The document discusses nuclear models, specifically the liquid drop model. It provides three key points:
1. The liquid drop model views the nucleus as similar to a liquid drop, with nucleons interacting through short-range forces like molecules in a liquid. This explains trends in binding energy with mass number.
2. The Beithe-Weizsacker formula provides a semi-empirical expression for binding energy as a function of mass and atomic number. It includes terms for volume, surface tension, electrostatic repulsion and asymmetry.
3. The formula allows predicting stability against alpha or beta decay. Alpha decay energy can be calculated and nuclei with mass over 200 are predicted to alpha decay. Mass parabol
1. Nuclear models like the liquid drop model and shell model describe aspects of nuclear structure and behavior. The liquid drop model treats the nucleus like a liquid drop while the shell model treats nucleons as moving independently in nuclear orbits.
2. The shell model explains nuclear magic numbers and properties like spin and parity. Magic numbers correspond to nuclear stability when the number of protons or neutrons equals 2, 8, 20, 28, 50, 82, etc. The shell model accounts for magic numbers in terms of closed nuclear shells.
3. While insightful, nuclear models have limitations and do not fully describe all nuclear phenomena. The liquid drop model cannot explain magic numbers while the shell model fails to explain the stability of certain
The document discusses nuclear models and nuclear forces. It describes three nuclear models: the liquid drop model, shell model, and collective model. The liquid drop model treats the nucleus as a liquid drop and examines its global properties. The shell model arranges nucleons into energy shells like electrons in an atom and explains magic numbers. The collective model incorporates aspects of the liquid drop and shell models. Nuclear forces operate very strongly within the nucleus, are attractive between protons and neutrons, and are responsible for nuclear stability.
The nuclear shell model was developed in 1949 and describes how protons and neutrons occupy discrete energy levels, or shells, within the nucleus, analogous to the way electrons occupy shells in atoms. It explains several nuclear properties that the liquid drop model could not, such as magic numbers and spin. Nuclei with magic numbers of protons or neutrons are particularly stable due to their filled shells. Evidence for the shell structure includes increased stability and separation energies at magic numbers, and the stable isotopes at the end of radioactive decay chains all having magic numbers of protons. The model makes assumptions like an average central force field and independent nucleon motion within orbits. However, it has limitations like not explaining schmidt lines or higher energy nuclear states fully
The document discusses various types of nuclear reactions. It defines nuclear reactions as processes where two nuclei or nuclear particles collide and produce different products than the initial particles. It describes several types of nuclear reactions including elastic and inelastic scattering, pickup and stripping reactions, compound nuclear reactions, radioactive capture, and photo disintegration. Elastic scattering involves the projectile and outgoing particles being the same, while inelastic scattering results in a loss of energy and particles scattered in different directions with different energies. Pickup reactions involve a gain of nucleons from the target, and stripping reactions involve one or more nucleons captured from the projectile. The document provides examples of each type of reaction.
The liquid drop model of the nucleus was first proposed by George Gamow and developed by Niels Bohr and John Archibold in 1937. It treats the nucleus as an incompressible nuclear fluid drop made up of nucleons (protons and neutrons) held together by the strong nuclear force. Each nucleon inside the nucleus moves like molecules in a liquid, bound by nuclear forces similar to intermolecular forces in liquids. When a heavy nucleus like U235 absorbs a neutron, surface oscillations deform its original shape as the Coulomb energy attempts to distort it further.
This document discusses elementary particles and the fundamental forces that govern their interactions. It begins by explaining that atoms were once thought to be elementary but are actually made up of protons, neutrons, and electrons. Many new unstable particles were discovered in the mid-20th century. Quarks were identified as the constituents of protons and neutrons, reducing the number of elementary particles. The four fundamental forces - strong, electromagnetic, weak, and gravitational - are described along with the particles that mediate each force. The discovery of antimatter by Dirac and pair production/annihilation are summarized. Pions were predicted by Yukawa to mediate the nuclear force. Feynman diagrams provide a graphical representation of particle interactions. Conservation laws including baryon
Nuclear Quadrupole Resonance Spectroscopy (NQR) is a chemical analysis technique that detects nuclear energy level transitions in the absence of a magnetic field through the absorption of radio frequency radiation. NQR is applicable to solids due to the quadrupole moment averaging to zero in liquids and gases. The interaction between a nucleus's quadrupole moment and the electric field gradient of its surroundings results in quantized energy levels. Transitions between these levels are detected as NQR spectra and provide information about electronic structure, hybridization, and charge distribution. NQR finds applications in studying charge transfer complexes, detecting crystal imperfections, and locating land mines.
1. Nuclear models like the liquid drop model and shell model describe aspects of nuclear structure and behavior. The liquid drop model treats the nucleus like a liquid drop while the shell model treats nucleons as moving independently in nuclear orbits.
2. The shell model explains nuclear magic numbers and properties like spin and parity. Magic numbers correspond to nuclear stability when the number of protons or neutrons equals 2, 8, 20, 28, 50, 82, etc. The shell model accounts for magic numbers in terms of closed nuclear shells.
3. While insightful, nuclear models have limitations and do not fully describe all nuclear phenomena. The liquid drop model cannot explain magic numbers while the shell model fails to explain the stability of certain
The document discusses nuclear models and nuclear forces. It describes three nuclear models: the liquid drop model, shell model, and collective model. The liquid drop model treats the nucleus as a liquid drop and examines its global properties. The shell model arranges nucleons into energy shells like electrons in an atom and explains magic numbers. The collective model incorporates aspects of the liquid drop and shell models. Nuclear forces operate very strongly within the nucleus, are attractive between protons and neutrons, and are responsible for nuclear stability.
The nuclear shell model was developed in 1949 and describes how protons and neutrons occupy discrete energy levels, or shells, within the nucleus, analogous to the way electrons occupy shells in atoms. It explains several nuclear properties that the liquid drop model could not, such as magic numbers and spin. Nuclei with magic numbers of protons or neutrons are particularly stable due to their filled shells. Evidence for the shell structure includes increased stability and separation energies at magic numbers, and the stable isotopes at the end of radioactive decay chains all having magic numbers of protons. The model makes assumptions like an average central force field and independent nucleon motion within orbits. However, it has limitations like not explaining schmidt lines or higher energy nuclear states fully
The document discusses various types of nuclear reactions. It defines nuclear reactions as processes where two nuclei or nuclear particles collide and produce different products than the initial particles. It describes several types of nuclear reactions including elastic and inelastic scattering, pickup and stripping reactions, compound nuclear reactions, radioactive capture, and photo disintegration. Elastic scattering involves the projectile and outgoing particles being the same, while inelastic scattering results in a loss of energy and particles scattered in different directions with different energies. Pickup reactions involve a gain of nucleons from the target, and stripping reactions involve one or more nucleons captured from the projectile. The document provides examples of each type of reaction.
The liquid drop model of the nucleus was first proposed by George Gamow and developed by Niels Bohr and John Archibold in 1937. It treats the nucleus as an incompressible nuclear fluid drop made up of nucleons (protons and neutrons) held together by the strong nuclear force. Each nucleon inside the nucleus moves like molecules in a liquid, bound by nuclear forces similar to intermolecular forces in liquids. When a heavy nucleus like U235 absorbs a neutron, surface oscillations deform its original shape as the Coulomb energy attempts to distort it further.
This document discusses elementary particles and the fundamental forces that govern their interactions. It begins by explaining that atoms were once thought to be elementary but are actually made up of protons, neutrons, and electrons. Many new unstable particles were discovered in the mid-20th century. Quarks were identified as the constituents of protons and neutrons, reducing the number of elementary particles. The four fundamental forces - strong, electromagnetic, weak, and gravitational - are described along with the particles that mediate each force. The discovery of antimatter by Dirac and pair production/annihilation are summarized. Pions were predicted by Yukawa to mediate the nuclear force. Feynman diagrams provide a graphical representation of particle interactions. Conservation laws including baryon
Nuclear Quadrupole Resonance Spectroscopy (NQR) is a chemical analysis technique that detects nuclear energy level transitions in the absence of a magnetic field through the absorption of radio frequency radiation. NQR is applicable to solids due to the quadrupole moment averaging to zero in liquids and gases. The interaction between a nucleus's quadrupole moment and the electric field gradient of its surroundings results in quantized energy levels. Transitions between these levels are detected as NQR spectra and provide information about electronic structure, hybridization, and charge distribution. NQR finds applications in studying charge transfer complexes, detecting crystal imperfections, and locating land mines.
The document provides an overview of the nuclear shell model. It discusses the historical development of the model from 1927 to 1935. It then presents three pieces of evidence from experiments that supported developing the shell model to describe nuclear properties, including excitation energies, neutron absorption cross-sections, and neutron separation energies. The rest of the document outlines how the shell model was developed theoretically by introducing a Woods-Saxon potential well and spin-orbit coupling to explain nuclear magic numbers and properties like ground and excited state configurations and nuclear magnetic moments. The model provides good predictions but has some limitations for deformed nuclei.
