Class 12 Physics CHAPTER 13 NUCLEI
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NCERT Notes For Class 12 Physics CHAPTER 13 NUCLEI
Class 12 Physics CHAPTER 13 NUCLEI
Atomic number (Z)
- It is the number of protons in the nucleus.
- It is denoted by Z.
Mass number (A)
- It is the total number of nucleons
- Total no. of nucleons = no. of protons + number of neutrons
- Mass number is denoted by A.
Neutron number (N)
- It is the total number of neutrons.
- Denoted by N and N= A-Z.
Representation of nuclei
- An atom is represented as ZXA.
- A- mass number, Z- atomic number
- Accurate measurement of atomic masses is carried out with a mass spectrometer.
- Atomic mass unit (u), is used for expressing atomic masses.
- It is defined as 1/12th of the mass of the carbon (12C) atom.
Composition of nucleus
- Nucleus contains protons and neutrons
- The mass of a proton is
- James Chadwick-discovered neutrons
- Mass of a neutron is
- A free neutron is unstable.
- It decays into a proton, an electron and a antineutrino (another elementary particle), and has a mean life of about 1000s.
- It is stable inside the nucleus
- Atomic species with same atomic number but different mass number are called isotopes.
- Hydrogen has three isotopes having masses 1.0078 u (protium), 2.0141 u (deuterium), and 3.0160 u (tritium).
- Tritium nuclei, being unstable, do not occur naturally and are produced artificially in laboratories
• All nuclides with same mass number A and different atomic number are called isobars. Eg:
• Nuclides with same neutron number N but different atomic number Z are called isotones
SIZE OF THE NUCLEUS
- The radius of a nucleus with mass number A is given by
- Thus the density of nucleus is a constant, independent of A, for all nuclei.
- The density of nuclear matter is
Mass – Energy
- Einstein showed that mass is another form of energy and one can convert massenergy into other forms of energy, say kinetic energy and vice-versa.
- In a reaction the conservation law of energy states that the initial energy and the final energy are equal provided the energy associated with mass is also included.
- The difference in mass of a nucleus and its constituents, ΔM, is called the mass defect, and is given by
- The atomic mass of 16 8O found from mass spectroscopy experiments is seen to be 15.99493 u.
- Substracting the mass of 8 electrons (8 × 0.00055 u) from this, we get the experimental mass of O nucleus to be
Nuclear Binding Energy
- It is the energy equivalent of mass defect.
- If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy Eb will be released in the process.
- The ratio of the binding energy Eb of a nucleus to the number of the nucleons, A, in that nucleus is called binding energy per nucleon
Plot of the binding energy per nucleon Ebn versus the mass number A
Features of the Graph
- The binding energy per nucleon, Ebn, is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number ( 30 < A < 170).
- The curve has a maximum of about 8.75 MeV for A = 56 and has a value of 7.6 MeV for A = 238
- Ebn is lower for both light nuclei (A<30) and heavy nuclei (A>170).
- A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound.
- Thus energy would be released when a heavy nucleus is broken into light nucleus- the process- nuclear fission
- Similarly when two light nuclei (A≤ 10) are joined together to form a heavy nucleus , energy is released- nuclear Fusion
- Force that binds the nucleons together.
- Strongest force in nature.
- Short range force.
- Does not depend on charge.
- The property that a given nucleon influences only nucleons close to it is also referred to as saturation property of the nuclear force.
- The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres
- Acts through the exchange of π-mesons
Plot of the potential energy between two nucleons as a function of distance
- The potential energy is a minimum at a distance r0 of about 0.8 fm.
- This means that the force is attractive for distances larger than 0.8 fm and repulsive if they are separated by distances less than 0.8 fm.
- H. Becquerel discovered radioactivity in 1896.
- Radioactivity is a nuclear phenomenon in which an unstable nucleus undergoes a decay. This is referred to as radioactive decay.
