron:

Neutron is emitted when Beryllium is bombarded by alpha particles.Bothe and Becker identified them as highly penetrating radiations. Joliot and Curie detected that they can knock out protons from hydrogenous substances. Chadwick discovered that their mass is nearly equal to that of protons and he is the one who named it as neutron.

   

Ø  Neutrons are changeless particles.

Ø  They are fundamental constituents of all nuclei except hydrogen ₁H¹.

Ø  It has greatest stability and has high penetrating power.

Ø  It cannot be deflected by electric and magnetic field

Ø  The free neutron is unstable, its half-life is 13 minutes and it decays into a proton, electron and antineutrino.

Ø  Slow neutrons have energy range between 0 to 1000 eV and fast neutrons have energy range between 0.5 MeV to 10 MeV.

Ø  Fast neutrons are slowed down by moderators. Since the slow neutrons are in thermal equilibrium with the medium through which they pass, they are also called as thermal neutrons. Paraffin, heavy water and graphite are used as moderators. Slow neutrons are capable of producing fission reaction when sent to uranium nucleus.

Nuclear fission:

Nuclear fission is the process of breaking a heavy nucleus into two smaller nuclei with the release of large amount of energy. For example when Uranium is bombarded with neutron it splits into Barium, Krypton, neutron and energy. ₉₂U²³⁵ and ₉₄Pu²³⁹ are fissionable materials, which are used as fuels in nuclear reactors. by neutrons of all energies. The material ₉₂U²³⁸ is fissionable only with fast neutrons.

Chain reaction:

Chain reaction is a self-propagating process in which number of neutrons goes on multiplying rapidly almost in geometrical progression during fission till whole of fission material is disintegrated.

Chain reaction consists of two types namely controlled chain reaction, which lead to nuclear reactor, and uncontrolled chain reaction, which lead to an atom bomb.

Multiplication factor:

The multiplication factor k is defined as the ratio of number of neutrons in any one generation to the number of neutrons in the preceding generation. The fission reaction is critical or steady when k = 1, is building up or super critical when k >1 and it is dying down or sub critical when k < 1.

Critical size:

Critical size of a system containing fissile material is defined as the minimum size for which the number of neutrons produced in the fission process just balance those lost by leakage and non fission capture.

Atom bomb:

The principle of fission is made use in the construction of the atom bomb. An atom bomb consists essentially of two pieces of uranium each smaller than the critical size and a source of neutron. A cylindrical third mass of uranium is propelled so that it will fuse together with the other tow pieces.

Parts of nuclear reactor:

                                      

Ø  Fuel or fissionable materials are mostly uranium and rarely plutonium, which are sealed in aluminium cylinders.

Ø  Neutron source gives thermal neutrons to induce fission reactions.

Ø  Moderators, which are heavy water, graphite and paraffin, used to slow down the fast neutrons.

Ø  Control rods, which are cadmium or boron, can absorb neutrons so that the fission reaction can be controlled.

Ø  Neutron reflector, which reflects the escaping neutrons back to the reactor.

Ø  Coolant, which is heavy water or liquid sodium, can absorb the heat generated.

Ø  Shielding can be done by thick lead lining surrounded by concrete wall to prevent harmful radioactive radiation.

Nuclear fusion:

Nuclear fusion is the process of fusing two or more light nuclei combine together to form a single heavy nucleus with the release of large amount of energy.For example when four hydrogen nuclei are fused together, a helium nucleus is formed. The mass of the single helium nucleus formed is less than the sum of the masses of four hydrogen nuclei. The difference is mass is converted into energy according to Einstein’s mass energy equation.

In the sun hydrogen and helium are in plasma state i.e. highly in ionized state. Proton-Proton cycle takes place in sun.  Carbon-Nitrogen cycle takes place in stars whose temperature is greater than that of the sun. In this cycle carbon is used as a catalyst.

Thermonuclear reactions:

The main difficulty is the fusion of nuclei is the electric force of repulsion between the positively charged nuclei. Fusion is possible when the kinetic energy of each of the nucleus is large enough to overcome the repulsion. Fusion reaction can take place only at very high temperatures of the order of 10⁷ to 10⁹ K.

Hydrogen bomb:

Hydrogen bomb is a device, which makes use of the principle of nuclear fusion. The very high temperature required for an uncontrolled thermonuclear reaction is obtained by the detonation of an atom bomb. The atom bomb by fission process produces a very high temperature at which thermonuclear reactions start resulting in the fusion of hydrogen to form helium and release of very high energy.