Neutrinos are elementary particles that have no electric charge and interact very weakly with matter. There are three types of neutrinos related to electrons, muons, and tau particles. Neutrinos are abundantly produced in nature by the sun, stars, and nuclear reactions. They pass through the body without interacting but can be detected underground using large detectors composed of layers of iron and detectors that observe the curvature of charged particles produced during neutrino interactions, revealing information about the neutrinos' energy. The INO laboratory under construction in India will also study neutrinos.
The document discusses the four fundamental forces: gravitational, electromagnetic, nuclear, and weak. It summarizes that the nuclear force was discovered after neutrons were discovered in 1932, and holds nucleons together in the nucleus. The nuclear force is charge independent, very strong but short range, repulsive at short distances, and acts through the exchange of pions between nucleons. The document provides details on the Yukawa potential and uncertainty principle as they relate to the nuclear force. It poses a multiple choice question about identifying an incorrect statement regarding the nuclear force.
The document discusses the Pauli Exclusion Principle and its importance in the periodic table. It explains that the principle states that no two electrons in an atom can have the same set of quantum numbers, and electrons must have opposite spins when occupying the same orbital. This principle allows electrons to be arranged in shells and is crucial for determining an element's chemical properties and for constructing the periodic table by blocks.
This document provides an overview of semiconductor theory and devices. It begins by introducing the three categories of solids based on electrical conductivity: conductors, semiconductors, and insulators. It then discusses band theory, which models the allowed energy states in solids as continuous bands separated by forbidden gaps. Semiconductors are defined as having energy gaps small enough for thermal excitation of electrons between bands. The document covers models like the Kronig-Penney model that explain energy gaps. It also discusses how temperature affects resistivity in semiconductors by increasing the number of electrons excited into the conduction band.
Russell Saunders coupling and J-J coupling describe different schemes for coupling angular momenta in atomic systems. Russell Saunders coupling occurs when spin-orbit interactions are weaker than interactions between electrons. It involves combining orbital angular momenta (L) and spins (S) into total angular momentum (J). J-J coupling occurs in heavy atoms where spin-orbit interactions are strong. It involves first combining orbital and spin angular momenta for individual electrons (j) and then combining the j values. The document also discusses the anomalous Zeeman effect, Paschen-Back effect, and applications of the Fabry-Perot interferometer for measuring Zeeman splitting.
This document provides an introduction to the field of nanophotonics. It defines nanophotonics as the science and engineering of light-matter interactions that take place on wavelength and subwavelength scales. Examples of nanophotonics in nature are discussed. The foundations of nanophotonics are explored, including similarities between the propagation of photons and electrons. Computational methods for modeling nanophotonic structures like finite difference time domain are also summarized. The effects of quantum confinement on the optical properties of nanostructures are described.
This document provides an overview of key concepts in nuclear physics covered in Chapter 43, including:
1) Properties of nuclei such as nucleon number, radius, density, isotopes, and nuclear magnetic moments.
2) Nuclear models including the liquid drop model and shell model to describe nuclear stability.
3) Nuclear binding energy and how it depends on proton and neutron numbers. The nucleus with the highest binding energy per nucleon is 62Ni.
4) Radioactivity and different types of nuclear decay processes, including alpha decay, beta decay, and gamma decay. Stable nuclides lie along an asymmetric line in the nuclear chart that favors more neutrons than protons for higher atomic masses.
The document discusses molecular orbital theory and its application to diatomic molecules. It introduces molecular orbital theory, developed in 1932, which uses linear combinations of atomic orbitals to form molecular orbitals. Bonding molecular orbitals contain electrons and increase stability, while antibonding orbitals contain electrons and decrease stability. The number of molecular orbitals formed equals the number of atomic orbitals combined. Molecular orbital theory can be used to predict the existence of molecules and explain their properties based on molecular configurations and bond orders.
Nuclear chain reaction. What is a chain reaction? Nuclear Fission process.Mechanism of the Fission process.Examples of Nuclear Fission Reaction, Fission as a chain mechanism.Critical Mass. Why we use Uranium-235 and Plutonium? Types of Fission chain process. Control Chain Reaction. Uncontrolled Chain reaction. Problem with Nuclear Fission Reactions. Advantages of the fission process. Disadvantages of the Fission process. Applications of the Fission process. A complete explanation by Syed Hammad Ali Gillani.
Q-switching is a technique used to produce high-power laser pulses. It involves preventing the laser from oscillating to allow the population inversion in the lasing medium to build up to a high level. Then, by suddenly allowing oscillation, all the stored energy is emitted in a single giant pulse with peak power much higher than during normal operation. The pulse duration is typically 10-7 to 10-8 seconds. Q-switching provides a means to drastically increase the laser power output through stimulated emission of a very large number of atoms in the active medium.
There are four main types of polarization that can occur in dielectric materials when an electric field is applied: 1) Electronic polarization, which is caused by the shifting of electron clouds relative to atomic nuclei. 2) Ionic polarization, which is the shifting of ionic charges in ionic compounds. 3) Orientational polarization, which is the alignment of permanent molecular dipoles along the field. 4) Space charge polarization, which is the separation of electric charges in the material. The total polarization of a dielectric is the sum of these individual polarization contributions.
This document provides an introduction to nuclear physics. It discusses the history and development of the field, from the discovery of radioactivity and the electron in the early 20th century to the proposal of the liquid drop model and development of the semi-empirical mass formula to describe nuclear structure. Key events discussed include Rutherford's discovery of the nuclear model of the atom, the discovery of the neutron by Chadwick, and Yukawa's proposal of the meson to explain nuclear forces. The introduction concludes by outlining the chapters to follow on topics like nuclear decay, fusion, fission, and reactor physics.
The document provides an introduction to basic concepts in nuclear physics, including:
- Binding energy and the liquid drop model, which describes the saturation of nuclear forces.
- Nuclear dimensions and the different energy scales involved.
- The Fermi gas model, which treats nuclei as two fermion gases and can provide constants for binding energy formulas.
- The shell model, which incorporates a mean field potential and spin-orbit potential to reproduce shell structure in nuclei.
- Isospin, which treats protons and neutrons as states of a single particle to explain similarities in their behavior.
Angular Momentum & Parity in Alpha decaysurat murthy
Angular momentum and parity play an important role in alpha decay. Alpha decay occurs when an alpha particle, which consists of two protons and two neutrons identical to a helium nucleus, tunnels through the potential barrier of the parent nucleus. The angular momentum of the alpha particle must be either even or odd depending on whether the initial and final nuclear states have the same or different parities. Measurements of the angular distribution of alpha particles can provide information about the possible values of orbital angular momentum involved in the decay process and help determine whether emission is more likely from the poles or equator of deformed nuclei.
This chapter discusses the optical properties of phonons in materials. It covers:
1) Optical and acoustic phonons - some interact directly with light, others cause light scattering.
2) Optical excitation of phonons - how phonons contribute to optical properties through the dielectric function.
3) Phonon polaritons - mixed phonon-photon excitations in crystals near resonance frequencies.
4) Light scattering - concepts of Brillouin, Raman, and Rayleigh scattering involving phonons.
5) Coherent Raman spectroscopy - an experimental technique that enhances weak Raman scattering signals.
This document discusses elementary particles and their classification. It begins with a brief history of elementary particles dating back to Democritus' idea of atoms. It then describes the four fundamental forces and some of the key particles discovered over time, including the electron, photon, neutron, and neutrino. The document classifies particles as fermions or bosons based on their statistics and behavior. It provides details on leptons, quarks, mesons, and baryons - the main constituents of matter. In closing, it mentions neutrinos, glueballs, and the interface between particle physics and cosmology.
In this video i have explained nuclear models. There are three types of nuclear models 1. liquid drop model
2. shell model
3.collective model
I explained liquid drop model in simple way.
1. Nuclear physics studies the composition and interactions of atomic nuclei. Nuclei are composed of protons and neutrons, which interact via the strong nuclear force.
2. Nuclear reactions such as fission, fusion, and radioactive decay involve changes in nuclear binding energies and mass defects. Fission releases energy as heavy nuclei split into lighter nuclei, while fusion releases energy by combining light nuclei into heavier ones.
3. Key concepts include the strong nuclear force, mass defect and binding energy, radioactive decay and half-lives, and the types of radiation involved in different nuclear reactions like fission and fusion.
This document provides an overview of nuclear chemistry and radioactivity. It defines nuclear chemistry as the study of reactions involving changes in atomic nuclei. It describes the basics of atomic structure and the components of the nucleus. It then covers various nuclear reactions like radioactive decay, and types of radiation emitted. Key concepts discussed include radioactive half-life, rate of decay, and factors affecting nuclear stability. Classification of nuclides and various nuclear reactions like alpha, beta, and gamma decays are also summarized.
The document provides information on nuclear chemistry and radioactivity. It defines nuclear chemistry as the study of reactions involving changes in atomic nuclei. It describes the basic structure of the atom and defines key terms like isotopes, nuclides, and nuclear reactions. The document also discusses the classification of nuclides based on stability and magic numbers, as well as the forces that bind nucleons together and concepts like binding energy, mass defect, and radioactive decay.
