Nuclear physics (PowerPoint) by veeru5656

VIEWS: 119 PAGES: 25

									                   Topic 8: Nuclear Physics
          • Nucleus
            – Nucleons (A) = Protons (Z) + Neutrons (N)
            – Density and stability

          • Radioactivity
             – Formula (exponential decay)

          • Radioactive Processes
             – a, b, and g-rays
             – Natural radioactivity series

          • Fusion/ Fission


Phys 320 - Baski                Nuclear Physics (Topic 8)   Page 1
                   Nucleus: Particle Composition


• Z protons + N neutrons = A nucleons (1 – 10 fm dia.).

• 1920: Rutherford hypothesized neutron = electron + proton.
   – Why not? Uncertainty principle violated!
     (Emin = 100 MeV in 10 Fm)
   – Nuclear moment too small.
     (Bohr magneton mB = 2000 × Nuclear magneton mN).

• 1932: Chadwick discovered neutron (new nucleon!).

• Isotope: same Z (# protons), different N (# neutrons).
   – 15O and 16O or 12C and 13C

Phys 320 - Baski              Nuclear Physics (Topic 8)        Page 2
                   Nucleus: Particle Properties

       Particle     Charge          amu                Spin     m
       Proton       +e          1.007276                1/2   +2.79mN
       Neutron       0          1.008665                1/2   – 1.91mN
       Electron     –e          5.4858×10-4             1/2   +1.00mB



• Proton, neutron and electron are all fermions (spin 1/2).
• Proton and neutron are “heavy” baryons composed of 3 quarks.
  [proton = up, up, down quarks and neutron = up, down, down]

    Electron is a “light” lepton.

Phys 320 - Baski                Nuclear Physics (Topic 8)                Page 3
                   Nucleus: Particle Potential Wells
• Electron is only bound with negative total energy, and can never
  escape.
• Nucleon can be bound with positive total energy, and can escape by
  tunneling through the Coulomb barrier  nuclear decay processes.
   – Leads to radioactive processes.

      Nucleon Nuclear Potential             Electron Coulombic Potential
        Energy




                          Radius r




Phys 320 - Baski                Nuclear Physics (Topic 8)          Page 4
                   Nucleus: Density Distribution

• Nucleus has ~uniform density




                                    Charge Density r (1025 C/m3)
  r with radius r.

• r = Ro A1/3 where Ro = 1.2 fm                                    He
 r varies by 4× from lightest to
 heaviest elements.

• ratom ~ 103 kg/m3
  rnucleus = 1017 kg/m3
  (mm3 = mass of supertanker!!)


                                                                                      Bi


Phys 320 - Baski              Nuclear Physics (Topic 8)            Radial Distance r (fm)5
                                                                                      Page
                   Nucleus: Stability vs. N/Z Ratio
                                                              Last stable element
 • 3000 known nuclei, but only
                                                                  Z = 83 (Bi)
   266 stable ones!
    –Z > 83 elements not stable!                          Line of Stability




                                      Neutron Number N
 • Tendency for N  Z,                                   100

   but N > Z for larger Z.
   (due to proton repulsion)
                                                                                N=Z
 • Unusual stability for
                                                         50
   “magic numbers.”
   Z, N = 2, 8, 20, 28, 50, 82, 126
   (analogous to electronic shells)

                                                                        50          100

Phys 320 - Baski               Nuclear Physics (Topic 8)                         Z
                                                                   Proton Number Page 6
                   Nucleus: Binding Energy B
• Nuclear mass is slightly less than mass of constituent protons and
  neutrons due to nuclear binding energy B.
                   Parts             Whole
  Bnuclear = [ Z mHc2 + N mnc2 ] – [ MAc2 ]
                  where mH = 1.007825amu and mn = 1.008665 amu




