STRUCTURE OF MATTER AND

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STRUCTURE OF MATTER AND NUCLEAR TRAMSFORMATIOMS
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????1. The Physics of Radiation Therapy 2.
Principles and Practice of RADIATION THERAPY
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STRUCTURE OF MATTER
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Structure of matter---The atoms

• All matter is composed of individual entities
  called elements. Each element is distinguishable
  from the others by the physical and chemical
  properties of its basic components --- the atom
• Each atom consists of a small central core, the
  nucleus, where most of the atomic mass is located
  and a surrounding "cloud" of electrons moving in
  orbits around the nucleus.

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Structure of matter---The atoms
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Structure of matter---The atoms

• The radius of the atom (radius of the electronic
  orbits) is approximately 10-10 m
• The nucleus has a much smaller radius, namely,
  about 10-14 m
• Thus, for a particle of size comparable to
  nuclear dimensions, it will be quite possible to
  penetrate several atoms of matter before a
  collision happens

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Structure of matter---The atoms

• it is important to keep track of those particles
  that have not interacted with the atoms
• --- the primary beam
• and those that have suffered collisions
• --- the scattered beam

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Structure of matter---The nucleus

• The properties of atoms are derived from the
  constitution of
• their nuclei and
• the number and the organization of the orbital
  electrons
• The nucleus contains protons and neutrons.
  Whereas protons are positively charged, neutrons
  have no charge

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Structure of matter---The nucleus

• The number of protons in the nucleus is equal to
  the number of electrons outside the nucleus, thus
  making the atom electrically neutral
• Atomic nomenclature

X atomic symbol A atomic mass number Z
atomic number A Z N (?????????)
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Terms used to describe a nucleus
Ei-Ef
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• 1.???(isotope)?????,?????
• 2.???(isotone)?????,?????
• 3.???(isobar) ?????,?????,
• ?????
• 4.?????(isomer)????,??????

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Structure of matter---The nucleus

• Certain combinations of neutrons and protons
  result in stable (nonradioactive) nuclides than
  others
• stable elements in the low atomic number
• --- N Z
• as Z increases beyond about 20, the N/P ratio for
  stable nuclei becomes gt 1 and increases with Z

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Structure of matter---The nucleus
combinations of neutrons and protons result in
stable
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Atomic mass and energy units

• atomic mass unit (amu)
• defined as 1/12 of the mass of a nucleus
• Thus the nucleus of is arbitrarily
  assigned the mass equal to 12 amu

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Masses and charges of the main subatomic particles
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Atomic mass and energy units

• mass defect ( binding energy )
• the mass of an atom is not exactly equal to the
  sum of the masses of constituent particles
• a certain mass is destroyed and converted into
  energy that acts as a "glue" to keep the nucleons
  together

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THE NUCLEUS
Binding Energy
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THE NUCLEUS

• Binding Energy
• Mass defect
• The difference between the atomic weight and the
  sum of the weights of the parts W - M
• W ZmH ( A-Z )mn
• M atomic weight
• BE ( W M )amu 931 MeV/amu

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Atomic mass and energy units

• The basic unit of energy is the joule (J)
• equal to the work done when a force of 1 newton
  acts through a distance of 1 m
• Energy unit in atomic and nuclear physics
• electron volt ( eV ),
• defined as the kinetic energy acquired by an
  electron in passing through a potential
  difference of 1 V

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Atomic mass and energy units
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Distribution of orbital electrons

• Rutherfords atomic model (1911)

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Distribution of orbital electrons

• Bohr atomic model (1913)

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Bohrs postulates

• 1.An electron in an atom moves in a circular
  orbit about the nucleus under the influence of
  the Coulomb attraction between the electron and
  the nucleus, and obeying the law of classical
  mechanics.
• 2.Instead of the infinity of orbits which would
  be possible in classical mechanics, it is only
  possible for an electron to move in an orbit for
  which its orbital angular momentum L is an
  integral multiple of Plancks constant h, divided
  by 2p. (Lnh)

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• 3.Despite the fact that it is constantly
  accelerating, an electron moving in such an
  allowed orbit does not radiate electromagnetic
  energy. Thus its total energy E remains
  constant.
• 4.Electromagnetic radiation is emitted if an
  electron, initially moving in an orbit of total
  energy Ei, discontinuously changes its motion so
  that it moves in an orbit of total energy Ef.
  The frequency of the emitted radiation ? is equal
  to the quantity (Ei - Ef) devided by Plancks
  constant h. (h? Ei - Ef)