The document provides an overview of the nuclear shell model. It discusses the historical development of the model from 1927 to 1935. It then presents three pieces of evidence from experiments that supported developing the shell model to describe nuclear properties, including excitation energies, neutron absorption cross-sections, and neutron separation energies. The rest of the document outlines how the shell model was developed theoretically by introducing a Woods-Saxon potential well and spin-orbit coupling to explain nuclear magic numbers and properties like ground and excited state configurations and nuclear magnetic moments. The model provides good predictions but has some limitations for deformed nuclei.
Neutrinos are elementary particles that have no electric charge and interact very weakly with matter. There are three types of neutrinos related to electrons, muons, and tau particles. Neutrinos are abundantly produced in nature by the sun, stars, and nuclear reactions. They pass through the body without interacting but can be detected underground using large detectors composed of layers of iron and detectors that observe the curvature of charged particles produced during neutrino interactions, revealing information about the neutrinos' energy. The INO laboratory under construction in India will also study neutrinos.
The document discusses the four fundamental forces: gravitational, electromagnetic, nuclear, and weak. It summarizes that the nuclear force was discovered after neutrons were discovered in 1932, and holds nucleons together in the nucleus. The nuclear force is charge independent, very strong but short range, repulsive at short distances, and acts through the exchange of pions between nucleons. The document provides details on the Yukawa potential and uncertainty principle as they relate to the nuclear force. It poses a multiple choice question about identifying an incorrect statement regarding the nuclear force.
The document discusses the Pauli Exclusion Principle and its importance in the periodic table. It explains that the principle states that no two electrons in an atom can have the same set of quantum numbers, and electrons must have opposite spins when occupying the same orbital. This principle allows electrons to be arranged in shells and is crucial for determining an element's chemical properties and for constructing the periodic table by blocks.
This document provides an overview of semiconductor theory and devices. It begins by introducing the three categories of solids based on electrical conductivity: conductors, semiconductors, and insulators. It then discusses band theory, which models the allowed energy states in solids as continuous bands separated by forbidden gaps. Semiconductors are defined as having energy gaps small enough for thermal excitation of electrons between bands. The document covers models like the Kronig-Penney model that explain energy gaps. It also discusses how temperature affects resistivity in semiconductors by increasing the number of electrons excited into the conduction band.
Russell Saunders coupling and J-J coupling describe different schemes for coupling angular momenta in atomic systems. Russell Saunders coupling occurs when spin-orbit interactions are weaker than interactions between electrons. It involves combining orbital angular momenta (L) and spins (S) into total angular momentum (J). J-J coupling occurs in heavy atoms where spin-orbit interactions are strong. It involves first combining orbital and spin angular momenta for individual electrons (j) and then combining the j values. The document also discusses the anomalous Zeeman effect, Paschen-Back effect, and applications of the Fabry-Perot interferometer for measuring Zeeman splitting.
This document provides an introduction to the field of nanophotonics. It defines nanophotonics as the science and engineering of light-matter interactions that take place on wavelength and subwavelength scales. Examples of nanophotonics in nature are discussed. The foundations of nanophotonics are explored, including similarities between the propagation of photons and electrons. Computational methods for modeling nanophotonic structures like finite difference time domain are also summarized. The effects of quantum confinement on the optical properties of nanostructures are described.
This document provides an overview of key concepts in nuclear physics covered in Chapter 43, including:
1) Properties of nuclei such as nucleon number, radius, density, isotopes, and nuclear magnetic moments.
2) Nuclear models including the liquid drop model and shell model to describe nuclear stability.
3) Nuclear binding energy and how it depends on proton and neutron numbers. The nucleus with the highest binding energy per nucleon is 62Ni.
4) Radioactivity and different types of nuclear decay processes, including alpha decay, beta decay, and gamma decay. Stable nuclides lie along an asymmetric line in the nuclear chart that favors more neutrons than protons for higher atomic masses.
The document discusses molecular orbital theory and its application to diatomic molecules. It introduces molecular orbital theory, developed in 1932, which uses linear combinations of atomic orbitals to form molecular orbitals. Bonding molecular orbitals contain electrons and increase stability, while antibonding orbitals contain electrons and decrease stability. The number of molecular orbitals formed equals the number of atomic orbitals combined. Molecular orbital theory can be used to predict the existence of molecules and explain their properties based on molecular configurations and bond orders.
Nuclear chain reaction. What is a chain reaction? Nuclear Fission process.Mechanism of the Fission process.Examples of Nuclear Fission Reaction, Fission as a chain mechanism.Critical Mass. Why we use Uranium-235 and Plutonium? Types of Fission chain process. Control Chain Reaction. Uncontrolled Chain reaction. Problem with Nuclear Fission Reactions. Advantages of the fission process. Disadvantages of the Fission process. Applications of the Fission process. A complete explanation by Syed Hammad Ali Gillani.
Q-switching is a technique used to produce high-power laser pulses. It involves preventing the laser from oscillating to allow the population inversion in the lasing medium to build up to a high level. Then, by suddenly allowing oscillation, all the stored energy is emitted in a single giant pulse with peak power much higher than during normal operation. The pulse duration is typically 10-7 to 10-8 seconds. Q-switching provides a means to drastically increase the laser power output through stimulated emission of a very large number of atoms in the active medium.
There are four main types of polarization that can occur in dielectric materials when an electric field is applied: 1) Electronic polarization, which is caused by the shifting of electron clouds relative to atomic nuclei. 2) Ionic polarization, which is the shifting of ionic charges in ionic compounds. 3) Orientational polarization, which is the alignment of permanent molecular dipoles along the field. 4) Space charge polarization, which is the separation of electric charges in the material. The total polarization of a dielectric is the sum of these individual polarization contributions.
This document provides an introduction to nuclear physics. It discusses the history and development of the field, from the discovery of radioactivity and the electron in the early 20th century to the proposal of the liquid drop model and development of the semi-empirical mass formula to describe nuclear structure. Key events discussed include Rutherford's discovery of the nuclear model of the atom, the discovery of the neutron by Chadwick, and Yukawa's proposal of the meson to explain nuclear forces. The introduction concludes by outlining the chapters to follow on topics like nuclear decay, fusion, fission, and reactor physics.
The document provides an introduction to basic concepts in nuclear physics, including:
- Binding energy and the liquid drop model, which describes the saturation of nuclear forces.
- Nuclear dimensions and the different energy scales involved.
- The Fermi gas model, which treats nuclei as two fermion gases and can provide constants for binding energy formulas.
- The shell model, which incorporates a mean field potential and spin-orbit potential to reproduce shell structure in nuclei.
- Isospin, which treats protons and neutrons as states of a single particle to explain similarities in their behavior.
Angular Momentum & Parity in Alpha decaysurat murthy
Angular momentum and parity play an important role in alpha decay. Alpha decay occurs when an alpha particle, which consists of two protons and two neutrons identical to a helium nucleus, tunnels through the potential barrier of the parent nucleus. The angular momentum of the alpha particle must be either even or odd depending on whether the initial and final nuclear states have the same or different parities. Measurements of the angular distribution of alpha particles can provide information about the possible values of orbital angular momentum involved in the decay process and help determine whether emission is more likely from the poles or equator of deformed nuclei.
This chapter discusses the optical properties of phonons in materials. It covers:
1) Optical and acoustic phonons - some interact directly with light, others cause light scattering.
2) Optical excitation of phonons - how phonons contribute to optical properties through the dielectric function.
3) Phonon polaritons - mixed phonon-photon excitations in crystals near resonance frequencies.
4) Light scattering - concepts of Brillouin, Raman, and Rayleigh scattering involving phonons.
5) Coherent Raman spectroscopy - an experimental technique that enhances weak Raman scattering signals.
This document discusses elementary particles and their classification. It begins with a brief history of elementary particles dating back to Democritus' idea of atoms. It then describes the four fundamental forces and some of the key particles discovered over time, including the electron, photon, neutron, and neutrino. The document classifies particles as fermions or bosons based on their statistics and behavior. It provides details on leptons, quarks, mesons, and baryons - the main constituents of matter. In closing, it mentions neutrinos, glueballs, and the interface between particle physics and cosmology.
In this video i have explained nuclear models. There are three types of nuclear models 1. liquid drop model
2. shell model
3.collective model
I explained liquid drop model in simple way.
1. Nuclear physics studies the composition and interactions of atomic nuclei. Nuclei are composed of protons and neutrons, which interact via the strong nuclear force.
2. Nuclear reactions such as fission, fusion, and radioactive decay involve changes in nuclear binding energies and mass defects. Fission releases energy as heavy nuclei split into lighter nuclei, while fusion releases energy by combining light nuclei into heavier ones.
3. Key concepts include the strong nuclear force, mass defect and binding energy, radioactive decay and half-lives, and the types of radiation involved in different nuclear reactions like fission and fusion.
