Composition of Matter All of matter is composed of at least three All of matter is composed of at least three fundamental particles (approximations): fundamental particles (approximations):Electron e- 9.11 x 10-31 kg -1.6 x 10-19 CProton p 1.673 x 10-27 kg +1.6 x 10-19 C 3 fmNeutron n 1.675 x 10-31 kg 0 3fm
DefinitionsA nucleon is a general term to denote a nuclear particle -that is, either a proton or a neutron.The atomic number Z of an element is equal to the numberof protons in the nucleus of that element.The mass number A of an element is equal to the totalnumber of nucleons (protons + neutrons).
Nuclear SizeThe shape of the nucleus is taken spherical, because fora given volume this shape possesses the least surfacearea. The nuclear density remains approximately constantover most of the nuclear volume. This means that thenuclear volume is proportional to the number of nucleonsi.e. mass number A. Rα A3 1Hence radius of nucleus R = Ro A 3 1 where Ro is a constant having value 1.48 x 10 -15 m
Atomic Mass Unit, uOne atomic mass unit (1 u) is equal to one-twelfth of the mass of the most abundant formof the carbon atom--carbon-12.Atomic mass unit: 1 u = 1.6606 x 10-27 kg Common atomic masses: Proton: 1.007276 u Neutron: 1.008665 u Electron: 0.00055 u Hydrogen: 1.007825 u
Mass and Energy Einstein’s equivalency formula for m and E: E = mc ; c = 3 x 10 m/s 2 8The energy of a mass of 1 u can be found: E = (1 u)c2 = (1.66 x 10-27 kg)(3 x 108 m/s)2 E = 1.49 x 10-10 J Or E = 931.5 MeV
The Mass DefectThe mass defect is the difference between the rest massof a nucleus and the sum of the rest masses of itsconstituent nucleons, A. Binding EnergyThe binding energy of a nucleus is the energy required toseparate a nucleus into its constituent parts. EB = mDc2 where mD is the mass defect
Binding Energy Vs. Mass NumberCurve shows that EB Binding Energy per nucleon 8increases with A andpeaks at A = 60. 6Heavier nuclei areless stable. 4Green region is for 2most stable atoms. 50 100 150 200 250 Mass number A For heavier nuclei, energy is released when they break up (fission). For lighter nuclei, energy is released when they fuse together (fusion).
Radioactivity• The phenomenon of spontaneous emission of radiations (α,β and γ radiations) from a substance (generally elements having their atomic number higher than 82 in the periodic table).• Discovered by Henry Bacquerel in 1896.• Properties of α,β and γ radiations- Composition, Ionization Power, Penetration power, Effect on photographic plate
Laws of Radioactive disintegrations-1- The Radioactive disintegrations happens due to the emission of α, β and γ radiations.2- The natural disintegration is totally statistical, i.e. which atom will disintegrate first is only a matter of chance.3- The number of atoms which disintegrate per second is proportional to the number remaining atoms present at any instant, i.e.- -dN/dt α N or -dN/dt = λN (where λ is a constant of proportionality and is known as the decay constant) or N = N0e-λt
Half Life Period (T)-• The time in which half of the radioactive substance gets disintegrates is known as half life of that material. T = 0.693/λ
General Properties of Nucleus—1- Nuclear mass= Mass of all Neutrons + Mass of all protonsmp= 1.67261 x 10-27 Kg = 1.007277 a.m.u.,mn= 1.67492 x 10-27 Kg = 1.008666 a. m. u.2- Nuclear Charge- Total charge due to the protons3- Nuclear radius- Nuclear radius is measured by the measurement of the directions of scattered protons/ neutrons / electrons. R = R0A1/3Where R0 is a constant with value = 1.4 x 10-15 MeterA = Mass Number of the element4- Nuclear density= Nuclear Mass/ [4/3( π R3)]
The Mass Difference and Nuclear Binding Energy-• The mass of the nucleus is always less than the sum of masses of its constituents.• The difference in measured mass (M in a. m. u.) and mass number (A) is called mass defect (∆M).• The Binding energy of the nucleus (E) = ∆M (in a.m.u.) x (931 MeV)
Nuclear Forces• A nucleus contains positively charged protons and uncharged neutrons.• A repulsive force works between protons inside the nucleus.• Nuclear forces overcome with these repulsive forces to give a stable nucleus.• Neutrons and protons can be converted in to each other by the exchange of a new particle meson.
Meson theory of Nuclear Forces by Yukawa (1935)• A meson may be π+, π- or π0. A neutron, by accepting a π+ meson converted in to a proton. A proton, by ejecting a π+ meson converted in to a neutron.• A neutron, by ejecting a π- meson converted in to a proton.• A proton, by accepting a π- meson converted in to a neutron.
• Two neutron can exchange π0 mesons, which result in the exchange forces between them.• This exchange of meson is responsible for the generation of exchange forces which is responsible for the stability of nucleus.
