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.
The document discusses Rutherford's experiment in 1909 where he investigated alpha particles passing through thin metal foils. The experiment found that a small percentage of alpha particles were deflected at very high angles, contrary to expectations based on Thomson's atom model. This led Rutherford to propose the nuclear model of the atom with a small, dense nucleus at the center containing positive charge and mass. It also discusses nuclear energy levels, radioactive decay processes including beta decay and neutrinos, and the use of mass spectrometers to determine atomic mass.
The document describes an experiment to measure Rydberg's constant using the emission spectrum of hydrogen. Electrons in hydrogen atoms absorb energy and transition to higher energy levels. When they drop down, they emit photons of specific wavelengths according to Planck's law. By measuring the wavelengths of photons emitted during transitions from higher to lower energy levels in the Balmer series, Rydberg's constant can be calculated and verified. Measurements of hydrogen's spectral lines will be used to calculate Rydberg's constant and compare to the accepted value.
Lecture 03; Boltzmann equation by Dr. Salma Amirsalmaamir2
This document discusses how temperature affects atomic spectroscopy. It explains that temperature determines the breakdown of samples into atoms and their distribution among ground, excited, and ionized states, influencing observed signals. The Boltzmann distribution describes the relative populations of energy states at thermal equilibrium. For example, in a 2600K acetylene-air flame, less than 0.02% of sodium atoms are in an excited state 3.371x1019 J above the ground state. A 10K rise increases the excited state population by 4%, significantly affecting emission intensity but not noticeably impacting absorption. Plasma is preferred for emission due to its stable high temperature.
The document discusses the history and development of models of the hydrogen atom. It begins by mentioning early observations of hydrogen. It then covers Thomson's "plum pudding" model, Rutherford's planetary model, Bohr's theory that electrons orbit the nucleus in distinct energy levels, and Schrodinger's wave equation solution that provides a more complete quantum mechanical description. The energy levels predicted by Bohr's theory and Schrodinger's equation match, both giving the ground state energy of the hydrogen atom as 13.6 electron volts.
The document discusses Rutherford's experiment in 1909 where he investigated alpha particles passing through thin metal foils. The experiment found that a small percentage of alpha particles were deflected at very high angles, contrary to expectations based on Thomson's atom model. This led Rutherford to propose the nuclear model of the atom with a small, dense nucleus at the center containing positive charge and mass. It also discusses nuclear energy levels, radioactive decay processes including beta decay and neutrinos, and the use of mass spectrometers to determine atomic mass.
The document describes an experiment to measure Rydberg's constant using the emission spectrum of hydrogen. Electrons in hydrogen atoms absorb energy and transition to higher energy levels. When they drop down, they emit photons of specific wavelengths according to Planck's law. By measuring the wavelengths of photons emitted during transitions from higher to lower energy levels in the Balmer series, Rydberg's constant can be calculated and verified. Measurements of hydrogen's spectral lines will be used to calculate Rydberg's constant and compare to the accepted value.
Lecture 03; Boltzmann equation by Dr. Salma Amirsalmaamir2
This document discusses how temperature affects atomic spectroscopy. It explains that temperature determines the breakdown of samples into atoms and their distribution among ground, excited, and ionized states, influencing observed signals. The Boltzmann distribution describes the relative populations of energy states at thermal equilibrium. For example, in a 2600K acetylene-air flame, less than 0.02% of sodium atoms are in an excited state 3.371x1019 J above the ground state. A 10K rise increases the excited state population by 4%, significantly affecting emission intensity but not noticeably impacting absorption. Plasma is preferred for emission due to its stable high temperature.
The document discusses the history and development of models of the hydrogen atom. It begins by mentioning early observations of hydrogen. It then covers Thomson's "plum pudding" model, Rutherford's planetary model, Bohr's theory that electrons orbit the nucleus in distinct energy levels, and Schrodinger's wave equation solution that provides a more complete quantum mechanical description. The energy levels predicted by Bohr's theory and Schrodinger's equation match, both giving the ground state energy of the hydrogen atom as 13.6 electron volts.
Measurement of the Lifetime of the 59.5keV excited State of 237Np from the Al...theijes
This document summarizes an experiment that measured the lifetime of the 59.5keV excited state of 237Np using delayed coincidence techniques. 241Am decays via alpha emission to both the 103keV and 59.5keV excited states of 237Np. The lifetime of the 59.5keV state was measured by detecting coincidences between alpha particles from 241Am decay and gamma rays from the decay of the 59.5keV state. A plastic scintillator detector was used to detect alpha particles and another thicker plastic scintillator was used to detect gamma rays. The measured lifetime of the 59.5keV state was 66 nanoseconds, close to the accepted value of 67 nanoseconds. Delayed coincidence methods provide an efficient way to study short-lived
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
ELECTRICAL DOUBLE LAYER-TYPES-DYNAMICS OF ELECTRON TRANSFER-MARCUS THEORY-TUNNELING - BUTLER VOLMER EQUATIONS-TAFEL EQUATIONS-POLARIZATION AND OVERVOLTAGE-CORROSION AND PASSIVITY-POURBAIX AND EVAN DIAGRAM-POWER STORAGE-FUEL CELLS
To detemine the wavelength of semiconductor laserPraveen Vaidya
The document describes an experiment to determine the wavelength of a semiconductor laser using diffraction. A laser beam is directed at a metal scale with graduations. The diffraction patterns are observed on a screen and the distances between the direct beam and diffraction spots are measured. These measurements are used to calculate the path difference and apply the diffraction equation to determine the laser's wavelength. The experiment is repeated to obtain an average wavelength value.