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ATOMIC ENERGY LEVELS

• Energy level diagram of the tungsten atom

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NUCLEAR FORCES

• There are four different forces in nature, in the
  order of their strengths
• strong nuclear force
• electromagnetic force
• weak nuclear force
• gravitational force

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NUCLEAR FORCES

• strong nuclear force
• responsible for holding the nucleons together in
  the nucleus
• electromagnetic force
• force between charged nucleons is quite strong,
  but it is repulsive and tends to disrupt the
  nucleus

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NUCLEAR FORCES

• weak nuclear force
• appears in certain types of radioactive decay
• gravitational force
• in the nucleus is very weak and can be ignored

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NUCLEAR FORCES

• The strong nuclear force is a short-range force
  that comes into play when the distance between
  the nucleons becomes smaller than the nuclear
  diameter

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NUCLEAR ENERGY LEVELS

• The shell model of the nucleus assumes that the
  nucleons are arranged in shells, representing
  discrete energy states of the nucleus similar to
  the atomic energy levels
• If energy is imparted to the nucleus, it may be
  raised to an excited state, and when it returns
  to a lower energy state , it will give off energy
  equal to the energy difference of the two states.

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NUCLEAR ENERGY LEVELS

• Sometimes the energy is radiated in steps,
  corresponding to the intermediate energy states,
  before the nucleus settles down to the stable or
  ground state

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PARTICLE RADIATION

• Radiation
• emission and propagation of energy through space
  or a material medium
• particle radiation
• energy propagated by traveling corpuscles that
  have a definite rest mass and within limits have
  a definite momentum and defined position at any
  instant

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PARTICLE RADIATION

• Besides protons, neutrons, and electrons , many
  other atomic and subatomic particles have been
  discovered
• Interact with matter and produce varying degrees
  of energy transfer to the medium

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ELECTROMAGNETIC RADIATION

• Wave Model
• in terms of oscillating electric and magnetic
  fields
• the mode of energy propagation for such
  phenomena as light waves, radio waves,
  microwaves, ultraviolet rays, g-rays, and x-rays
• with the speed of light ( 3 x 108 m/sec in
  vacuum)

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Electromagnetic radiation

• A. Wave model
• ? C/?

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ELECTROMAGNETIC RADIATION

• Quantum Model
• wavelength becomes very small or the frequency
  becomes very large, the dominant behavior of
  electromagnetic radiations can only be explained
  by considering their particle or quantum nature

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Electromagnetic radiation

• B. Quantum model
• E h? hc /?
• h Plancks constant (6.6210-34 J?sec)
• c3108 m/sec
• E (keV) 1.24 /?(nm)

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NUCLEAR TRAMSFORMATIOMS
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NUCLEAR TRAMSFORMATIOMS

• RADIOACTIVITY
• Radioactivity, first discovered by Henri
  Becquerel in 1896, is a phenomenon in which
  radiation is given off by the nuclei of the
  elements
• This radiation can be in the form of particles ,
  electromagnetic radiation, or both.

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NUCLEAR TRAMSFORMATIOMS

• RADIOACTIVITY
• a radioactive nucleus has excess energy that is
  constantly redistributed among the nucleons by
  mutual collisions
• As a matter of probability, one of the particles
  may gain enough energy to escape from the
  nucleus, thus enabling the nucleus to achieve a
  state of lower energy

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NUCLEAR TRAMSFORMATIOMS

• RADIOACTIVITY
• Also, the emission of a particle may still leave
  the nucleus in an excited state. In that case,
  the nucleus will continue stepping down to the
  lower energy states by emitting particles or g
  rays until the stable or the ground state has
  been achieved.

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NUCLEAR TRAMSFORMATIOMS

• DECAY CONSTANT
• where l is a constant of proportionality called
  the decay constant

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NUCLEAR TRAMSFORMATIOMS

• ACTIVITY
• The rate of decay is referred to as the activity
  of a radioactive material
• where A is the activity remaining at time t, and
  A0 is the original activity equal to lN0

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NUCLEAR TRAMSFORMATIOMS

• ACTIVITY
• The unit of activity is the curie (Ci)
• 1 Ci 3.7 x 1010 disintegrations/sec (dps)
• The SI unit for activity is becquerel (Bq). The
  becquerel is a smaller but more basic unit than
  the curie and is defined as
• 1 Bq l dps 2.70 x 10-11 Ci

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NUCLEAR TRAMSFORMATIOMS

• THE HALF-LIFE AND THE MEAN LIFE
• The term half-life ( T1/2 ) of a radioactive
  substance is defined as the time required for
  either the activity or the number of radioactive
  decay to half the initial value

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NUCLEAR TRAMSFORMATIOMS

• THE HALF-LIFE AND THE MEAN LIFE
• The mean or average life is the average lifetime
  for the decay of radioactive atoms

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NUCLEAR TRAMSFORMATIOMS

• Example
• 1. Calculate the number of atoms in 1g of 226Ra.
• 2. What is the activity of 1 g of 226Ra
  (half-life 1,622 years)?