This document provides an overview of nuclear chemistry and radioactivity. It defines nuclear chemistry as the study of reactions involving changes in atomic nuclei. It describes the basics of atomic structure and the components of the nucleus. It then covers various nuclear reactions like radioactive decay, and types of radiation emitted. Key concepts discussed include radioactive half-life, rate of decay, and factors affecting nuclear stability. Classification of nuclides and various nuclear reactions like alpha, beta, and gamma decays are also summarized.
The document provides information on nuclear chemistry and radioactivity. It defines nuclear chemistry as the study of reactions involving changes in atomic nuclei. It describes the basic structure of the atom and defines key terms like isotopes, nuclides, and nuclear reactions. The document also discusses the classification of nuclides based on stability and magic numbers, as well as the forces that bind nucleons together and concepts like binding energy, mass defect, and radioactive decay.
Nuclear physics describes the structure and interactions of atomic nuclei. Rutherford discovered the nucleus through alpha scattering experiments. Protons and neutrons were later identified. Isotopes have the same number of protons but different numbers of neutrons. Mass defect and binding energy explain why atomic nuclei are more stable than separated nucleons. Radioactive decay occurs spontaneously at a rate proportional to the number of unstable nuclei. Exponential decay and half-life are described by the decay constant. Nuclear reactions conserve nucleon number and charge. Energy is released or absorbed through mass-energy equivalence. Fission and fusion occur under different conditions according to binding energy. Controlled fission in reactors uses moderation and feedback to sustain a chain reaction. Fusion
Norman John Brodeur worked at MIT’s instrumentation lab which later became Draper Labs. My responsibility was instrumentation and guidance systems for the Apollo command module and the lunar module. Previous to that I worked for Avco-Everett Research Lab in Everett. There we focused on testing materials for the vehicle’s heat shield. I was doing heat studies of various materials and what we eventually developed would just burn off and the heat with it.
This document provides an introduction to nuclear physics and radioactivity. It discusses:
1) The discovery of radioactivity and the nucleus. Rutherford's scattering experiment in 1911 revealed the existence of the nucleus as the source of radioactivity.
2) The structure of the nucleus, including its composition of protons and neutrons (nucleons), atomic number, mass number, isotopes, and typical size.
3) Nuclear stability and binding energy. The strong nuclear force holds nuclei together, and nuclei with intermediate mass numbers have the highest binding energy per nucleon. Only certain combinations of protons and neutrons produce stable nuclei.
1. Rutherford's alpha scattering experiment showed that the positive charge and mass of an atom are concentrated in a tiny nucleus at the center. Some alpha particles were deflected through large angles, including backwards, indicating the presence of a dense, positively charged nucleus.
2. The binding energy curve shows that binding energy per nucleon initially rises rapidly then levels off at a maximum around iron before dropping again. Nuclides with binding energies close to the maximum are most stable.
3. Radioactive decay follows predictable laws: the rate of decay is proportional to the amount of radioactive material and independent of conditions; decay occurs randomly between nuclei. Half-life is the time for half the nuclei to decay.
1. Rutherford's alpha scattering experiment showed that the positive charge and most of the mass of an atom is concentrated in a very small nucleus at the center. Some alpha particles were deflected through large angles, even backwards, indicating the presence of a dense, positively charged nucleus.
2. The binding energy curve shows that binding energy per nucleon initially rises rapidly then levels off at a maximum around iron before dropping again. Nuclides with binding energies close to the maximum are most stable. The curve shape indicates that low-mass nuclides can undergo fusion to become more stable while high-mass nuclides can undergo fission.
3. Radioactive decay occurs spontaneously via the emission of alpha, beta
Atomic_Nucleus.ppt for general physics 2JosephMuez2
1. Rutherford's alpha scattering experiment showed that the positive charge and mass of an atom are concentrated in a tiny nucleus at the center. Some alpha particles were deflected through large angles, including backwards, indicating the presence of a dense, positively charged nucleus.
2. The binding energy curve shows that binding energy per nucleon increases initially with mass number, peaks at iron-56, then decreases, making very large and very small nuclei unstable. Nuclides with mass numbers from 40-120 have binding energies close to the maximum, making them highly stable.
3. Radioactive decay occurs spontaneously via emission of alpha, beta, or gamma radiation. The rate of decay is proportional to the amount of radioactive material and
1. Rutherford's alpha scattering experiment demonstrated that the positive charge and most of the mass of an atom is concentrated in a small, dense nucleus at the center.
2. The binding energy curve shows that binding energy per nucleon increases rapidly at first, peaks at iron-56, then gradually decreases, indicating the relative stability of nuclei.
3. Radioactive decay follows predictable laws: the rate of decay is proportional to the amount of radioactive material and independent of conditions; it occurs randomly with individual atoms. The decay constant λ defines the rate of decay.
This document provides an introduction to nuclear chemistry. It discusses the basic components of atoms and how nuclear reactions differ from chemical reactions. It describes the three types of nuclear radiation (alpha, beta, gamma) and their properties. The document also covers radioactive decay and concepts such as decay constant, half-life, and average life. Additional topics include nuclear stability factors, mass defect and binding energy, and the application of radioisotopes as tracers and in radiotherapy, mutation breeding, and carbon dating.
1) In 1932, Chadwick proposed that the new radiation produced by alpha particles striking beryllium consisted of neutral particles called neutrons, estimating their mass to be close to the modern value of 1.0087 atomic mass units.
2) Neutrons have no electric charge, allowing them to penetrate matter more easily than charged particles and induce nuclear reactions. Their magnetic moments are on the same order of magnitude as protons, indicating they are not composed of electrons.
3) The deuteron, consisting of one proton and one neutron, has a binding energy of 2.22 MeV as determined through photodisintegration experiments. Its nuclear magnetic moment is slightly less than the sum of the proton and neutron magnetic moments
1. Rutherford's alpha scattering experiment provided evidence for the nuclear model of the atom, showing that the mass and positive charge of an atom are concentrated in a small, dense nucleus. Alpha particles scattering at large angles indicated a small, dense region at the center of the atom.
2. The document discusses properties of atomic nuclei including composition, size, density, binding energy, nuclear forces, radioactive decay, and the binding energy curve. Nuclear size is typically on the order of femtometers, and density is around 2.3×1017 kg/m3. Binding energy explains nuclear stability and radioactive decay. Nuclear forces are explained by meson exchange theory.
3. Key features of the binding energy curve
1. Rutherford's alpha scattering experiment demonstrated that the positive charge and most of the mass of an atom are concentrated in a small, dense nucleus at the center. 2. The binding energy curve shows that binding energy per nucleon increases initially with mass number, peaks at iron-56, then decreases, making very large and very small nuclei unstable. 3. Radioactive decay follows predictable exponential laws, with the decay constant λ representing the probability of decay per unit time and half-life the time for half the nuclei to decay.
In 1909, Rutherford performed the Gold Foil Experiment and suggested the following characteristics of the atom:
It consists of a small core, or nucleus, that contains most of the mass of the atom
This nucleus is made up of particles called protons, which have a positive charge
The protons are surrounded by negatively charged electrons, but most of the atom is actually empty space.
In 1913, Bohor proposed the Atomic Model, which suggests that electrons travel around the nucleus of an atom in orbits or definite paths.
Atom consists of a tiny nucleus.
Each orbit has fixed energy that is quantatized.
The energy is emitted or absorb only when an electron jumps from one orbit to another.
Electron can revolve in orbits of fixed angular momentum mvr.
Liquid Drop Model
The nuclei of all elements are considered to be behave like a liquid drop of incompressible liquid of very high density.
In an equilibrium state the nuclei of atoms remain spherically symmetric under the action of strong attractive nuclear forces just like the drop of a liquid which is spherical due to surface tension.
The density of a nucleus is independent of its
size just like the density of liquid which is also
independent of its size.
The protons and neutrons of the nucleus move about
within a spherical enclosure called the nuclear
potential barrier just like the movement of the
molecules of a liquid within a spherical drop of liquid.
. The binding energy per nucleon of a nucleus is constant
Binding Energy
The binding energy, BE, of a nucleus is a measure of the strong force and represents the energy required to separate the nucleus into its constituents protons and neutrons;
Greater the binding energy, the more stable the nucleus.
Volume
The volume of the nucleus is directly proportional to the total number of nucleons present in it.
Density
The density of the nucleus is nearly constant.
1. Nuclear chemistry deals with changes in the nucleus of atoms, which are the source of radioactivity and nuclear power. It studies nuclear particles, forces, and reactions.
2. Nuclear reactions differ from chemical reactions in that the nucleus of an element takes part rather than just electrons, and a much larger amount of energy is evolved. Reaction rates of nuclear reactions are dependent on nuclear concentration but not influenced by temperature or catalysts.