Nuclear Fission• The phenomenon of breaking of heavy nuclie in to two or more light nuclei of almost same masses is known as the nuclear fission.• Discovered by Otto Hahn and Strassman (Germans) in 1939.• In nuclear fission large amount of energy is liberated
• Theory of Nuclear Fission- Liquid Drop Model-• By Bohr and Wheeler• The nucleus is assumed to be similar to a drop of the liquid.• Nucleus remains in balance due to the exchangeforces and the repulsive forces between its constituents.• Due to this balance nucleus remains in spherical size.• When this balance is disturbed by the incident neutrons, the spherical shape is distorted.• The surface tension force tend to recover the spherical size, so drop attains a dumb-bell shape.• Due to disbalance in the exchange and coulombic forces, the dumb- bell breaks in two spherical parts (i.e. two separate nuclie).
• Nuclear fusion is the formation of a heavier nucleus by fusing of two light nuclei.• In this process mass of the resulting nucleus is less than the masses of constituent , therefore according to Einstein’s mass energy equivalence, enormous amount of energy is released.• Fusion reactions take place at very high temperature.
Spontaneous FissionSome radioisotopes contain nuclei which are highlyunstable and decay spontaneously by splitting into 2smaller nuclei. Th234 90 Gamma ray U238 92 He4 2Energy is being released as a result of the fission reaction.
Induced FissionNuclear fission can be induced by bombarding atoms withneutrons resulting in the splitting of nuclei into two smallernuclei.Induced fission decays are also accompanied by therelease of neutrons. 235 92 U + n→ Ba + Kr +3 n 1 0 141 56 92 36 1 0Energy is being released as a result of the fission reaction.
Nuclear FusionIn nuclear fusion, two nuclei with low mass numberscombine to produce a single nucleus with a higher massnumber. 2 1 H + H → He+ n + Energy 3 1 4 2 1 0
Hydrogen (proton) fusionLike electrical charges repel. So, protons in a gas avoid`collisions’ p+ p+
Hydrogen (proton) fusionHowever, as a gas temperature goes up, the average speedof the particles goes up and the protons get closer beforerepelling one another. If the proton get very close, the short-range nuclear force fuses them together. p+ p+
Antimatter When two protons fuse, almost immediately one turns into a neutron by emitting a positively charged electron (known as a positron). The e+ is antimatter. When it comes into contact with its matter partner (e-) it annihilates entirely into energy. NeutrinoThis is a chargeless, perhaps massless particle which has atiny crossection for interaction with other types of matter.The mean free path in lead is five light years.Neutrinos were first postulated in 1932 to account formissing angular momentum and energy in beta-decayreactions (when a proton becomes a neutron and emits apositron).
Nuclear ForceThe nuclear force is the force between two or more nucleons.It is responsible for binding of protons and neutrons intoatomic nuclei.The force is powerfully attractive between nucleons at distancesof about 1 femtometer (fm) between their centers, but rapidlydecreases to insignificance at distances beyond about 2.5 fm.At very short distances less than 0.7 fm, it becomes repulsive,and is responsible for the physical size of nuclei, since thenucleons can come no closer than the force allows.At short distances (less than 1.7 fm or so), the nuclear force isstronger than the Coulomb force between protons; it thusovercomes the repulsion of protons inside the nucleus.
Proton-Proton Cycle• The net result is 4H1 --> He4 + energy + 2 neutrinos where the released energy is in the form of gamma rays. Each cycle releases ~25 MeV For the proton-proton cycle the gas temperature needs to be >107K
Source of Energy of Stars• The source of energy of stars is Fusion reaction.• Our sun shares the “Proton-Proton Fusion Cycle” with the smallest known stars.• Larger stars known to “burn” with different cycles, such as the “carbon cycle”
Nuclear Radiation Measurements All the methods for detection of radioactivity are based oninteractions of the charged particles because interaction results inthe production of ions and release of energy. Detectors are used to detect and record the number of particlesemitted in various experiments involved in the study of nuclearradiation, disintegration and transmutation. Detectors Based on Ion Based on Light collection method emission method Example: Proportional Example: Scintillation Counter, G.M. Counter Counter
Types of detectors– Gas-filled detectors consist of a volume of gas between two electrodes– In scintillation detectors, the interaction of ionizing radiation produces UV and/or visible light– Semiconductor detectors are especially pure crystals of silicon, germanium, or other materials to which small amounts of I mpurity atoms have been added so that they act as diodes
Types of detectors (cont.)• Detectors may also be classified by the type of information produced: – Counters indicate the number of interactions occurring in the detector. – Spectrometers yield information about the energy distribution of the incident radiation. – Dosimeters indicate the net amount of energy deposited in the detector by multiple interactions.
Modes of operation• In pulse mode, the signal from each interaction is processed individually• In current mode, the electrical signals from individual interactions are averaged together, forming a net current signal
Dead time• The minimum time taken by a radiation detector in between two successive detections.• GM counters have dead times ranging from tens to hundreds of microseconds, most other systems have dead times of less than a few microseconds.
Detection efficiency• The efficiency (sensitivity) of a detector is a measure of its ability to detect radiation• Efficiency of a detection system is defined as the probability that a particle or photon emitted by a source will be detected.