Mass spectroscopy by dr. pramod r. padolepramod padole
Mass spectroscopy is a technique that determines the molecular mass of compounds by ionizing molecules and measuring their mass-to-charge ratios. It works by first volatilizing and ionizing molecules via electron bombardment, which produces molecular ions. The molecular ions are then accelerated and separated based on their mass-to-charge ratios using electric and magnetic fields. Finally, the ions are detected, and a mass spectrum is produced by plotting the relative abundances of each ion versus the mass-to-charge ratio. Key terms include molecular ion peak, daughter ion peaks, base peak, and metastable ions. Mass spectroscopy is widely used in science to determine molecular structures and isotopic abundances.
This document discusses lattice vibrations in solids. It begins by introducing different types of elementary excitations in solids including phonons, which are quantized elastic waves in a crystal. It then describes lattice vibrations as waves that propagate through the crystal as planes of atoms moving in and out of phase. Both longitudinal and transverse polarization of these waves are discussed. Equations of motion are provided and solved to show the wave-like behavior of lattice vibrations. The document also covers phonon dispersion relations, group velocity, Brillouin zones, phonons in diatomic crystals, quantization of elastic waves, phonon momentum, heat capacity of lattices, and early models like Einstein and Debye models to explain temperature-dependent
The document discusses key concepts in quantum mechanics including:
1. Photons carry energy and momentum that depends on their frequency or wavelength. Electrons also behave as both particles and waves with an associated wavelength.
2. Heisenberg's uncertainty principle establishes that the more precisely one property of a particle is measured, the less precisely its complementary property can be known.
3. Atomic spectra are unique to each element and arise from electrons transitioning between discrete energy levels in atoms. The wavelength of emitted photons corresponds to energy differences between levels.
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.
B.Tech sem I Engineering Physics U-IV Chapter 1-ATOMIC PHYSICSAbhi Hirpara
Atomic physics describes phenomena at the scale of atoms and subatomic particles. It emerged in the early 20th century to address limitations in classical physics' ability to describe certain phenomena. Quantum physics recognizes that there is less difference between waves and particles than previously thought. It is probabilistic and counterintuitive, describing particles that can behave as waves and vice versa. Quantum physics underlies our understanding of atomic and subatomic systems and is crucial to fields like chemistry, materials science, and astrophysics. Planck's quantum hypothesis proposed that atoms can only absorb or emit energy in discrete quanta, initiating the development of quantum theory. Einstein later theorized that electromagnetic radiation consists of discrete photon particles, helping explain the photoelectric effect.
The Franck-Hertz experiment demonstrated quantization of energy levels in atoms. When electrons were accelerated through mercury vapor in a glass tube, the current dropped sharply at 4.9eV, indicating the energy needed to excite mercury atoms. Current also dropped at multiples of 4.9eV. For neon gas, current dropped periodically at around 19eV, demonstrating its quantized energy levels. This supported the quantum theory that electrons occupy only discrete energy states in atoms.
Lecture 02.; spectroscopic notations by Dr. Salma Amirsalmaamir2
The document discusses spectroscopic notations used to describe the quantum states of atoms and ions. It introduces the principal, azimuthal, magnetic, and spin quantum numbers that are used to quantitatively describe observed atomic transitions. The spectroscopic notation describes the atomic state using these quantum numbers, written as 2S+1LJ, where S, L, and J are the spin, orbital, and total angular momentum quantum numbers. Examples are given for the ground and excited states of helium.
Study the emission of spectroscopy of low pressure gas( hydrogen ).UCP
This document summarizes an experiment to study the emission spectroscopy of low pressure hydrogen gas. The experiment uses a diffraction grating to separate the light from a hydrogen gas lamp into distinct color lines corresponding to the Balmer series. Measurements of the positions of the red, blue-green, and violet lines are used to calculate the wavelengths and energies of the photons emitted in the spectral lines. The results confirm that the hydrogen spectrum is an atomic line spectrum as predicted by Bohr's quantum model of the hydrogen atom.
1. Spectra provide insight into the structure of atoms and distant astronomical objects. The electromagnetic spectrum ranges from gamma rays to radio waves.
2. The diagram shows the electromagnetic spectrum divided into regions by wavelength, frequency, and photon energy. There are no abrupt boundaries between regions.
3. Line spectra occur when atoms are excited and energy is released as light at specific wavelengths. The hydrogen spectrum contains distinct lines that are explained by differences in electron energy levels.
Gamma Interactions and Gamma Spectroscopy with Scintillation DetectorsDaniel Maierhafer
The document discusses gamma ray interactions and spectroscopy using scintillation detectors. It describes the three main types of gamma ray interactions: photoelectric absorption, Compton scattering, and pair production. It also discusses energy spectra resulting from these interactions and how detector size affects the response function. The experiment used two sizes of NaI:TL scintillators (2"x2" and 5"x5") along with associated electronics to collect gamma ray spectra from various sources and determine properties like energy resolution and unknown source identification. Procedures and results are presented for analyzing spectra from the sources using a single channel analyzer and multi-channel analyzer.
This document provides an overview of electron spin resonance (ESR) spectroscopy. It discusses how ESR works by applying a magnetic field to induce transitions between electron spin energy levels, which are split due to interactions between unpaired electrons and their environment. Specifically, it describes how orbital interactions and nuclear hyperfine interactions affect the ESR spectrum. It also discusses experimental considerations like microwave frequencies, magnetic field strengths, sensitivity, saturation effects, and nuclear hyperfine interactions. The goal is to provide fundamentals of ESR spectroscopy and introduce its capabilities for studying organic and organometallic radicals and complexes.
The document discusses Planck's quantum theory of blackbody radiation. It begins by explaining the failures of classical physics to accurately describe blackbody radiation. Planck introduced the idea that electromagnetic radiation exists in discrete quantized energy levels (quanta), with the energy of each quantum directly proportional to the radiation's frequency. This explained the experimental observations. Later, Einstein extended this idea by proposing that electromagnetic radiation itself consists of particle-like photons, with the energy of each photon determined by its frequency.
1) The experiment used gamma-ray spectroscopy to analyze spectra from various radioactive sources. Spectra were recorded at different photomultiplier tube voltages to study resolution and efficiency.