                                   Binding Energy / Nucleon ( MeV)
• Binding energy per nucleon
  peaks at A = 56
  (~8 MeV/nucleon) and                                               Peaks at Fe
  slowly decreases.                                                   (A = 56)
                                                                                    Fission
• Energy is released when a                                                        (A ~ 200)
  heavy nucleus (A~200)
  fissions into lighter nuclei
  near A~60.
Phys 320 - Baski                                      Nucleon
                                 Nuclear Physics (Topic 8)                 Number A Page 7
                   Radioactivity: Historical Overview
• 1896: Becquerel accidentally discovered that uranyl crystals emitted
  invisible radiation onto a photographic plate.
• 1898: Marie and Pierre Curie discovered polonium (Z=84) and radium
  (Z = 88), two new radioactive elements.
• 1903: Becquerel and the Curie’s received the Nobel prize in physics
  for radioactive studies.
• 1911: Marie Curie received a 2nd Nobel prize (in chemistry) for
  discovery of polonium and radium.
• 1938: Hahn (1944 Nobel prize) and Strassmann discovered nuclear
  fission - Lisa Meitner played a key role!
• 1938: Enrico Fermi received the Nobel prize in physics for producing
  new radioactive elements via neutron irradiation, and work with
  nuclear reactions.

Phys 320 - Baski               Nuclear Physics (Topic 8)        Page 8
                        Radioactivity: Why?
• Number of protons & neutrons
  in nucleus is limited.                                    Neutron Dripline

    –Limits marked by driplines
      (outside dripline, nucleus                            Line of Stability




                                        Neutron Number N
      spontaneously emits proton or                        100
      neutron).

• Nuclei decay to stable isotopes
  (Z  83) via radiation.
                                                           50
• Initial mass of a radioactive                                          Proton Dripline
  nucleus is greater than its final
  mass plus any decay product
  masses. (E = mc2)
                                                                        50          100

Phys 320 - Baski                 Nuclear Physics (Topic 8)       Proton Number ZPage 9
                   Radioactivity: Relevant Equations
• Radioactivity is the decay of nuclei to more stable configurations via
  emission of “radiation” (a or b particles, g rays, etc.).
• Decay rate dN/dt is proportional to the number of nuclei N, leading to
  a 1st order differential equation with an exponential solution.
           dN
               l N                           N  N 0 e  lt
           dt
        N          t               dN
           dN                   R        N 0 l e  lt  R0 e  lt
         N  l  dt
        No         0
                                    dt
            N                            ln 2
                                   t1/ 2         t ln 2
        ln       l t                               l
            No 
• where l = decay constant
  t = 1/l = lifetime (or 37% original), t1/2 = half-life (50% original)
Phys 320 - Baski               Nuclear Physics (Topic 8)          Page 10
          Radioactivity: Graphical Representation

• Quick formula:
   –(rate %) (half-life in yrs) = 70

• Where is the 70 from?

• If an animal species is dying at a
  10% annual rate, how long until
  the population is halved?

• If you have a 5% return on your
  money, how long until it is
  doubled?

• If you double your money in 7
  years, what is the growth rate?
Phys 320 - Baski                Nuclear Physics (Topic 8)   Page 11
                   Radioactivity: Overview of Units

• Activity: Becquerel (Bq) = 1 decay / s
            1 curie (Ci) = 3.7×1010 decays / s (or Bq)
            (disintegration rate of 1g of radium)

• Ion Dose: Ionizing behavior of radiation is most damaging to us!
            Roentgen = 2.6×10–4 C/ kgair (or 0.0084 j/kg)
• Energy Dose: rad = 0.01 j/kg
      – Energy Dose for Human Health Considerations:
               rem = # rads × quality factor (a = 10 and b,g = 1)

• Dosages: 0.5 rem / yr = natural background
           5 rem / yr = limit for nuclear power plant workers
           500 rem = 50% die within a month
           750 rem = fatal dose (5000 rem = die within 1 week)
Phys 320 - Baski               Nuclear Physics (Topic 8)            Page 12
              Radioactivity: Half-life/Rate Problem

   The counting rate R from a radioactive source is 1000 s–1 at time
   t = 0, and 250 s–1 at time t = 5 s. Find the half-life t1/2 and the rate R
   at t = 12 s.


