# NCERT Notes For Class 12 Physics CHAPTER 13 NUCLEI

## Class 12 Physics CHAPTER 13 NUCLEI

NCERT Notes For Class 12 Physics CHAPTER 13 NUCLEI, (Physics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions with inside the very last asked from those.

Sometimes, students get stuck with inside the exercises and are not able to clear up all of the questions.  To assist students, solve all of the questions and maintain their studies without a doubt, we have provided step by step NCERT Notes for the students for all classes.  These answers will similarly help students in scoring better marks with the assist of properly illustrated Notes as a way to similarly assist the students and answering the questions right.

## 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

## Atomic mass

• 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

• 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

## Isotopes

• 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

## Isobars

• All nuclides with same mass number A and different atomic number are called isobars. Eg:

## Isotones

• 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

• Where

• 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.

## Mass Defect

• 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

15.99053 u.

## 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).

Conclusions:

• 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

## NUCLEAR FORCE

• 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.

• 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.
• Thus

• 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

• Thus

N = No e– λt

## Decay Rate

• 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.

Thus

• 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

## Alpha decay

• 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.

## Beta decay

• 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.
• Eg:

• 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,
• Eg:

• 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.

## Gamma decay

• 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.

## NUCLEAR ENERGY

• 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.

## Nuclear Fission

• Enrico Fermi found that when neutrons bombard various elements, new radioactive elements are produced.
• Eg:

• 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.

## Nuclear reactor

• 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.

Multiplication factor

• 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

Pressurized-water reactor

• 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.

## Nuclear fusion

• 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.