2) Analysis found the number of dynodes in the photomultiplier tube to be 6.5, and resolution R was determined to be inversely proportional to gamma ray energy as expected.
3) Activity of a potassium chloride sample was estimated using detector efficiency calculations, finding 1.7×10^17 40K nuclei, consistent with the expected amount.
Alpha decay occurs when an unstable nucleus releases an alpha particle to achieve stability. Three key laws are obeyed: conservation of charge, nucleons, and momentum. The alpha particle carries most of the disintegration energy (Q-value) away from the daughter nucleus. Alpha particle velocity and energy can be determined using a magnetic spectrograph which measures particle deflection in a magnetic field. Alpha particles have a well-defined range in a material and become fully absorbed. The Geiger-Nuttall law shows a correlation between an alpha emitter's half-life and the range or energy of its alpha particles.
Analytical class atomic absorption spectroscopy, P K MANIP.K. Mani
This document discusses atomic absorption spectroscopy and atomic emission spectroscopy. It begins by explaining the basic principles of how atomic absorption spectroscopy works, where atomic vapors are subjected to UV-VIS radiation which causes electron excitation. The extent of absorption is then used to quantitatively measure the concentration of atomic vapors. It then explains atomic emission spectroscopy, where a sample is excited by a flame, plasma or discharge, causing electron excitation and emission of radiation in the UV-VIS region. The wavelength and intensity of emission provides qualitative and quantitative information. Key concepts like oscillator strength, line widths, and sources of broadening like Doppler effect and collisions are then discussed. Details are provided about hollow cathode lamps and how they are used as light sources.
Measurement of the Lifetime of the 59.5keV excited State of 237Np from the Al...theijes
This document summarizes an experiment that measured the lifetime of the 59.5keV excited state of 237Np using delayed coincidence techniques. 241Am decays via alpha emission to both the 103keV and 59.5keV excited states of 237Np. The lifetime of the 59.5keV state was measured by detecting coincidences between alpha particles from 241Am decay and gamma rays from the decay of the 59.5keV state. A plastic scintillator detector was used to detect alpha particles and another thicker plastic scintillator was used to detect gamma rays. The measured lifetime of the 59.5keV state was 66 nanoseconds, close to the accepted value of 67 nanoseconds. Delayed coincidence methods provide an efficient way to study short-lived
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
ELECTRICAL DOUBLE LAYER-TYPES-DYNAMICS OF ELECTRON TRANSFER-MARCUS THEORY-TUNNELING - BUTLER VOLMER EQUATIONS-TAFEL EQUATIONS-POLARIZATION AND OVERVOLTAGE-CORROSION AND PASSIVITY-POURBAIX AND EVAN DIAGRAM-POWER STORAGE-FUEL CELLS
To detemine the wavelength of semiconductor laserPraveen Vaidya
The document describes an experiment to determine the wavelength of a semiconductor laser using diffraction. A laser beam is directed at a metal scale with graduations. The diffraction patterns are observed on a screen and the distances between the direct beam and diffraction spots are measured. These measurements are used to calculate the path difference and apply the diffraction equation to determine the laser's wavelength. The experiment is repeated to obtain an average wavelength value.
Mass spectroscopy by dr. pramod r. padolepramod padole
Mass spectroscopy is a technique that determines the molecular mass of compounds by ionizing molecules and measuring their mass-to-charge ratios. It works by first volatilizing and ionizing molecules via electron bombardment, which produces molecular ions. The molecular ions are then accelerated and separated based on their mass-to-charge ratios using electric and magnetic fields. Finally, the ions are detected, and a mass spectrum is produced by plotting the relative abundances of each ion versus the mass-to-charge ratio. Key terms include molecular ion peak, daughter ion peaks, base peak, and metastable ions. Mass spectroscopy is widely used in science to determine molecular structures and isotopic abundances.
This document discusses lattice vibrations in solids. It begins by introducing different types of elementary excitations in solids including phonons, which are quantized elastic waves in a crystal. It then describes lattice vibrations as waves that propagate through the crystal as planes of atoms moving in and out of phase. Both longitudinal and transverse polarization of these waves are discussed. Equations of motion are provided and solved to show the wave-like behavior of lattice vibrations. The document also covers phonon dispersion relations, group velocity, Brillouin zones, phonons in diatomic crystals, quantization of elastic waves, phonon momentum, heat capacity of lattices, and early models like Einstein and Debye models to explain temperature-dependent
The document discusses key concepts in quantum mechanics including:
1. Photons carry energy and momentum that depends on their frequency or wavelength. Electrons also behave as both particles and waves with an associated wavelength.
2. Heisenberg's uncertainty principle establishes that the more precisely one property of a particle is measured, the less precisely its complementary property can be known.
3. Atomic spectra are unique to each element and arise from electrons transitioning between discrete energy levels in atoms. The wavelength of emitted photons corresponds to energy differences between levels.
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.
B.Tech sem I Engineering Physics U-IV Chapter 1-ATOMIC PHYSICSAbhi Hirpara
Atomic physics describes phenomena at the scale of atoms and subatomic particles. It emerged in the early 20th century to address limitations in classical physics' ability to describe certain phenomena. Quantum physics recognizes that there is less difference between waves and particles than previously thought. It is probabilistic and counterintuitive, describing particles that can behave as waves and vice versa. Quantum physics underlies our understanding of atomic and subatomic systems and is crucial to fields like chemistry, materials science, and astrophysics. Planck's quantum hypothesis proposed that atoms can only absorb or emit energy in discrete quanta, initiating the development of quantum theory. Einstein later theorized that electromagnetic radiation consists of discrete photon particles, helping explain the photoelectric effect.
The Franck-Hertz experiment demonstrated quantization of energy levels in atoms. When electrons were accelerated through mercury vapor in a glass tube, the current dropped sharply at 4.9eV, indicating the energy needed to excite mercury atoms. Current also dropped at multiples of 4.9eV. For neon gas, current dropped periodically at around 19eV, demonstrating its quantized energy levels. This supported the quantum theory that electrons occupy only discrete energy states in atoms.