3. Radioactive decay occurs via three types of radiation: alpha, beta, and gamma. Alpha decay decreases mass and atomic number by units of 4 and 2, respectively. Beta decay does not change mass number but increases atomic number by 1. Gamma decay does not change mass or atomic number
The document discusses the concept of effective nuclear charge. It explains that the actual charge experienced by valence electrons is less than the true nuclear charge due to shielding by inner electrons. This decreased charge is called the effective nuclear charge (Zeff). Slater's rules provide a method to calculate the screening constant σ and thus determine Zeff. The concept of Zeff is applied to explain trends in ionization energy, filling of electron shells, and properties of cations, anions, and across the periodic table.
1. Lord Rutherford discovered the nucleus through alpha particle scattering experiments, finding that atoms consist of a small, dense, positively charged nucleus surrounded by orbiting electrons.
2. The nucleus contains positively charged protons and neutral neutrons, collectively called nucleons. The number of protons is the atomic number and the total number of protons and neutrons is the mass number.
3. Isotopes are atoms with the same atomic number but different mass numbers, such as the three isotopes of hydrogen: deuterium, ordinary hydrogen, and tritium.
Nuclear physics covers many topics including the discovery of the nucleus, nuclear properties, nuclear binding energies, radioactivity, and nuclear models. Rutherford's gold foil experiment in 1911 provided evidence for the small, dense nucleus by detecting alpha particles scattered at large angles. The nucleus was found to be about 100,000 times smaller than the atom but containing almost all of its mass. Nuclear binding energy refers to the energy required to separate a nucleus into its constituent protons and neutrons and provides a measure of nuclear stability, with the most tightly bound nuclei having the greatest binding energy per nucleon.
Assignment Physical Chemistry By Anam FatimaNathan Mathis
1. The document discusses nuclear chemistry concepts including nuclear stability factors, mass defect vs binding energy, nuclear reactions such as fission and fusion, and atomic bombs.
2. It provides examples of calculating binding energy and discusses the difference between mass defect and binding energy. Mass defect represents the mass of energy binding nuclei while binding energy is the energy required to split a nucleus.
3. Nuclear fission is described as the splitting of atomic nuclei when bombarded by neutrons or other particles, releasing energy. Uranium-235 and plutonium-239 undergo fission, splitting into smaller nuclei along with neutron release. Neutrons are ideal for inducing fission since they have no charge.
This document discusses radioactivity and properties of the nucleus. It begins by defining radioactivity as the spontaneous emission of alpha, beta, and gamma rays by heavy elements. It then covers structure and properties of the nucleus, nuclear forces, radioactive decay, and laws of radioactive decay. Key points include: the nucleus contains protons and neutrons; nuclear forces bind protons and neutrons together; radioactive decay occurs via alpha, beta, or gamma emission; and the rate of radioactive decay follows an exponential decay model defined by the half-life. Binding energy is released during nuclear decay and is related to nuclear stability.
The document discusses several network theorems including superposition, Thevenin's, and Norton's theorems. Superposition theorem states that the total response of a network with multiple sources is the sum of the responses of each source acting alone. Thevenin's theorem shows that any linear network can be reduced to an equivalent circuit with a voltage source and single output resistance. Norton's theorem represents a network as a current source and parallel output resistance. Both theorems simplify analysis of complex networks. Maximum power transfer occurs when the load and source resistances are equal.
1. The document discusses direct current (DC) and alternating current (AC). DC flows in one direction while AC periodically reverses direction.
2. Simple AC circuits containing a resistor, capacitor, or inductor are examined. A resistor allows both DC and AC. A capacitor blocks DC but allows AC, while an inductor opposes rapid changes in current.
3. Impedance, phase factor, and resonance effects are also covered. Impedance represents the total opposition to current flow. Resonance occurs at the frequency where capacitive and inductive reactances cancel out, producing a maximum current.
Magnetic Field and Electromagnetic Induction KC College
1) A magnetic field is defined as the space around a magnet or current-carrying conductor. Magnetic field lines indicate the direction of the field.
2) Faraday's experiments showed that a changing magnetic field induces an electromotive force (emf) in a nearby circuit. This is known as electromagnetic induction.
3) Lenz's law states that the direction of the induced current will always oppose the change that caused it. This ensures the conservation of energy.
Nuclear forces are discussed qualitatively in terms of meson theory. Meson exchange interactions are depicted in Feynman diagrams showing a meson cloud surrounding nucleons. Pion exchange is shown as interacting between nucleons through the exchange of a meson.
Nuclear energy involves asymmetrical fission, where an atom splits into fragments of different sizes, mass yield from fission is non-uniform, and a nuclear reaction occurs through a self-sustaining chain reaction driven by neutrons according to the four factor formula in a thermal nuclear reactor.
The document describes two types of particle accelerators:
1) The Van de Graaff generator uses a belt and rollers to generate a high voltage potential difference of over 1 million volts, which was used to accelerate proton beams.
2) Cyclotrons use a magnetic field and alternating electric field to accelerate ions in a circular path, gaining energy with each orbit. The frequency of the electric field must match the orbital frequency for resonance. Synchrocyclotrons can accelerate particles to relativistic energies by adjusting the frequency over time.
1) Gamma rays are electromagnetic radiation emitted during nuclear transitions between excited and lower energy states. They were discovered in 1900 and have shorter wavelengths than X-rays.
2) Gamma ray properties include being unaffected by electric and magnetic fields and having penetrating abilities dependent on their energy. Their energies can range from thousands to millions of electron-volts.
3) Gamma emission and absorption follow selection rules regarding angular momentum and parity conservation. Transitions are characterized by their electric or magnetic multipole type, such as electric quadrupole or magnetic dipole.
Beta decay occurs in three types: beta minus, beta plus, and electron capture. All three processes involve a change in the atomic number Z of the parent nucleus by one unit, while the mass number A remains unchanged. Beta minus decay occurs when a neutron transforms into a proton, increasing Z by one. Beta plus decay occurs when a proton transforms into a neutron, decreasing Z by one. Electron capture occurs when an orbital electron is captured by a proton, transforming it into a neutron and decreasing Z by one. Experiments show beta decay results in a continuous spectrum of electron energies, violating conservation of energy and angular momentum principles. This led to the proposal of the neutrino hypothesis to resolve these issues.
This document provides information about alpha decay and alpha particles. It discusses:
1) Unstable nuclei attain stability through emission of alpha particles, which are made up of 2 protons and 2 neutrons.
2) Alpha decay involves the emission of an alpha particle from an unstable nucleus, leaving a lighter nucleus. Conservation laws apply.
3) The range of alpha particles is very small, usually only a few centimeters in air or solid materials, due to their high ionization which causes energy loss. Their short range makes them easily stopped.
This document outlines the syllabus and content for a Physics I course. The syllabus covers 3 units: Electric Field, Magnetic Field, and Electrical Circuits. Some key topics discussed in the document include electric charge, Coulomb's law, electric field strength and lines of force, Gauss' law, Poisson's equation, and the Laplace equation. The document provides historical context and examples to explain these fundamental concepts in electromagnetism and classical electrostatics.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
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The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
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তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
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How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
1. NUCLEAR MODELS
Inventory of Stable Nuclides:
1000 nuclides known to exist.
25% are stable.
Rest of the nuclei are radioactive and are mainly produced artificially.
Most of the heavy nuclei undergo 𝛽 – decay, few nuclei disintegrate by 𝛼 – decay.
3. Elements with even value of Z have larger number of stable isotopes than with odd Z.
Number of stable isotopes associated with a nuclei having even number of Z can vary from 5 to
10.
Example:
Calcium (Z = 20) , Selenium(Z = 34), Krypton (Z = 36) ------ Six stable isotopes
Zinc (Z = 30), Germanium (Z = 32), Zirconium (Z = 40) ------ Five stable isotopes
Cadmium (Z = 48) -------- Eight stable isotopes
Tin (Z = 50) -------- Ten stable isotopes.
4. Ratio of N/Z for stable nuclides is
confined within a narrow range.
For lighter nuclei:
number of protons and neutrons are
nearly equal N/Z = 1.
Stability line – equally inclined to Z
and N axes.
5. For heavier nuclei:
Number of neutrons is higher than
the number of proton.
N/Z > 1
Highest value is 1.6 for a very heavy
nuclei.
Stability line steeper at higher Z.
6. Isotopes of different elements (Z = constant) lie on different vertical lines.
Nuclides with different Z having same mass number (A = constant) lie along a line inclined at
1350 to the Z – axis known as isobars.
Segre chart:
Plot of N v/s Z.
Nuclides with same number of neutrons (N = constant) lie along different horizontal lines known
as isotones.
7. Isotopes of all elements can be classified into four groups:
Sr No Combination of protons and neutrons Abundance Number of
Stable isotopes
1 Even Z – Even N (e – e) 60 % 164
2 Even Z – Odd N (e – o)
comprise 20%
and
are equal in number
54
3 Odd Z – Even N (o – e) 50
4 Odd Z – Odd N (o – o) Smallest 4
8. Equality of Z and N for the lighter nuclei indicate:
Proton – proton and neutron – neutron forces are approximately equal with in a nuclei.
Known as charge – symmetry of the nuclear force.