- Three types of radioactive decay occur in nature :
- α-decay in which a helium nucleus (He) is emitted;
- β-decay in which electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of electron) are emitted;
- γ-decay in which high energy (hundreds of keV or more) photons are emitted.
Law of radioactive decay
- This law states that the number of nuclei undergoing the decay per unit time is proportional to the total number of nuclei in the sample.
- If a sample contains N undecayed nuclei and let dN nuclei disintegrate in dt second, thus the rate of disintegration
- The negative sign shows that the number of nuclei decreases with time.
- Where λ is called the radioactive decay constant or disintegration constant.
- Now, integrating both sides of the above equation, we get
- Here N0 is the number of radioactive nuclei in the sample at some arbitrary time t0 and N is the number of radioactive nuclei at any subsequent time t.
- Setting t0 = 0
N = No e– λt
- It gives the number of nuclei decaying per unit time
- Here R0 is the radioactive decay rate at time t = 0, and R is the rate at any subsequent time t.
- The total decay rate R of a sample of one or more radionuclide’s is called the activity of that sample.
- The SI unit for activity is becquerel, named after the discoverer of radioactivity.
- 1 becquerel = 1Bq = 1 decay per second
- An older unit, the curie, is still in common use.
Half life period (T1/2)
- It is the time in which the number of undecayed nuclei falls into half of its original number.
- Thus it is the time at which both N and R have been reduced to one-half their initial values.
Mean life (τ)
- It is the average life of all the nuclei in a radioactive sample.
- Mean life = total life time of all nuclei / total number of nuclei present initially
- The number of nuclei which decay in the time interval t to t + Δt is
- Each of them has lived for time t. Thus the total life of all these nuclei would be
- Therefore mean life is given by
- When a nucleus undergoes alpha-decay, it transforms to a different nucleus by emitting an alpha-particle (a helium nucleus)
- The difference between the initial mass energy and the final mass energy of the decay products is called the Q value of the process or the disintegration energy.
- This energy is shared by the daughter nucleus and the alpha particle,in the form of kinetic energy
- Alpha-decay obeys the radioactive law
- Alpha particles are positively charged particles
- Can be deflected by electric and magnetic fields.
- Can affect photographic plates.
- A nucleus that decays spontaneously by emitting an electron or a positron is said to undergo beta decay.
- In beta-minus decay, a neutron transforms into a proton within the nucleus according to
- Where ν is the antineutrino
- In beta minus (β −) decay, an electron is emitted by the nucleus.
- When β – particles are emitted, the atomic number increases by one.
- In beta-plus decay, a proton transforms into neutron (inside the nucleus)
- Where ν is the neutrino
- In beta plus (β+ ) decay, a positron is emitted by the nucleus,
- When β+ particles are emitted the atomic number decreases by one.
Neutrinos and Antineutrinos
- The particles which are emitted from the nucleus along with the electron or positron during the decay process.
- Neutrinos interact only very weakly with matter; they can even penetrate the earth without being absorbed.
- There are energy levels in a nucleus, just like there are energy levels in atoms.
- When a nucleus is in an excited state, it can make a transition to a lower energy state by the emission of electromagnetic radiation.
- As the energy differences between levels in a nucleus are of the order of MeV, the photons emitted by the nuclei have MeV energies and are called gamma rays.
- Most radionuclides after an alpha decay or a beta decay leave the daughter nucleus in an excited state.
- The daughter nucleus reaches the ground state by a single transition or sometimes by successive transitions by emitting one or more gamma rays.
- In conventional energy sources like coal or petroleum, energy is released through chemical reactions.
- One kilogram of coal on burning gives 107 J of energy, whereas 1 kg of uranium, which undergoes fission, will generate on fission 1014 J of energy.
- Enrico Fermi found that when neutrons bombard various elements, new radioactive elements are produced.
- The fragment nuclei produced in fission are highly neutron-rich and unstable.
- They are radioactive and emit beta particles in succession until each reaches a stable end product.