Lecture 02.; spectroscopic notations by Dr. Salma Amirsalmaamir2
The document discusses spectroscopic notations used to describe the quantum states of atoms and ions. It introduces the principal, azimuthal, magnetic, and spin quantum numbers that are used to quantitatively describe observed atomic transitions. The spectroscopic notation describes the atomic state using these quantum numbers, written as 2S+1LJ, where S, L, and J are the spin, orbital, and total angular momentum quantum numbers. Examples are given for the ground and excited states of helium.
Study the emission of spectroscopy of low pressure gas( hydrogen ).UCP
This document summarizes an experiment to study the emission spectroscopy of low pressure hydrogen gas. The experiment uses a diffraction grating to separate the light from a hydrogen gas lamp into distinct color lines corresponding to the Balmer series. Measurements of the positions of the red, blue-green, and violet lines are used to calculate the wavelengths and energies of the photons emitted in the spectral lines. The results confirm that the hydrogen spectrum is an atomic line spectrum as predicted by Bohr's quantum model of the hydrogen atom.
1. Spectra provide insight into the structure of atoms and distant astronomical objects. The electromagnetic spectrum ranges from gamma rays to radio waves.
2. The diagram shows the electromagnetic spectrum divided into regions by wavelength, frequency, and photon energy. There are no abrupt boundaries between regions.
3. Line spectra occur when atoms are excited and energy is released as light at specific wavelengths. The hydrogen spectrum contains distinct lines that are explained by differences in electron energy levels.
Gamma Interactions and Gamma Spectroscopy with Scintillation DetectorsDaniel Maierhafer
The document discusses gamma ray interactions and spectroscopy using scintillation detectors. It describes the three main types of gamma ray interactions: photoelectric absorption, Compton scattering, and pair production. It also discusses energy spectra resulting from these interactions and how detector size affects the response function. The experiment used two sizes of NaI:TL scintillators (2"x2" and 5"x5") along with associated electronics to collect gamma ray spectra from various sources and determine properties like energy resolution and unknown source identification. Procedures and results are presented for analyzing spectra from the sources using a single channel analyzer and multi-channel analyzer.
This document provides an overview of electron spin resonance (ESR) spectroscopy. It discusses how ESR works by applying a magnetic field to induce transitions between electron spin energy levels, which are split due to interactions between unpaired electrons and their environment. Specifically, it describes how orbital interactions and nuclear hyperfine interactions affect the ESR spectrum. It also discusses experimental considerations like microwave frequencies, magnetic field strengths, sensitivity, saturation effects, and nuclear hyperfine interactions. The goal is to provide fundamentals of ESR spectroscopy and introduce its capabilities for studying organic and organometallic radicals and complexes.
The document discusses Planck's quantum theory of blackbody radiation. It begins by explaining the failures of classical physics to accurately describe blackbody radiation. Planck introduced the idea that electromagnetic radiation exists in discrete quantized energy levels (quanta), with the energy of each quantum directly proportional to the radiation's frequency. This explained the experimental observations. Later, Einstein extended this idea by proposing that electromagnetic radiation itself consists of particle-like photons, with the energy of each photon determined by its frequency.
1) The experiment used gamma-ray spectroscopy to analyze spectra from various radioactive sources. Spectra were recorded at different photomultiplier tube voltages to study resolution and efficiency.
2) Analysis found the number of dynodes in the photomultiplier tube to be 6.5, and resolution R was determined to be inversely proportional to gamma ray energy as expected.
3) Activity of a potassium chloride sample was estimated using detector efficiency calculations, finding 1.7×10^17 40K nuclei, consistent with the expected amount.
Alpha decay occurs when an unstable nucleus releases an alpha particle to achieve stability. Three key laws are obeyed: conservation of charge, nucleons, and momentum. The alpha particle carries most of the disintegration energy (Q-value) away from the daughter nucleus. Alpha particle velocity and energy can be determined using a magnetic spectrograph which measures particle deflection in a magnetic field. Alpha particles have a well-defined range in a material and become fully absorbed. The Geiger-Nuttall law shows a correlation between an alpha emitter's half-life and the range or energy of its alpha particles.
Analytical class atomic absorption spectroscopy, P K MANIP.K. Mani
This document discusses atomic absorption spectroscopy and atomic emission spectroscopy. It begins by explaining the basic principles of how atomic absorption spectroscopy works, where atomic vapors are subjected to UV-VIS radiation which causes electron excitation. The extent of absorption is then used to quantitatively measure the concentration of atomic vapors. It then explains atomic emission spectroscopy, where a sample is excited by a flame, plasma or discharge, causing electron excitation and emission of radiation in the UV-VIS region. The wavelength and intensity of emission provides qualitative and quantitative information. Key concepts like oscillator strength, line widths, and sources of broadening like Doppler effect and collisions are then discussed. Details are provided about hollow cathode lamps and how they are used as light sources.
CBSE Class 11 Chemistry Chapter 2 (The Structure of Atom)Homi Institute
The document summarizes key concepts about the structure of atoms and types of radiation. It discusses three common types of radiation emitted during radioactive decay - alpha particles, beta particles, and gamma rays. It provides examples of nuclei that undergo alpha and beta decay, such as U-238 and Th-230. The document also explains that a beta particle is a high energy electron emitted from the nucleus during beta decay.
The document presents an analytical approach to estimate the range of alpha particles emitted from radon gas. It discusses the stopping power and range of charged particles as they pass through matter. Equations from Bohr and Bethe are provided to calculate stopping power. The results of simulations using SRIM2013 software to calculate alpha particle range and detection probabilities in air are presented and compared to previous SRIM versions. Tables and figures show trends in stopping power and range as alpha energy increases.