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NUCLEAR TRAMSFORMATIOMS

• specific activity
• The activity per unit mass of a radionuclide is
  termed
• One reason why cobalt-60 is preferable to
  cesium-137, in spite of its lower half-life (5.26
  years for 60Co versus 30.0 years for 137Cs) is
  its much higher specific activity

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NUCLEAR TRAMSFORMATIOMS

• Example
• 1) Calculate the decay constant for cobalt-60 (
  T1/2 5.26 years) in units of month-1.
• 2) What will be the activity of a 5,000-Ci 60Co
  source after 4 years?

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NUCLEAR TRAMSFORMATIOMS

• THE HALF-LIFE AND THE MEAN LIFE
• When will 5 mCi of 131I (T1/2 8.05 days) and 2
  mCi of 32P (T1/2 14.3 days) have equal
  activities?

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RADIOACTIVE SERIES

• 103 elements known today. the first 92 (from Z
  1 to Z 92) naturally. The others artificially
• the number of particles inside the nucleus
  increases, the chances of panicle emission are
  increased.
• This is suggested by the observation that all
  elements with Z greater than 82 ( lead ) are
  radioactive
• the uranium series, the actinium series, and the
  thorium series

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RADIOACTIVE SERIES

• The uranium series originates with 238U having a
  half-life of 4.51x109 years
• The actinium series starts from 235U with a
  half-life of 7.13 x108 years
• The thorium series begins with 232Th with
  half-life of 1.39 x 1010 years
• All the series terminate at the stable isotopes
  of lead with mass numbers 206, 207, and 208

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RADIOACTIVE SERIES
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RADIOACTIVE EQUILIBRIUM

• Radioactive nuclides transformation
• original nuclide, called the parent
• radioactive produce nuclide, called the daughter
• If the half-life of the parent is longer than
  that of the daughter, equilibrium will be
  achieved
• the ratio of daughter activity to parent activity
  will become constant.
• If the half-life of the parent is not much longer
  than that of the daughter
• transient equilibrium

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RADIOACTIVE EQUILIBRIUM

• If the half-life of the parent is not much longer
  than that of the daughter
• transient equilibrium
• If the half-life of the parent is much longer
  than that of the daughter
• secular equilibrium

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RADIOACTIVE EQUILIBRIUM

• Transient equilibrium, parent 99Mo (T1/2 67h)
  and the daughter 99mTc (T1/2 6 h)

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RADIOACTIVE EQUILIBRIUM

• Secular equilibrium, 222Rn (T1/2 3.8 days)
  achieving
• equilibrium with its parent, 226Ra(T1/2 1,622
  years)

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SERIAL TRANSFORMATION
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RADIOACTIVE EQUILIBRIUM

• A practical example of the transient equilibrium
• 99Mo generator producing 99mTc for diagnostic
  procedures.
• sometimes called "cow" because the daughter
  product, in this case 99mTc, is removed or
  "milked" at regular intervals.

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SERIAL TRANSFORMATION
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MODES OF RADIOACTIVE DECAY

• a Particle Decay
• Radioactive nuclides with very high atomic
  numbers (greater than 82) decay most frequently
  with the emission of an a particle
• where Q represents the total energy released in
  the process and is called the disintegration
  energy

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Alpha Decay (????)
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MODES OF RADIOACTIVE DECAY

• b Particle Decay
• accompanied by the ejection of a positive or a
  negative electron from the nucleus, is called the
  b decay
• antineutrino and neutrino, are identical panicles
  but with opposite spins. They carry no charge and
  practically no mass.