Elementary particles

Baryons or heavy particles:

Proton and particles heavier than proton form this group. Protons and neutrons are called stable baryons and particles having masses greater than nucleons are called unstable baryons. Every baryon has an antiparticle.

Hyperons:

Hyperons are special cases of baryons called unstable baryons characterized by time decay of the order of 10^-10 second. Hyperons have mass value greater than the mass of nucleons or the mass value intermediate between those of neutron and deuteron. There are four types of hyperons namely Lambda, sigma, Xi and omega.

Leptons:

This group contains particles of mass less than the mass of p mesons or pions. electrons, positrons, neutrino, antineutrino, positive and negative muons are leptons.

Mesons:

The rest mass of these particles varies between 250m_e and 1000m_e. The mesons are agents of interaction between particles inside the nucleus. Baryons and mesons are jointly called hadrons and are the particles of strong interaction.

Radioactivity:

Natural radioactivity was discovered by Henry Becquerel in 1896. The rays emitted from uranium were called Becquerel rays.Madame curie and here husband Pierre Curie discovered the highly radioactive element radium

Natural radioactivity is the spontaneous emission of alpha, beta and gamma rays by elements whose atomic number are greater than 82. That is, all elements having atomic number greater than lead are natural radioactive elements.

Radioacivity was not affected by strongest physical and chemical treatment and excessive heating or cooling or powerful reagent.

The electrons orbiting the nucleus are not responsible for radioactivity. The source of radioactivity is the nucleus of an atom. Radioactivity is the result of the disintegration of an unstable nucleus.

The half-life period of a radioactive material is the time taken by the element for half the number of its atoms to disintegrate. The half-life period of a radioactive element is inversely proportional to the decay constant of the element. T = 0.6931/l.

The mean life of a radioactive material is the average or mean lifetime of all the atoms of a radioactive element present. The mean life t = total life time of all the atoms/total number of atoms = 1/l.

The unit of radiation is roentgen. The quantity of radiation that produces 1.6 x 10¹² ion pairs in 1 gm of air is defined as roentgen.

Alpha decay

The emission of alpha particle by a nucleus leads to a decrease of atomic number decreases by 2 and a decrease of mass number by 4.

Beta decay

The emission of beta particle by a nucleus leads to an increase in atomic number by 1 and mass number remains the same.

Gamma decay

The emission of gamma rays by a nucleus leaves the atomic number mass number remain unaltered.

Geiger Nuttal law:

The range of R of an alpha particle and the disintegration constant l of the radioactive element that emits it are related as logl  = A+B log R. According to this relation when the disintegration constant is high the range is also high. Since the range depends on the energy we conclude that the radioactive substances of large decay constant emit higher nervy alpha particles.

The neutrino theory of beta decay:

In 1934 Fermi developed a theory to explain the continuous beta ray emission. According to this theory, during beta decay a neutron disintegrates into a proton, electron and a neutrino. The proton remains inside the nucleus and the electron and antineutrino are released from the nucleus.

Artificial radioactivity:

Artificial radioactivity discovered in 1934 by Curie and Joliot. The disintegration of light elements leads to artificial radioactivity. Artificial radioactive substances emit electron, neutron and positron or gamma ray and they do not emit alpha rays.

The transmutation of one element into another by artificial means is called artificial transmutation or artificial radioactivity.

Radioisotopes can be produced by bombarding the element with accelerated particle from a cyclotron. An element can be converted into a radioisotope by continuous bombardment of neutron inside the reactor.

Applications of radioisotopes

Radio-hosphorous-30 is used to determine the rate of absorption of an element in a fertilizer.

Radio-cobalt-60 is used to treat malignant tumour-cancer.

Radio-iodine 131 is used to locate brain tumour, to find the extent of enlargement of thyroid gland.

Radio-sodium-24 is used to check the blood circulation in heart and other parts

Radio-carbon-14 is used to determine the age of fossils and relics.

Uranium 235 and Lead 206 are used to determine the age of rocks.

Radio carbon dating:

Living being takes carbon-14 with food and air. When death occurs the intake of carbon-14 stops. Thencarbon-14 deacy and get converted into nitrogen-14. By determining the percentatge of carbon-14 in dead matter the age of specimen can be estimated. This method is used to find the age of mummies and relics. Thus carbon-14 provides radioactive clock for anthropologists.