Krishna Tripathi presented on NMR spectroscopy. The presentation covered the basic principles of NMR, including spin quantum number, resonance frequency, chemical shifts, and factors that influence chemical shifts. It also discussed instrumentation, relaxation processes, coupling constants, and applications of NMR including 1H NMR, 13C NMR, and electron nuclear double resonance. The presentation provided an overview of the key concepts and applications of NMR spectroscopy.
The document discusses band theory of solids, which explains the electrical, thermal, and magnetic properties of solids. It begins by covering classical and quantum free electron theories, before introducing band theory. Band theory states that the motion of free electrons in solids is characterized by allowed energy bands separated by forbidden bands. The width of bands and size of gaps depends on factors like the periodic potential of the lattice and strength of scattering. Semiconductors have a small forbidden band gap, allowing electrical conductivity to be controlled by doping with impurities.
This document discusses the discovery of artificial radioactivity by Curie and Joliot in 1934. When boron and aluminum were bombarded with alpha particles, the target nuclei continued emitting radiation even after the alpha source was removed. Through experiments, they determined the radiation consisted of positrons, positively charged particles with mass equal to electrons. Curie and Joliot explained that bombarding the elements created unstable nuclei that spontaneously disintegrated. For boron, this produced radioactive nitrogen that decayed to stable carbon with a half-life of 10.1 minutes by emitting a positron. For aluminum, it produced radioactive phosphorus with a half-life of about 3 minutes that decayed to stable phosphorus. This demonstrated the
This document provides an overview of nuclear magnetic resonance (NMR) spectroscopy. It discusses key concepts such as Larmor precession, spin-spin and spin-lattice relaxation, relative line intensities, and the quantum mechanical treatment of the AB spin system. The document is a seminar presentation that covers the basic principles and applications of NMR spectroscopy for structure determination of organic and inorganic compounds.
This document summarizes the key electrical properties of metals and semiconductors. It discusses Ohm's law and how electrical conductivity in metals is influenced by drift velocity and current density. It also explains how resistivity is related to temperature in metals. For semiconductors, it describes the band structure of insulators, metals and semiconductors and how conductivity varies with intrinsic carrier concentration and temperature in intrinsic semiconductors. It then discusses the effects of doping on carrier concentrations and conductivity in n-type and p-type extrinsic semiconductors. Finally, it provides an overview of compound semiconductors made of two or three elements.
This document discusses the electronic structure of atoms and the periodic table. It covers:
- Electrons arranged in energy levels and orbitals defined by quantum numbers
- Atomic spectra produced when electrons change energy levels
- Bohr and quantum mechanical models of the atom explaining electron arrangements
- Electron configurations written using quantum numbers that relate to positions on the periodic table.
The document describes an experiment to measure the refractive index of HCl gas using a Michelson interferometer. A HeNe laser beam is split into two paths, with one path passing through an evacuated glass cell. As the cell is pumped out, the interference fringes shift due to the changing optical path length. Counting the number of fringe shifts allows calculating the refractive index from the changing wavelength of light in the gas versus vacuum. The experiment is performed at varying HCl pressures and temperatures, with results corrected to standard temperature and pressure for comparison to literature values of the molar refractivity and effective molecular radius of HCl.
Structure of atom plus one focus area notessaranyaHC1
The document discusses the structure of the atom, including:
1) Rutherford's nuclear model of the atom based on alpha particle scattering experiments. This established the atom's small, dense nucleus at the center with electrons in orbits around it.
2) Planck's quantum theory and the photoelectric effect, which demonstrated light behaving as discrete packets of energy called quanta and supported the nuclear model.
3) Bohr's model of the hydrogen atom incorporating Planck's quanta and explaining atomic spectra through electron transitions between discrete energy levels.
4) Later developments including de Broglie's matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave mechanical model describing electrons as
The document discusses magnetostatics and provides definitions and explanations of key concepts including magnetic field, magnetic flux, Biot-Savart law, Ampere's law, solenoids, ballistic galvanometers, and damping conditions. Specific topics covered include the magnetic field produced by steady currents, magnetic field lines, curl and divergence of magnetic fields, theory and operation of ballistic galvanometers, and current and charge sensitivity of galvanometers. Examples and derivations of equations for magnetic fields and forces on conductors in fields are also provided.
This document discusses Bohr's model of the hydrogen atom. It outlines three postulates of Bohr's theory: 1) Electrons revolve in circular orbits around the nucleus, 2) Electrons' angular momentum is quantized in integer multiples of h/2π, and 3) Electrons emit/absorb photons when transitioning between orbits. It then describes the five hydrogen spectral series - Lyman, Balmer, Paschen, Brackett, and Pfund - which correspond to electronic transitions to different orbital levels, and the regions of the electromagnetic spectrum where each series appears.
Crystals have an ordered internal arrangement of atoms in a symmetrical lattice structure. Symmetry operations like rotations and reflections result in no change to the appearance of a crystal. Moseley measured the frequencies of characteristic x-rays from elements and discovered they varied directly with the square of the atomic number, allowing correct ordering of elements in the periodic table by atomic number rather than atomic weight.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
STRUCTURE OF ATOM
Sub atomic Particles
Atomic Models
Atomic spectrum of hydrogen atom:
Photoelectric effect
Planck’s quantum theory
Heisenberg’s uncertainty principle
Quantum Numbers
Rules for filling of electrons in various orbitals
Ernest Rutherford's alpha ray scattering experiment led him to propose the nuclear model of the atom. The key findings were:
1) Most alpha particles passed through the thin gold foil with little deflection, but a small percentage were deflected by large angles, including backwards.
2) This could only be explained if the positive charge of the atom was concentrated into a very small, dense nucleus.
3) Rutherford concluded atoms have a small, dense nucleus containing its positive charge and mass, with electrons orbiting the nucleus.