Number detectedEfficiency = Number emitted Number reaching detectorEfficiency = × Number emitted Number detected Number reaching detectorEfficiency = Geometric efficiency × Intrinsic efficiency
Gas-filled detectors• A gas-filled detector consists of a volume of gas between two electrodes, with an electrical potential difference (voltage) applied between the electrodes• Ionizing radiation produces ion pairs in the gas• Positive ions (cations) attracted to negative electrode (cathode); electrons or anions attracted to positive electrode (anode)• In most detectors, cathode is the wall of the container that holds the gas and anode is a wire inside the container
Types of gas-filled detectors• Three types of gas-filled detectors in common use: – Ionization chambers – Proportional counters – Geiger-Mueller (GM) counters• Type determined primarily by the voltage applied between the two electrodes• Ionization chambers have wider range of physical shape (parallel plates, concentric cylinders, etc.)• Proportional counters and GM counters must have thin wire anode
GM counters: Main Features• GM counters used for the detection of α,β,γ rays, protons etc.• Gas amplification produces billions of ion pairs after an interaction.• The only difference with a Proportional Counter is of operating voltage.• Operating voltage is 800-2000 Volts• Works on pulse mode.
CONSTRUCTION-A Metallic tube with thin wire (anode) in center,wall of the tube works as cathode.Tube is usually filled with noble gas (e.g. argon) at low pressure, withsome additives as quenchers e.g. carbon dioxide, methane,isobutane)-Charged particle in gas ⇒ ionization ⇒ electrons liberated;-Electrons accelerated in electric field ⇒ liberate other electrons byionization which in turn are accelerated and ionize ⇒ “avalanche ofelectrons”;-Quenching is the process of terminating the discharge after eachdetection.- The time taken for this is known as dead time of the counter
Mixture of Argon and ethyl alcohol ANODE PULSECathode Pulse Counter
Geiger-Muller CounterThe efficiency of the counter is defined as the ratio of theobserved counts/sec to the number of ionizing particlesentering the counter per second.Counting efficiency is its ability of counting, if at least oneion-pair is produced in it. ∈= 1 − e slp Where, s = specific ionization at one atmosphere p = pressure in atmosphere l = path length of the ionization particle in the counter
Proportional Counters: similar in construction to Geiger-Müller counter,but works in different HV regime . (200- 800 Volts) metallic tube with thin wire in center, filled withgas, HV between wall (-, “cathode”) and central wire(+,”anode”); ⇒ strong electric field near wire; gas is usually noble gas (e.g. argon), with someadditives e.g. carbon dioxide, methane,isobutane,..) as “quenchers”; Radiation detected - α,β,γ rays
Scintillation CounterIncident LightRadiation Pulse Photomultiplier Phosphor tube Electric Pulse Amplifier scaler and register
Scintillation detectors• Scintillators are used in conventional film-screen radiography, many digital radiographic receptors, fluoroscopy, scintillation cameras, most CT scanners, and PET scanners• Scintillation detectors consist of a scintillator and a device, such as a PMT, that converts the light into an electrical signal
Scintillators• Desirable properties: – High conversion efficiency – Decay times of excited states should be short – Material transparent to its own emissions – Color of emitted light should match spectral sensitivity of the light receptor – For x-ray and gamma-ray detectors, µ should be large – high detection efficiencies – Rugged, unaffected by moisture, and inexpensive to manufacture
Scintillators (cont.)• Amount of light emitted after an interaction increases with energy deposited by the interaction• May be operated in pulse mode as spectrometers• High conversion efficiency produces superior energy resolution
Materials• Sodium iodide activated with thallium [NaI(Tl)], coupled to PMTs and operated in pulse mode, is used for most nuclear medicine applications – Fragile and hygroscopic• Bismuth germanate (BGO) is coupled to PMTs and used in pulse mode as detectors in most PET scanners
Photomultiplier tubes• PMTs perform two functions: – Conversion of ultraviolet and visible light photons into an electrical signal – Signal amplification, on the order of millions to billions• Consists of an evacuated glass tube containing a photocathode, typically 10 to 12 electrodes called dynodes, and an anode
Dynodes• Electrons emitted by the photocathode are attracted to the first dynode and are accelerated to kinetic energies equal to the potential difference between the photocathode and the first dynode• When these electrons strike the first dynode, about 5 electrons are ejected from the dynode for each electron hitting it• These electrons are attracted to the second dynode, and so on, finally reaching the anode
Βeta minus (β -) decayexample: 6C14 7N14 + -1β 0 + 0υ 0 A neutron turned into a proton by emitting an electron; however, one particle [the neutron] turned into two [the proton and the electron]. Charge and mass numbers are conserved, but since all three (neutron, proton, and electron) are fermions [spin 1/2 particles], angular momentum, particle number, and energy are not! Need the anti-neutrino [0 υ 0] to balance everything!
Positron (β ) decay +example: 6C11 5B11 + +1β 0 + 0υ 0 A proton turns into a neutron by emitting a positron; however, one particle [the proton] turned into two [the neutron and the positron]. Charge and mass numbers are conserved, but since all three are fermions [spin 1/2 particles], angular momentum, particle number, and energy are not! Need the neutrino [0 υ 0] to balance everything!