For heavier nuclei:
Coulomb repulsion between the protons weaken the binding.
To compensate for this, the number of neutrons relatively larger than the number of protons –
increases the strength of binding.
9. 𝛽−
active nuclei:
Nuclei lying to the left of the stability line –
number of neutrons increased keeping Z constant.
Neutron transforms into a proton spontaneously.
𝛽+
active nuclei:
Nuclei lying to the right of the stability line-
number of protons increased keeping N constant.
Protons transforms into a neutron spontaneously.
10. Nuclear Models:
To understand the observed properties of the nucleus of an atom it is
necessary –
Adequate knowledge about the nature of internucleon interaction.
Inside the nucleus –
Short range force exists – exact mathematical form of this interaction is still
unknown.
If the exact nature of the internucleon interaction were known….the
difficulties encountered –
Structure of nucleus consists of large number of protons and neutrons.
Impossible to solve the Schrodinger equation exactly for such a many body
problem.
11. Theory of atomic structure – What makes it easy to
understand????
Nature of interacting forces acting on the electrons in an atom
is electromagnetic force which is well understood.
Quantum mechanical theory of atomic structure is extensively
developed and agrees well with the experimental data.
To explain difficulties in developing a satisfactory theory of
nuclear structure –
Different models proposed for the nucleus.
Each model explains some of the characteristics of the nuclei.
12.
13. LIQUID DROP MODEL:
Liquid Drop model first proposed by:
N. Bohr and F. Kalckar in 1937
Later developed by C.F.von Weizsacker and H.A.Bethe to develop a semi – empirical formula for
the binding energy.
14. Similarity between a liquid drop and a nucleus:
Saturation of the force:
Each individual molecule within a liquid drop exerts an attractive force
upon group of molecules in its immediate neighbourhood.
Force of attraction does not extend to all molecules within the drop.
Calculating the potential energy:
Number of interacting pairs of molecules within a drop must be known.
If each molecule interacts with all the molecules in a drop, the number of
interacting pairs – N(N – 1)/2 where N is the total number of molecules.
15. If N is large, the number of pairs = 𝑁2
Potential energy ∝ 𝑁2
.
If each molecule interacts with a limited number of molecules in its immediate
vicinity –
Number of interacting pairs ∝ N
Potential energy ∝ N
Above relation supported by experimental facts.
E.g. total amount of heat required for evaporating a drop of liquid (latent heat) is
linearly proportional to the number of molecules within a liquid.
Amount of heat required to evaporate 2 g of a liquid is twice that required to
evaporate 1 g.
16. Binding energy of a nucleus:
Binding energy 𝐸𝐵 of a nucleus is proportional linearly to the number of
nucleons within it.
Mathematically: Binding energy 𝐸𝐵 ∝ Number of nucleons in the nucleus.
Binding fraction 𝑓𝐵 (binding energy per nucleon) ~ constant (8MeV) for
most nuclei.
Shows close resemblance of the nucleus with the liquid drop.
Conclusion:
Internucleon force within a nucleus attain a saturation value.
Each nucleon interacts with a limited number of nucleons in its close
vicinity.
17. Certain other points of resemblances between
the nucleus of an atom and a liquid drop:
Attractive force near the nuclear surface is
similar to the force of surface tension on a
surface of a liquid drop.
20. Density:
Density of a liquid drop is independent of the volume of the liquid.
Similarly, density of nuclear matter is independent of the volume.
21.
22.
23. Different types of particles, e.g. neutrons, protons, deuteron, 𝛼 – particles are emitted during
nuclear reactions.
Processes analogous to the emission of the molecules from a liquid drop during evaporation.
24.
25. Internal energy of the nucleus is analogous to the heat energy within the liquid drop.
26. Formation of a short lived nuclide:
Formation of a short lived compound nucleus by the absorption of a nuclear particle in a
nucleus during a nuclear reaction is analogous to the process of condensation from the vapour
phase to the liquid phase in the case of a liquid drop.
27. BEITHE – WEIZSACKER FORMULA:
This semi – empirical formula for the nuclear masses (or nuclear binding energies) gives a
connection between the theory of the nuclear matter with the experimental information.
Based on the liquid drop model of the nucleus.
If M(A,Z) be the atomic mass of the isotope of an element X of atomic number Z and mass
number A, then we can write:
M(A,Z) = Z 𝑀𝐻 + N𝑀𝑛 - 𝐸𝐵
where 𝐸𝐵 is the nuclear binding energy
𝑀𝐻 and 𝑀𝑛 are the masses of the hydrogen atom and neutron.
N = A – Z is the number of neutrons in the nucleus.
28. The binding energy 𝐸𝐵can be expressed as the sum of a number of terms as given below:
1. Volume energy
2. Surface energy
3. Coulomb energy
4. Asymmetry energy
5. Pairing energy
30. Surface energy term:
Nuclear force similar to surface tension.
Nucleons acted by attractive force due to
nucleons inside the sphere.
No forces acting from outside.
Existence of surface force tends to reduce
the binding energy of the nucleus by an
amount proportional to the surface area of
the latter.
𝐸𝑆 = -𝑎2𝐴2 3
34. Corrections in the coulomb energy
term:
1)non- uniformity of the nuclear
charge distribution.
35. the requirement of discrete arrangement of the charges on the proton.
Effect of uncertainty in the localization of the protons.
Non- sphericity of the nucleus.
Corrections of the positions of protons.
43. Value of different constants in MeV in Semi – Empirical mass formula:
M(A,Z) = Z 𝑀𝐻 + N𝑀𝑛 - 𝐸𝐵
The pairing energy term (𝜹) is subtracted for e – e nuclei and is added for o – o nuclei.
M(A,Z) = Z 𝑀𝐻 + (A – Z)𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3
+ 𝒂𝟑
𝒁𝟐
𝑨𝟏 𝟑 + 𝒂𝟒
(𝑨 −𝟐𝒁)𝟐
𝑨
- 𝜹
44. APPLICATIONS OF THE SEMI – EMPIRICAL MASS FORMULA:
1. Alpha Decay
2. The Mass Parabolas and prediction of stability against beta activity
3. 𝛽 – disintegration energy of the mirror nuclei.
45. Alpha Decay:
If a nucleus ZXA undergoes 𝛼 – decay into the nucleus Z-2YA-4
ZXA
Z-2YA-4 + 2He4
The 𝛼 – disintegration energy –
𝑄𝛼 = M(A,Z) - M(A – 4, Z-2) – M[2He4]
written in terms of the binding energies 𝐸𝐵 of the nuclei involved:
𝑄𝛼 = 𝐸𝐵(A – 4, Z – 2) + 𝐸𝐵[2He4] - 𝐸𝐵 (A, Z)
= 𝑎1(𝐴 − 4) - 𝑎2(𝐴 − 4)2 3- 𝑎3
(𝑍−2)2
(𝐴 −4)1 3 - 𝑎4
(𝐴 −2𝑍)2
𝐴 −4
- 𝑎1𝐴 + 𝑎2𝐴2 3+ 𝑎3
𝑍2
𝐴1 3 + 𝑎4
(𝐴 −2𝑍)2
𝐴
+ 𝐸𝐵[2He4]
46. On simplification:
𝑄𝛼 = 28.3 - 4𝑎1 +
8
3
𝑎2 𝐴−1 3 +
4𝑎3𝑧
𝐴1 3 [1 -
𝑍
3𝐴
] -
4𝑎4
𝐴
(𝐴 −2𝑍)2
𝐴 −4
---------------------------------- [1]
Important note:
Pairing energy term has been neglected.
Binding energy of the 𝛼 – particle is taken to be 28.3 MeV.
Using the numerical values of 𝑎1, 𝑎2, 𝑎3, 𝑎4 expressed in MeV are used in equation [1] gives
𝑄𝛼 >0 for A > 160.
Nuclei with A > 160 should be 𝛼 – disintegrating according to equation [1]
Observation: Nuclei with A > 200 undergo 𝛼 – disintegration.
For light nuclei (A < 200) the energy release is so small that barrier penetration probability is very
small.
47. Mass Parabolas: Stability of Nuclei against 𝜷 – Decay:
M(A,Z) = Z 𝑀𝐻 + (A – Z)𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3+ 𝑎3
𝑍2
𝐴1 3 + 𝑎4
(𝐴 −2𝑍)2
𝐴
Above equation can be rewritten as:
M(A,Z) = 𝑓𝐴 + pZ + q 𝑍2
------------------------------------------------------[1]
where 𝑓𝐴 = A(𝑀𝑛 - 𝑎1+ 𝑎4) + 𝑎2 𝐴2 3
p = -4𝑎4 - (𝑀𝑛 - 𝑀𝐻)
q =
1
𝐴
(𝑎3 𝐴2 3
+ 4𝑎4)
Equation [1] is the equation to a parabola for a given A.