This nuclear model replaced the plum pudding model, but had its own limitations that were later addressed by Niels Bohr's model of electron orbits and quantization
Crystals have an ordered internal arrangement of atoms in a symmetrical lattice structure. Symmetry operations, like rotations and reflections, can be performed on crystals without changing their appearance due to this ordered internal structure. Moseley measured the frequencies of characteristic x-rays from elements and discovered they followed a linear relationship with the element's atomic number, allowing improvements to be made in arranging the periodic table.
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.
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) 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 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.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
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.
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Answers about how you can do more with Walmart!"
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.
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
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.
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
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
2. ALPHA DECAY
INTRODUCTON:
Nuclei with certain combination of protons and neutrons have unstable configuration.
[radioactive]
Unstable nuclei attain stability by emission of certain particles.
α- decay: The emission of α-particles by a unstable radioactive nuclei.
3. Alpha particle:
a positively charged particle emitted by a radioactive nucleus.
made up of 2 protons and 2 neutrons.
α-particle is the nucleus of a helium atom [2He4].
4. The process of alpha decay is given as:
ZMA
Z-2MA-4 + 2He4
where ZMA and Z-2MA-4 are the parent and daughter nuclides and
2He4 is the alpha particle.
5. Energetics of Spontaneous Alpha Decay:
The process of alpha decay is given as:
ZXA
Z-2YA-4 + 2He4
where Y is the residual nucleus of mass number A-4 are the parent and atomic number Z-2.
If the masses of the α-particle [2He4] and the residual nucleus be 𝑀𝛼 and 𝑀1 respectively, and
𝑣𝛼 and 𝑣1 their respective velocities then conservation of momentum requires that:
𝑀𝛼𝑣𝛼 = 𝑀1𝑣1------------------------------------------------------------[1]
6. If Q is the α-disintegration energy, which is the total energy released in the disintegration
process,
Q =
1
2
𝑀𝛼𝑣α
2
+
1
2
𝑀1𝑣1
2
Using equation [1] and on simplification, we get:
Q = 𝐸𝛼
𝑀1+ 𝑀α
𝑀1
7. Masses of the nuclei in the unit of atomic masses are close to their mass numbers, we can
write 𝑀1= A-4 and 𝑀𝛼 = 4.
Alpha disintegration energy-
Q = 𝐸𝛼
𝐴
𝐴−4
----------------------------------------------------------------[2]
Q can be determined from equation [1] as 𝐸𝛼 can be determined experimentally.
Example: 210Po, the α disintegration energy is 𝐸𝛼 = 5.305 MeV which gives Q = 5.408 MeV.
8. Accurate measurement of α disintegration energy is important from theoretical point of view.
The energy released during the nuclear transformation has its origin in the mass of the
transformation nucleus.
A part of this mass is converted into energy according to Einstein’s mass-energy equivalent
principle……….
The large quantity of energy released in α disintegration energy has also the same origin.
9. A part of the mass of the disintegrating nucleus is converted into energy as the α disintegration
energy.
Possibility of the α disintegration process:
α disintegration process is possible when the mass M of the disintegrating parent nucleus is greater
then the sum of the masses of the α-particle and the product nucleus.
M > 𝑀𝛼+ 𝑀1
The α disintegration energy is given by:
Q = (M - 𝑀𝛼 - 𝑀1)𝑐2
10. The masses in the above equation are the atomic masses and not the nuclear masses though
the α -emission takes place as a result of the transformation of the nucleus .
This is possible because the electronic masses cancel out in the above equation.
11. Range of α – particles:
α–particles from natural radio-active elements are easily absorbed in matter.
They can pass through thin paper or a very thin foil of mica or aluminium, but cannot penetrate
a few layers of these.
α–particles can travel up to a distance of few centimetres from the source in air at S.T.P.
They lose their entire kinetic energy.
12. Range of α–particle:
The monoenergetic α–particle from a given source can travel a definite maximum distance
from the source within a given substance.
The range of α–particle is very small in solid or in a liquid ≈ 10−3
mm for α–energy of few MeV.
Range of α–particle is relatively longer in gases because of low-density of gas.
In case of a gas the range depends on the temperature and the pressure of the gas.
13. With increase of pressure, the range decreases, while it increases with increase of
temperature.
The range of the α–particle depends on their initial velocity or kinetic energy.
Accurate measurements of the ranges of α–particles of different velocities gives the
relationship between the two quantities R = R(v).
14. Experiment to measure the Range of α–particle:
W.H.Bragg [England] – first to determine the range of α–particle.
Measured the ionization produced by α–particle at different distances from the sources along
their path within the medium.
Experimental set-up:
α–particles produced by the source S are collimated by a slit within the plate P.
A and B are two parallel wire-gauzes with a very small gap between them.
The positions of these wire-gauzes can be changed without altering the distance between
them.
15. The collimated beam of α–particles enter the region between A and B.
α–particles ionize the gas through which they pass.
During travel through the gas, an α–particle suffers repeated collisions with the gas atoms and
lose small fraction of energy to these atoms which get ionized.
Large number of ion-pairs is produced between A and B.
Ion pairs produced are attracted to towards these due to potential difference applied between
them which gives rise to ionization current.
16. Ionization current can be measured with the help of electrometer.
The potential difference between A and B is so adjusted that all
ion-pairs produced between them are drawn to them, thereby
producing saturation current.
The saturation current is proportional to the number of ion-pairs
produced between A and B.
Bragg moved the wire-gauzes to different distances from the
source and measured the saturation ion current between them
and plotted it as a function of the mean distance of the gauzes
from the source.
17. Ionizing power of the α–particles rises with
increasing distance of its travel from the
source.
The increase is first slow, but is more rapid
afterwards.
After reaching a maximum the ion current
rapidly begins to go down and falls to zero at
a definite distance from the source known as
the range of α–particles.
19. The steeply falling portion of the ionization current graph bends to the right just before the
current becomes zero.
The bend portion arises due to the straggling of the range.
20. SPECIFIC IONIZATION:
The number ∆𝑛
∆𝑥 of ion-pairs produced per unit length of its travel by an α–particle in a gas at
one atmospheric pressure.