- The energy released (the Q value ) in the fission reaction of nuclei like uranium is of the order of 200 MeV per fissioning nucleus.
- The disintegration energy in fission events first appears as the kinetic energy of the fragments and neutrons.
- Eventually it is transferred to the surrounding matter appearing as heat.
- The source of energy in nuclear reactors, which produce electricity, is nuclear fission.
- The enormous energy released in an atom bomb comes from uncontrolled nuclear fission.
- Neutrons liberated in fission of a uranium nucleus were so energetic that they would escape instead of triggering another fission reaction.
- Slow neutrons have a much higher intrinsic probability of inducing fission in U (235) than fast neutrons.
- The average energy of a neutron produced in fission of U (235) is 2 MeV.
- In reactors, light nuclei called moderators are provided along with the fissionable nuclei for slowing down fast neutrons.
- The moderators commonly used are water, heavy water (D2O) and graphite.
- The Apsara reactor at the Bhabha Atomic Research Centre (BARC), Mumbai, uses water as moderator.
- The other Indian reactors, which are used for power production, use heavy water as moderator.
- It is the ratio of number of fission produced by a given generation of neutrons to the number of fission of the preceding generation.
- It is the measure of the growth rate of the neutrons in the reactor.
- For K = 1, the operation of the reactor is said to be critical, which is what we wish it to be for steady power operation.
- If K becomes greater than one, the reaction rate and the reactor power increases exponentially.
- Unless the factor K is brought down very close to unity, the reactor will become supercritical and can even explode.
- The explosion of the Chernobyl reactor in Ukraine in 1986 is a sad reminder that accidents in a nuclear reactor can be catastrophic.
- The reaction rate is controlled through control-rods made out of neutronabsorbing material such as cadmium.
- In addition to control rods, reactors are provided with safety rods which, when required, can be inserted into the reactor and K can be reduced rapidly to less than unity.
- The abundant U(238) isotope, which does not fission, on capturing a neutron leads to the formation of plutonium.
- Plutonium is highly radioactive and can also undergo fission under bombardment by slow neutrons
- In such a reactor, water is used both as the moderator and as the heat transfer medium
- In the primary-loop, water is circulated through the reactor vessel and transfers energy at high temperature and pressure (at about 600 K and 150 atm) to the steam generator, which is part of the secondaryloop.
- In the steam generator, evaporation provides high-pressure steam to operate the turbine that drives the electric generator.
- The low-pressure steam from the turbine is cooled and condensed to water and forced back into the steam generator.
- A kilogram of U(235) on complete fission generates about 3 × 104 MW.
- in nuclear reactions highly radioactive elements are continuously produced.
- Therefore, an unavoidable feature of reactor operation is the accumulation of radioactive waste, including both fission products and heavy transuranic elements such as plutonium and americium.
- Energy can be released if two light nuclei combine to form a single larger nucleus, a process called nuclear fusion.
- The fusion reaction in the sun is a multistep process in which hydrogen is burned into helium, hydrogen being the ‘fuel’ and helium the ‘ashes’.
- The proton-proton (p, p) cycle by which this occurs is represented by the following sets of reactions:.
- The combined reaction is
- In sun it has been going on for about 5 × 109 y, and calculations show that there is enough hydrogen to keep the sun going for about the same time into the future.
- In about 5 billion years, however, the sun’s core, which by that time will be largely helium, will begin to cool and the sun will start to collapse under its own gravity.
- This will raise the core temperature and cause the outer envelope to expand, turning the sun into what is called a red giant.
- If the core temperature increases to 108 K again, energy can be produced through fusion once more – this time by burning helium to make carbon.
Controlled thermonuclear fusion
- The first thermonuclear reaction on earth occurred at Eniwetok Atoll on November 1, 1952, when USA exploded a fusion device, generating energy equivalent to 10 million tons of TNT (one ton of TNT on explosion releases 2.6 × 10’22 MeV of energy).
- A sustained and controllable source of fusion power is considerably more difficult to achieve.