48. Differentiating equation (1) w.r.t Z for a given A and setting it equal to zero gives the lowest
point Z = 𝑍𝐴 :
𝜕𝑀
𝜕𝑍 𝐴
= p + 2qZ
p + 2q𝑍𝐴 = 0
𝑍𝐴 = -
𝑝
2𝑞
=
(𝑀𝑛 − 𝑀𝐻+4𝑎4)A
2(𝑎3 𝐴2 3 + 4𝑎4)
50. M(A,Z) - M(A, 𝑍𝐴) = q (𝑍 − 𝑍𝐴)2
Important note:
Above equation proves that the mass parabolas for a given isobar A( A = constant) has the
lowest point at Z = 𝑍𝐴, since R.H.S is positive.
M(A,Z) has the smallest value for a given A at Z = 𝑍𝐴 nucleus has the largest binging
energy amongst the isobars for a given A.
𝑍𝐴 gives the value of Z for the most stable isobar given by:
𝑍𝐴 =
𝐴
1.98+0.015𝐴2 3
Equation doesn’t yield integral value for 𝑍𝐴. Value of Z nearest to 𝑍𝐴 corresponds to the actual
stable nucleus for a given A.
56. 𝜷 – disintegration of mirror nuclei:
Mirror Nuclei: Mirror nuclei are pairs of isobaric nuclei in which the proton and neutron
numbers are interchanged and differ by one unit.
Examples: (1H3, 2He3), (3Li7, 4Be7), (5B11, 6C11).
Members of the pairs of higher Z are usually found to be 𝛽+
emitters such as:
6C11
5B11 + 𝛽+
+ 𝜈.
The (A – 2Z) value in the asymmetry term in the mass formula can be written as:
A – 2Z = N + Z – 2Z = N – Z
N – Z = ±1
A – 2Z = ±1
57. Semi – Empirical mass formula for Odd A nuclei:
M(A,Z) = Z 𝑀𝐻 + N𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3
+ 𝑎3
𝑍2
𝐴1 3 + 𝑎4
(𝐴 −2𝑍)2
𝐴
M(A,Z) = Z 𝑀𝐻 + (Z – 1)𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3+ 𝑎3
𝑍2
𝐴1 3 +
𝑎4
𝐴
--------------------------- (1)
For daughter nuclei:
M(A,Z - 1) = (Z – 1) 𝑀𝐻 + Z𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3
+ 𝑎3
(𝑍−1)2
𝐴1 3 +
𝑎4
𝐴
---------------------------(2)
59. Figure shows plot of the disintegration energy
against 𝐴2 3 is a straight line with slope 𝑎3.
From 𝑎3 - determined from the graph the
nuclear radius parameter 𝑟0 can be found.
Value of 𝑟0 = 1.44 X 10−15m.
Above estimate is on the higher side because
of limitations imposed by the presence of
Coulomb energy term.
With corrections more precise value of the
Coulomb energy 𝐸𝑐 term can be deduced.
60. Energetics of Symmetric Fission:
Nuclear Fission: Process of breaking up of a nucleus into two fragment nuclei of comparable
masses.
It can be induced:
by an external agent
or
can occur spontaneously.
Fission of the heavy nuclei (e.g. uranium) induced by neutrons.
61. In spontaneous fission a nucleus ZXA undergoes the spontaneous transformation:
ZXA
𝑍1
𝐴1
𝑋1 + 𝑍2
𝐴2
𝑋2
where the two product nuclei have mass numbers and atomic numbers of comparable values.
𝐴1 + 𝐴2 = 𝐴 and 𝑍1 + 𝑍2 = 𝑍
𝐴1 = 𝐴2 = 𝐴/2 and 𝑍1 = 𝑍2 = 𝑍/2 -------------[Symmetric Fission]
62. Above process can occur if the Q – value of the transformation is positive:
𝑄𝑓 = M(A,Z) – M(𝐴1,𝑍1) - M(𝐴2,𝑍2) > 0
where all quantities are expressed in terms of atomic masses.
For a symmetric fission:
𝑄𝑓 = M(A,Z) – 2 X M(A/2,Z/2) > 0
In terms of binding energies:
𝑄𝑓 = 2 X B(A/2,Z/2) - B(A,Z)
= 2 X (A/2)𝑓𝐵
′
- 𝑓𝐵
𝑄𝑓 = A (𝑓𝐵
′
- 𝑓𝐵) = A . ∆𝑓𝐵
63. For 𝑄𝑓 to be positive 𝑓𝐵
′
> 𝑓𝐵
Binding fraction of the product nuclei > binding fraction of the parent nucleus.
In terms of the semi – empirical mass formula:
M(A,Z) = Z 𝑀𝐻 + (A – Z)𝑀𝑛 - 𝑎1𝐴 + 𝑎2𝐴2 3+ 𝑎3
𝑍2
𝐴1 3 + 𝑎4
(𝐴 −2𝑍)2
𝐴
---------------------------[1]
M(A/2,Z/2) = Z/2 𝑀𝐻 + N/2𝑀𝑛 - 𝑎1(𝐴/2) + 𝑎2(𝐴/2)2 3+ 𝑎3
(
𝑍
2
)2
(𝐴/2)1 3 + 𝑎4
(𝐴 −2𝑍)2
2𝐴
------- [2]
64. 𝑄𝑓 = M(A,Z) – 2 X M(A/2,Z/2)
On simplifying:
𝑄𝑓 = - 0.26 𝑎2𝐴2 3 + 0.37𝑎3
𝑍2
𝐴1 3
Symmetric fission energetically possible (𝑄𝑓 > 0) if
𝑍2
𝐴
>
0.26 𝑎2
0.37𝑎3
Substituting the values of 𝑎2 = 0.019114 u and 𝑎3 = 0.0007626 u:
𝑍2
𝐴
> 17.6
65. 𝑍2
𝐴
> 17.6
The condition is fulfilled for A > 90 and Z > 40.
For A = 90, Z = 40,
𝑍2
𝐴
> 17.8
Important note:
For nuclei for which A > 90, symmetric fission energetically possible.
Uncommon phenomena.
Rarely observed even amongst the nuclei of the heaviest atoms in the periodic table e.g.
uranium.
For instance, only one S.F. per hour in 1 g of 235U corresponding to a half – life of 2 X 1017 yr.
66. Reason:
Quantum mechanical Barrier penetration.
Problem is much more acute in S.F., since the nuclei of the fission fragments carry much higher
charges than the 𝛼 – particle.
67. Stability Limit Against Spontaneous Fission:
[Neutron bombarded on a target nucleus and gets captured.
Distorts spherical shape and induces oscillations.]
[Deviation from spherical shape [ redistribution of electric charges gives
tendency to move far apart]
Activation energy not sufficient, Surface energy > Coulomb energy [nucleus
retains its shape]]
Dumbbell shape [Surface energy < Coulomb energy fission takes place]
69. Shape of the distorted nucleus is expressed in terms of
spherical coordinates:
R(𝜃) = 𝑅0 ( 1 + 𝑎2 cos 𝜃 + 𝑎3 cos 𝜃 +……….)
where a’s are small numbers that determine the amount of
distortion called distortion parameters.
P’s represent the Legendre’s polynomials.
𝑅0 is the radius of the undistorted spherical nucleus.
70. If 𝑎2 = 𝑎3 = ……….= 0, the nucleus is undistorted sphere for which R = 𝑅0.
UNDISTORTED NUCLEI DISTORTED NUCLEI
COULOMB ENERGY TERM [𝐸𝐶
0
] 𝑎3
𝑍2
𝐴1 3 =
0.71 𝑍2
𝐴1 3 (MeV) 𝐸𝐶
0
[ 1 -
𝑎2
2
5
- ……]
SURFACE ENERGY TERM [𝐸𝑆
0
] 𝑎2𝐴2 3
= 17.80 𝐴2 3
(MeV) 𝐸𝑆
0
[ 1 +
2𝑎2
2
5
+ …..]
71. Highers powers of the distortion parameters a are neglected.
Total deformation energy:
𝐸𝑇 = 𝐸𝐶 + 𝐸𝑆
Change in the energy:
∆𝐸 = (𝐸𝐶 + 𝐸𝑆) – (𝐸𝐶
0
+ 𝐸𝑆
0
)
∆𝐸 =
1
5
𝑎2
2
(2 𝐸𝑆
0
- 𝐸𝐶
0
)
72. 𝐸𝑆
0
is positive ; 𝐸𝐶
0
is negative.
Stability of a nucleus against spontaneous fission is defined in terms of ∆𝐸.
Difference in energy Condition to be satisfied Nucleus
∆𝐸 > 0 𝐸𝐶
0
< 2 𝐸𝑆
0 Nucleus is Stable
∆𝐸 < 0 𝐸𝐶
0
> 2 𝐸𝑆
0 Nucleus is Unstable
73. For spontaneous fission ∆𝐸 < 0
𝐸𝐶
0
> 2 𝐸𝑆
0
Coulomb energy is greater than twice the surface energy.
0.71 𝑍2
𝐴1 3 ≥ 2 X 17.80 𝐴2 3
0.71
33.6
(𝑍)2
𝐴
≥ 1
(𝒁)𝟐
𝑨
≥ 50
above is stability limit against spontaneous fission.