∆𝑛 is number of ion-pairs produced in a distance ∆𝑥.
The specific ionization depends on the distance travelled by the α–particle from the source.
Example: For RaC’ α–particles [E = 7.68 MeV], the maximum value of the specific ionization is
about 6000 ion-pairs per millimetre.
21. Specific ionization increases as the distance travelled by the α–particle from the source
increases.
As the α–particle moves farther away from the source, its velocity decreases due to loss of
energy by ionization of the atom of the gas.
The slower α–particle spend longer time near the atoms in the gas.
There is a greater probability of their interaction with the electrons in the atom which is the
cause of ionization of the atoms.
22. For this reason, when α–particles are near the end of their paths the specific ionization is
maximum.
23. Measurement of range of α–particle by measuring the intensity of the beam:
Another method for the measurement of the range of α–particles is to determine the intensity
of the collimated beam of α–particles at different distances from the source.
This remains unchanged with distance till the end of the path of the α–particles.
M.S.Holloway and M.G.Livingston used this method to determine the α–ranges accurately with
the help of a shallow ionization chamber as the α–detector.
24. A collimated beam of α–particles from a given source falls on the scintillation phosphor (e.g.
ZnS) attached to a photomultiplier.
The photomultiplier tube records the current proportional to the intensity of the α–beam.
The distance between the source and the scintillation detector is gradually increased and graph
of the intensity versus the distance obtained.
The graph is known as integral range curve.
25. For a monoenergetic beam of α–particles, the intensity
falls abruptly to zero at a definite distance from the source.
The intensity I follows a straight line which has a very steep
and a finite slope.
If all the α–particles having the same initial energy made an
equal number of identical collisions in the absorber the
intensity drops to zero abruptly at a distance d equal to the
range of the α–particles.
The steep slope should fall off vertically down.
26. What does the finite slope indicate?????????........... The finite slope shows there is a
statistical fluctuation in the number of collisions suffered by the different α–particles.
The tail of the bent portion is due to straggling of the range.
The linear portion of the graph is extrapolated to zero intensity, we get an extrapolated range.
27. MEAN RANGE [R]: The distance from the source at which the intensity is half the initial
intensity which is a few millimetres shorter than Rex.
The mean range has a value such that 50% of the α–particles in the incident beam have ranges
greater than R while 50% have ranges less than R.
For a given energy of the incident α–particles, the different ranges defined above have slightly
different values.
Example: 210Po α–rays [𝐸𝛼 = 5.3007 MeV], the following values were obtained:
Ionization extrapolated range 𝑅𝑖 = 3.870 cm, extrapolated range 𝑅𝑒𝑥 = 3.897 cm, Mean range:
3.842cm.
28. Range-energy relationship for α–particles:
From the measured values of the ranges and energies of the α–particles, the following
mathematical relationship between the two quantities can be established:
R = 𝑎𝐸3/2
It is an empirical relationship, valid in a limited energy range known as Geiger’s law.
For E in MeV and R in centimetre, the constant a = 0.315.
If v be the velocity in cm/s then v α 𝐸.
29. The relationship for the range in terms of velocity:
R = b𝑣3
where b is another constant: b = 9.416 x 10−28
In the case of a solid, the range Rs[ in centimetre] is related to the range R in air as follows:
𝑅𝑠 =
0.312 𝑅𝐴1/2
𝜌
where 𝜌 is the density of solid of mass number A.
30. Geiger-Nuttall law
Geiger-Nuttall [1911] discovered an empirical relationship between the ranges of the α–
particles and the disintegration constants of the naturally radioactive substances emitting them.
This is known as Geiger-Nuttall law.
The relationship is given by:
log 𝝀 = A + B log R. ----------------------------------------------------[1]
where A and B are constants.
According to this law, the α–particles emitted by the substances having larger disintegration
constants [shorter half-lives] have longer ranges and vice-versa.
31. Equation [1] shows the graph of log 𝜆 and log R is a straight line with a slope B.
For different radioactive series, different straight lines are obtained, which are parallel to one
another, so that B is same for all of them.
Using equation [1] it is possible to determine the disintegration constant and the half life 𝜏 of a
radioactive substance if the range of α–particles emitted by it is known accurately.
33. The range R α 𝐸3/2, the Geiger-Nuttall can be written as:
log 𝝀 = C + D log E
where C and D are two other constants.
34. The half-life 𝜏 = ln 2 𝜆, the Geiger-Nuttall law can also be expressed by relating the variation
log 𝜏 with log R or log E.
In this case we get straight line graphs, but with negative slopes.
35. IMPORTANT NOTE:
The ranges of the α–particles from different radioactive isotopes are of the order of few
centimetres in air.
The half-lives of the radioactive isotope range from less than a millionth of a second to more
than billion[109
] years.
36. Example:
The half life of ThC’ is 3 X 10−7s, while that of 232Th is 1.38 X 1010 years.
The range of the α–particles emitted by them are 8.57 cm and 2.49 cm.
The corresponding energies are 8.78 MeV and 3.97 MeV.
The example shows that for an increase of the α–energy by a factor of 2.24, the half-life
decreases by a factor of 1024
.
Such enormous change of the half-life due to relatively small change of the α–energy can be
explained by the quantum mechanical theory of potential barrier penetration.
37. Alpha Ray Spectra:
α–particles are emitted with a very high velocity from the radioactive substances.
The velocity of the RaC’ α–particles is 1.92 X 107
m/s which is about 1/16 the velocity of light.
Rutherford and Robinson’s experiment on the determination of q/M of the particles gave their
velocity.
S. Rosenblum designed a magnetic spectrograph to measure the α–particle velocities from
different sources accurately.
38. The instrument is similar to the one used for the measurement of the 𝛽-ray spectra.
In this instrument, a very thin wire on which the radioactive substance is deposited is used as
the source.
The α–particles from the source are collimated by a system of slits.
The collimated beam is subjected to homogenous magnetic field at right angles to the direction
of beam.