Uranium dating:

The age of earth has been determined by the amount of uranium-235 and Lead-206 present in the specimen

Geiger Muller counter:

Geiger Muller counter is a device used to detect the radiation. The neon gas is used for ionization. The principle of this counter is based on the property of alpha particles have the highest ionizing power, beta particles have lower ionizing power and gamma rays have lowest ionizing power. The Geiger Muller counter has a cylinder containing a gas and if the radioactive rays sent to the gas it gets ionized based on the type of radioactive ray. The emf developed due to ionization is amplified to activate an electronic counter.

Nuclear interaction and particle accelerators:

The rearrangement of nucleons leading to the formation of new nuclei when two or more nuclei are close together is called nuclear interaction. Nuclear reactions are produced by bombardment with energetic projectiles like protons, deuterons, alpha particles, neutrons and electrons.

Cyclotron:

The cyclotron is one of the particle accelerators, which accelerates particles to very high kinetic energy. The cyclotron is a spiral type accelerator and was developed by Lawrence in 1930. It has a hollow cylinder divided into tow sections known as Dees. The Dees are connected to high frequency oscillator. A magnetic field perpendicular to the place of the Dees is applied.

By the action of high frequency oscillator and magnetic field the ion inside the Dees describes a circular path of angular velocity w = v/r = Bq/m is a constant. The frequency of rotation in a cyclotron is equal to Bq/2pm and the time period of rotation is equal to 2pm/Bq.

The advantages of cyclotron:

Ø  Cyclotron can accelerate protons, deuterons and alpha particles.

Ø  It requires comparatively low voltages and occupies a comparatively low space.

The limitations of cyclotron:

Ø  It is difficult to arrange an intense magnetic field over a large area and the deflector plates consume a large voltage.

Ø  At very high voltages the frequency Bq/2pm is not a constant and thus lead to phase instability. The frequency of the ion can be kept constant by increasing the magnetic field. In another form of apparatus the frequency of the applied ac is varied so that it is always equal to the frequency of rotation of the ion.

Ø  Electrons cannot be accelerated by cyclotrons due to their relativistic mass variation eve at low energy level of 20 keV.

Synchrocyclotron:

Synchrocyclotron is a modified form of the Lawrance cyclotron. This consists of only one Dee placed in a vacuum chamber between the poles of an electromagnet. Instead of second Dee opposite the opening of the Dee there is a metal sheet connected to the earth. The alternate potential difference applied to the Dee is made to ruse and fall periodically instead of remaining constant.

The frequency is changed at such a rate that as the ion lags a little due to the increase in mass caused by increase in velocity the electric field frequency also automatically lags in variation. Hence the particle always enters the Dee at the correct moment when it can experience maximum acceleration.

The Betatron:

Betatron is a device used to accelerate electrons (beta particles) to very high energies. D.W.Kerst constructed it in 1941. It consists of a doughnut shaped vacuum chamber placed between the pole pieces of an electromagnet. The electromagnet is energized by an alternating current. The magnet produces a strong magnetic field in the doughnut. The electrons are produced by an electron gun and are allowed to move in a circular orbit to constant radius in the vacuum chamber. The magnetic field varies very slowly compared with the frequency of the electrons in the equilibrium orbit.

The linear accelerator:

The linear accelerator consists of a series of coaxial hollow metal cylinders or drift tubes 1,2,3,4,5, etc. They are arranged linearly in a glass vacuum chamber. The alternate cylinders are connected together, the odd numbered cylinders being joined to one terminal and the even numbered ones the second terminal of the high frequency oscillator. After half a cycle the polarities are revered ie 1 and 3 will be negative and 2 and 4 positive.

The positive ions enter along the axis of the accelerator during the half cycle, when the drift tube 1 is negative so that the positive ions pass through the first tube with a velocity. The length of the tube 1 is so adjusted that as the positive ions come out of it, the tube has a positive potential and the next tube 2 has a negative potential and thus the positive ions are accelerated with high kinetic energy.

The limitations of linear accelerator:

Ø  The length of the accelerator becomes inconveniently large and it is difficult to maintain vacuum in a large chamber.

Ø  The ion current available is in the form of short interval impulses because the ions are injected at an appropriated moment.