Nuclei stable against spontaneous fission have value of
(𝑍)2
𝐴
less than the limiting value.
74.
75. Nuclear Shell Structure:
Different nuclear models proposed explain limited features of the nuclei.
Liquid Drop Model explains:
Observed variation of the nuclear binding energy with mass number,
Fission of the heavy nuclei.
Liquid Drop Model predicts:
Closed spacing of the energy levels in the nuclei [at low energies]
76. Observations:
Low lying excited states widely spaced.
Cannot be explained by Liquid Drop Model.
To explain certain properties of the nuclei following consideration to be taken into account:
Motion of individual nucleons in a potential well.
Potential well gives rise to existence of a nuclear shell structure.
Similar to the electronic shells in the atoms.
77. Extra – nuclear electrons in an atom are arranged in a number of shells.
Principal Quantum Number (n) Shell
1 K
2 L
3 M
4 N
78. Each shell has number of sub – shells characterized by different values of the azimuthal
quantum number (𝒍).
Principal Quantum Number (n) Azimuthal Quantum Number(𝒍)
1 0
2 0,1
3 0,1,2
4 0,1,2,3
79. A sub – shell of a given 𝒍 contains a maximum of 𝟐(𝟐𝒍 + 𝟏) electrons.
Azimuthal Quantum
Number(𝒍)
Notation Maximum number of
electrons in the given shell
2(2𝑙 + 1)
0 s 2
1 p 6
2 d 10
3 f 14
80. Inert Gas elements:
Ne (Z = 10), Ar (Z = 18), Kr (Z = 36), Xe (Z = 54), Rn (Z = 86) outermost p sub – shells are
completely filled up.
Lightest inert gas He (Z = 2) 1s sub shell is completely filled.
Electrons are tightly bound.
First ionization potentials are high.
83. Electrons arranged in certain discrete levels Nucleons in the nuclei also arranged in
discrete levels.
Pointed out first by W.M. Elasser (1933)
Maria Gopert Meyer (1948) and independently O. Haxel, J.H.D Jensen and H.E.Suess (1949) -
showed nuclei containing the following numbers of protons and neutrons exhibit very high
stability.
Protons 2 8 20 28 50 82
Neutrons 2 8 20 28 50 82 126
84. Above numbers are known as magic numbers.
Analogous to the atomic number of the inert gases.
85. Evidence of the Existence of Shell Structure within the Nuclei:
Nuclei magic number of protons and neutrons show high stability compared to nuclei
with containing one or more nucleon of the same kind.
Measurement of the separation energy 𝑆𝑛 of a neutron shows –
𝑆𝑛 (nuclei with magic number of neutrons) > > nuclei (containing one more neutron)
Measurement of the separation energy 𝑆𝑝 of a proton shows –
𝑆𝑝 (nuclei with magic number of protons) > > nuclei (containing one more proton)
88. Nuclei with magic number of neutrons or protons have their first excited states at higher
energies than in cases of the neighbouring nuclei.
89. Neutron capture cross – section
of the nuclei with magic numbers
of neutrons are low.
Neutrons shells are filled up.
Probabilities of capturing
additional neutron is small.
90. Single Particle States in Nuclei:
Theoretical understanding of the origin of the nuclear structure based on assumption:
Existence of a dominant spherically symmetric central field of force.
Force governs the motion of individual nucleons in the nuclei.
Central field force in an atom: Electrostatic Force
91. Central field force in the nucleus:
Average field due to all nucleons in the nucleus.
No residual interaction exists in the nucleons.
Existence of potential energy of the form: 𝑉 = 𝑉(𝑟).
Possible to obtain a solution of the Schrodinger wave equation.
92. Assumption:
Presence of an infinite three dimensional
harmonic oscillator potential of the form:
𝑉(𝑟) = - 𝑉0 + ½ 𝑀𝜔2𝑟2
𝑀 = nucleon mass
𝑉0 = well – depth
𝜔 = circular frequency of the simple harmonic
oscillator
93. Three dimensional Schrodinger equation for the harmonic oscillator can be solved using
spherical polar coordinates.
Time independent Schrodinger equation:
-
ħ
2
2𝑚
𝜕2𝜓
𝜕𝑥2 + V𝜓 = E𝜓
Substituting the value of potential gives and using the variable separable form:
Radial equation:
1
𝑟2
𝑑
𝑑𝑟
(𝑟2 𝑑𝑅𝑙
𝑑𝑟
) +
2𝑀
ℏ2 {E - 𝑉(𝑟) -
𝑙(𝑙+1)ℏ2
2𝑀𝑟2 }𝑅𝑙 = 0
𝑅𝑙(𝑟) radial function.
94. Angular part of the wavefunction in the spherical harmonic: 𝑌𝑖
𝑚
(𝜃, 𝜑).
Total wavefunction:
𝜓𝑛𝑙𝑚 = 𝑅𝑙(𝑟) 𝑌𝑖
𝑚
(𝜃, 𝜑)
Energy (harmonic oscillator):
E = (𝜆 +
3
2
) ℏ𝜔
96. Discrete set of energy values, Degenerate energy levels, Eigen – functions classified according to 𝒏 and 𝒍
𝑛 𝑙 0 1 2 3 4 5
1 0 1 2 3 4 5
2 2 3 4 5 6 7
3 4 5 6 7 8 9
4 6 7 8 9 10 11
5 8 9 10 11 12 13
6 10 11 12 13 14 15
97. Diagonal lines connect the levels with different possible combinations of 𝑛 and 𝑙 values.
IMPORTANT NOTE:
Angular part of the wave – function: 𝑌𝑖
𝑚
(𝜃, 𝜑)
Degeneracy (2𝑙 + 1) for a given 𝑙 with magnetic quantum numbers 𝑚 = 𝑙, 𝑙 − 1, … . . −𝑙,
Each level with a given set of (𝑛, 𝑙) has a degeneracy (2𝑙 + 1).
Each level of a given energy (given 𝜆) contains several states of different (𝑛, 𝑙) values.
Degeneracy of a state: 2(2𝑙 + 1) over different values of 𝑙 values for a given 𝜆.
Factor 2 is due to the two possible spin orientations of the neutron and proton.
98. For a given 𝑙𝑚𝑎𝑥 = 𝜆.
Possible number of nucleons for a given 𝜆:
𝜆 – even: 𝑁𝑒 = 2(1 + 5 + 9+………. 2𝜆 + 1) = (𝜆 +1) (𝜆 +2)
𝜆 –odd: 𝑁𝑜 = 2(3 + 7 + 11+………. 2𝜆 + 1) = (𝜆 +1) (𝜆 +2)
Total number of nucleons up to a maximum value 𝜆𝑚 of 𝜆:
N = (𝜆𝑖+1)(𝜆𝑖+2) =
1
3
(𝜆𝑚+1)(𝜆𝑚+2)(𝜆𝑚+3)
2(2𝑙 + 1) degenerate states for a given energy having different combinations of of
𝑛, 𝑙, 𝑚𝑙, 𝑚𝑠 values determine a sub level of a given energy.
99. 𝜆 Energy in unit of
ℏ𝝎
Degenerate states
(𝑛, 𝑙)
No of nucleons
filling up the
shell:
2(2𝑙 + 1)
Total number of
nucleons for shell
closure
0 3/2 (1,0) 2 2
1 5/2 (1,1) 6 8
2 7/2 (2,0),(1,2) 12 20
3 9/2 (2,1),(1,3) 20 40
4 11/2 (3,0),(2,2),(1,4) 30 70
5 13/2 (3,1),(2,3),(1,5) 42 112
6 15/2 (4,0),(3,2),(2,4),(1,6) 56 168
7 17/2 (4,1),(3,3),(2,5),(1,7) 72 240
100. Levels of different azimuthal quantum numbers 𝑙 are designated by symbols used in atomic
spectroscopy:
𝑙 Symbol
0 s
1 p
2 d
3 f
4 g
5 h
6 i
101. To explain the above discrepancies at higher magic numbers, Mayer and independently Haxel,
Jensen and Suess –
Suggested that a spin – orbit interaction term should be added to the central potential given by
𝑉(𝑟) = - 𝑉0 + ½ 𝑀𝜔2𝑟2
Spin – orbit potential, which is non – central given as:
𝑉𝑙𝑠 = - 𝜙 𝑟 𝑙. 𝑠
where
𝜙 𝑟 = 𝑏
1
𝑟
(
𝜕𝑓
𝜕𝑟
)
𝑙 and 𝑠 are azimuthal and spin angular momenta of the nucleon under consideration.
102. Strong coupling between the spin and orbital angular momenta of each individual nucleon
giving rise to a total angular momentum 𝑗 for each given by:
𝑗 = 𝑙 + 𝑠
𝑠 = ½ for each nucleon; the two possible values of 𝑗 = 𝑙 + ½ and 𝑙 − 1/2
103. Figure: Sequence for nuclear
levels according to shell model
taking into account spin orbit
interaction