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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Negatron Emission
• with an excessive number of neutrons or a high
  neutron-to-proton (n/p) ratio

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Beta Decay (????)
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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Negatron Emission
• The energy Q is shared between the emitted
  particles (including g rays if emitted by the
  daughter nucleus) and the recoil nucleus. The
  kinetic energy possessed by the recoil nucleus is
  negligible because of its much greater mass
  compared with the emitted particles

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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Positron Emission
• Positron-emitting nuclides have a deficit of
  neutrons, and their n/p ratios are lower than
  those of the stable nuclei of the same atomic
  number

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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Positron Emission

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Positron Emission (????)
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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Electron Capture
• The electron capture is a phenomenon in which one
  of the orbital electrons is captured by the
  nucleus, thus transforming a proton into a neutron

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Electron Capture (????)
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MODES OF RADIOACTIVE DECAY

• b Particle Decay---Internal Conversion
• The excess nuclear energy is passed on to one of
  the orbital electrons, which is then ejected from
  the atom. The process can be crudely likened to
  an internal photoelectric

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Internal Conversion (???)
conversion electron
electron vacancy
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NUCLEAR REACTIONS

• The a,p Reaction
• The first nuclear reaction was observed by
  Rutherford in 1919

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NUCLEAR REACTIONS

• The a,p Reaction
• Thus the above reaction is endoergic, that is, at
  least 1.19 MeV of energy must be supplied for the
  reaction to take place. This minimum required
  energy is called the threshold energy for the
  reaction and must be available from the kinetic
  energy of the bombarding particle
• a,p Reaction

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NUCLEAR REACTIONS

• The a,n Reaction
• This was the first reaction used for producing
  small neutron sources.
• A material containing a mixture of radium and
  beryllium has been commonly used as a neutron
  source.

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NUCLEAR REACTIONS

• Proton Bombardment

• Deuteron Bombardment

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NUCLEAR REACTIONS

• Neutron Bombardment
• The neutrons do not have to possess high kinetic
  energies in order to penetrate the nucleus.
• As a matter of fact, slow neutrons or thermal
  neutrons (neutrons with average energy equal to
  the energy of thermal agitation in a material,
  which is about 0.025 eV at room temperature) have
  been found to be extremely effective in producing
  nuclear transformations .

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NUCLEAR REACTIONS

• Neutron Bombardment
• The previous reaction forms the basis of neutron
  detection.
• In practice, an ionization chamber is filled with
  boron gas such as BF3.
• The a particle released by the n, a reaction with
  boron produces the ionization detected by the
  chamber

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NUCLEAR REACTIONS

• Neutron Bombardment
• The most common process of neutron capture is the
  n,g reaction.
• These g rays, called capture g rays, can be
  observed coming from a hydrogenous material such
  as paraffin used to slow down (by multiple
  collisions with the nuclei) the neutrons and
  ultimately capture some of the slow neutrons .

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NUCLEAR REACTIONS

• Neutron Bombardment
• Products of the n, g reaction, in most cases,
  have been found to be radioactive, emitting b
  particles

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NUCLEAR REACTIONS

• Neutron Bombardment
• n,p reaction

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NUCLEAR REACTIONS

• Neutron Bombardment
• It should be pointed out that whether a reaction
  will occur with fast or slow neutrons depends on
  the magnitude of the mass difference between the
  expected product nucleus and the bombarded
  nucleus.
• For example, in the case of an n,p reaction, if
  this mass difference exceeds 0.000840 amu (mass
  difference between a neutron and a proton), then
  only fast neutrons will be effective in producing
  the reaction

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NUCLEAR REACTIONS

• Photo Disintegration
• An interaction of a high energy photon with an
  atomic nucleus can lead to a nuclear reaction and
  to the emission of one or more nucleons
• threshold, 10.86 MeV
• Because the rest energies of many nuclei are
  known to a very high accuracy, the
  photodisintegration process can be used as a
  basis for energy calibration of machines
  producing high energy photons

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NUCLEAR REACTIONS

• Fission
• This type of reaction is produced by bombarding
  certain high atomic number nuclei by neutrons
• in the above reaction, averages more than 200
  MeV. This energy appears as the kinetic energy of
  the product particles as well as g rays
• chain reaction
• critical mass

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NUCLEAR REACTIONS

• Fusion
• Nuclear fusion may be considered the reverse of
  nuclear fission that is, low mass nuclei are
  combined to produce one nucleus.
• In the above example, the loss in mass is about
  0.0189amu, which gives Q 17.6 MeV.

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ACTIVATION OF NUCLIDES

• The yield of a nuclear reaction depends on
  parameters
• number of bombarding particles, neutrons
• the number of target nuclei
• the probability of the occurrence of the nuclear
  reaction
• Another important aspect of activation is the
  growth of activity
• Saturation activity, the rate of activation
  equals the rate of decay
• As mentioned earlier, the slow (thermal) neutrons
  are very effective in activating nuclides

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