40. Under the influence of the magnetic field, a slightly divergent beam of alpha particles describes
a semi-circular paths.
The beam are focussed at one point on the plate for a given energy.
Let B be the magnetic induction field, v be the velocity and R the radius of the semi-circular
path of the α–particles.
The expression we get: Bqv = 𝑀𝑣2 𝑅
41. Rosenblum used magnetic induction fields up to 3.6T [36,000] gauss.
Results:
The velocities of the α–particles emitted by the radioactive substances are of the order of
107
m/s.
For some radio-elements, only one line is obtained in the α–spectrum on the photographic
plate, which shows that they emit α–particles of a single velocity.
42. In some cases a number of parallel lines separated from one another [discrete spectrum] are
obtained, which shows that a number of different mono-energetic groups of α–particles are
emitted by the substances.
Each group has a definite velocity.
The velocities of the different groups are different.
The kinetic energies of the α–particles emitted from naturally radioactive substances are usually
in the range of 4 to 10 MeV.
44. Short Range Alpha Particles:
α–particles emitted with discrete energies lead to the conclusion that the nucleus has sharply
defined energy levels.
If the difference in the energy of the parent nuclei and the daughter nuclei is sufficiently large
then the daughter nuclei can be formed in the ground state or in one of the excited states.
Short range α–particles of different energies are emitted having different ranges.
The daughter nuclei comes to the ground state by emitting gamma photons of appropriate
energies.
45. By measurements of 𝛾-energy and α–energy, the energy levels of the nucleus can be found.
Rosenblum showed by using semi-circular focussing magnetic spectrograph that the α–rays
from ThC [𝐵𝑖212] are not monoenergetic.
It consists of several closely spaced mono-energetic groups or α–ray lines
47. The interpretation of complex α–particle spectra in terms of nuclear energy levels is illustrated
by the case of ThC [ Bi212].
It emits six groups of short-range α–particles with energies shown in the figure.
49. Long-Range Alpha Particles:
Long range alpha particles first observed by E. Rutherford and Wood.
Po214 and Po212 emit a few long range particles.
The origin of the long-range α–particles can be interpreted in terms of energy level as shown in
figure.
The nucleus can be in the excited state before the α–disintegration.
50. The excitation can be due to previous disintegration.
Emission of 𝛽 ray leaves the newly formed nucleus in the excited state.
Most probable case: the nucleus goes to the ground state by emitting 𝛾-ray of proper energy.
In some cases, if the life time for α–emitter the is comparable with the life-time for 𝛾-decay,
the newly formed excited nucleus emits α–particles with energy greater than that of the normal
particles.
52. The existence of long range α–particles can be explained as being caused by the decay of an
excited nucleus.
The extra energy of the α–particles measures the excitation energy of the initial nucleus.
53. Gamow’s Theory of Alpha Decay:
Results from the experiments on the scattering of the α–particles show that:
while approaching the nucleus the α–particle is acted by the Coulomb repulsive potential 𝑽𝒄 =
1/r up to the nuclear surface.
Anomalous scattering of the α–particles observed at larger angles in case of some lighter atoms
shows that the nature of the force is different from the Coulomb repulsion for a very close
distance of approach.
54. Present day knowledge of Nuclear structure:
neutrons and protons forming the nucleus of an atom are very strongly attracted to one
another.
It is a strongly bound structure, known as the nucleus of the atom.
Range of the attractive force: 2 X 𝟏𝟎−𝟏𝟓
m
Nature of the nuclear force holding the protons and the neutrons together: Short range force.
55. In α–disintegration of the heavy nuclei, two protons and two neutrons sometimes form a
cluster known as the α–particle.
Forces acting on the α–particle:
Inside the nucleus, short range nuclear attractive force.
Outside the nucleus , the Coulomb repulsion due to the residual nucleus of positive charge
(Z-2)
57. Outside the nucleus:
the Coulomb potential energy 𝑽𝒄 =
2(𝑧−2)𝑒2
4𝜋𝜀0𝑟
is positive.
For r < R, the nuclear radius:
It is an attractive potential,
Exact nature of this potential is not known.
58. Transition from the repulsive Coulomb potential to attractive potential in the nucleus takes
place at the nuclear surface r = R.
The value of the repulsive Coulomb potential is maximum at r = R :
𝑽𝒄 =
2(𝑧−2)𝑒2
4𝜋𝜀0𝑅
59. Example:
222Rn is formed during the α–disintegration of 226Ra (Z=88).
Value of 𝑽𝒔 = 34 MeV.
α–disintegration Q = 4.88 MeV <<< 𝑽𝒔
This is the energy the α–particle has in the disintegrating nucleus.
60. Classical Mechanics explanation:
To escape from the nucleus or to penetrate inside the nucleus: the energy of the α–particle
must be at least equal to 𝑽𝒔
If it is lower, then in some region between the steeply falling curve and the vertical line the
potential energy of the particle will be greater than its total energy. This is the classically
forbidden region.
61. Kinetic energy of the α–particle is positive:
If the α–particle is inside the nucleus
or
At points to the right of line b.
Kinetic energy is negative:
In the region ab where the total energy of the α–particle is less than potential energy.
Known as potential barrier region or classically forbidden region.
α–particle neither can escape nor enter the nucleus.
62. Quantum Mechanical Approach:
Quantum mechanically, such classically forbidden phenomena may occur.
Quantum mechanics - particle is represented by a wave – obeying the Schrodinger equation.
The wave equation for the different regions by substituting the corresponding potentials acting
on the α–particle in these regions.
If these equations are solved with appropriate boundary conditions, then it is found that an α–
particle initially inside the nucleus has a finite probability of coming out of it.
63. Quantum Mechanical Tunnel Effect: the escape of the α–particle from the nucleus as if they
leak out through tunnels in the potential barrier.
Gives a mathematical relationship between the initial α–energy and the half-life of the
disintegrating nucleus.