Solving for τ in the decay equation R  Ro exp  t t  gives:
        t        5 s
τ                       3.61 s and t1/ 2  τ ln 2  (3.61 s)(0.693)  2.5 s
       Ro      1000 
   ln      ln  250 
       R            
R  Ro exp  t t   (1000 s 1 ) exp  12 s 3.61 s   36 s 1




Phys 320 - Baski                   Nuclear Physics (Topic 8)            Page 13
                   Radiation Processes: a, b, g

Type of Radiation                       Charge/Mass         Penetration
alpha a = He nucleus (2p + 2n)          +2q/4mp             sheet of paper
beta b  electron or positron           –q/me or +q/me      few mm metal
gamma g = high-energy photon            no charge           several cm lead

                            ×     ×     ×      ×
                            ×     ×     ×      ×        a
                            ×     ×     ×      ×        g
                         e– ×     ×     ×      ×
                            ×     ×     ×      ×
                                  B field
Phys 320 - Baski                Nuclear Physics (Topic 8)             Page 14
               Radiation Processes: Alpha Decay
               Before                                  After              a
                         226                                   222
                         88    Ra                              86    Rn
                         Parent                                Daughter
• Parent nucleus decays to daughter nucleus plus an alpha particle.
• Disintegration energy Q appears as kinetic energy.
  (= negative binding energy)
      – Lighter a particle carries away most of the kinetic energy.
      – Why? Conservation of momentum!
                                          A 4
                                A
                                Z   X    Z 2   D     4
                                                        2   He
                   Q   M  Z X   M  Z 4 D   M  2 He  c 2
                       
                             A           A
                                           2
                                                        4
                                                              
Phys 320 - Baski                              = 4.002603amu
                                  where mHePhysics (Topic 8)
                                      Nuclear                                 Page 15
     Radiation Processes: b– Decay (e– Emission)
• Parent nucleus decays to daughter nucleus plus electron and anti-
  neutrino.
   – Anti-neutrino is 3rd particle that explains range of electron kinetic
     energies.
• If atom (Z) has greater mass than its right neighbor (Z+1), then b–
  decay is possible.
• Free neutron can decay into a proton.
   – t1/2 = 10.8 min, Q = 939.57 – (938.28 + 0.511) = 0.78 MeV

                         A
                         Z   X       A
                                    Z 1   D  e  v
            Q ( MeV )   Mass  Z X   Mass  Z A1 D   c 2
                        
                                 A
                                                        
                   *electron mass included in daughter nucleus
Phys 320 - Baski                  Nuclear Physics (Topic 8)       Page 16
        Radiation : b– Decay for Carbon Dating
•    b-decay of 14C used to date organic samples.
     – 14C  14N + e– + ne

• When organisms are alive, cosmic rays create
  14C in atmosphere to give constant 14C/12C

  ratio in CO2 gas.
   – 14C / 12C = 1.2×10–12 in living organism

• When organisms die, 14C is no longer
  absorbed and 14C/12C ratio decreases with
  time.
   – Half-life t1/2 of 14C = 5730 yr.

• Measure age of material by finding 14C
  activity per unit mass.
   – Effective for 1,000 to 25,000 years ago.
Phys 320 - Baski               Nuclear Physics (Topic 8)   Page 17
Radiation Processes: b+ Decay (Positron Emission)
• Parent nucleus decays to daughter nucleus plus positron and neutrino.

• Free proton cannot decay into a neutron via positron emission.
   – Contrasts free neutron decay into a proton.

• Bound proton inside nucleus can sometimes emit a positron due to
  nuclear binding energy effects.
   – Only natural positron emitter is 40K.


                          A
                          Z   X       A
                                     Z 1   D  e  v
                       Mass  Z X   Mass  Z A1 D   2me  c 2
          Q ( MeV )          A
                                                            
                      *explicitly add electron/positron masses

Phys 320 - Baski                 Nuclear Physics (Topic 8)       Page 18
            Radiation Processes: Electron Capture

• Parent nucleus captures one of its own orbital electrons and converts a
  nuclear proton to a neutron.

• If atom (Z) has greater mass than its left neighbor (Z–1), then electron
  capture is possible.
   – Note: If mass difference between atom (Z) and neighboring atom
      (Z–1) is greater than 2me, then positron decay is also possible.

                          A
                          Z   X  e           A
                                              Z 1   Dv
                          Mass  Z X   Mass  Z A1 D  c 2
             Q ( MeV )          A
                                                        
                       *added electrons on both sides cancel


Phys 320 - Baski                   Nuclear Physics (Topic 8)     Page 19
             Radiation Processes: Gamma Decay

• In gamma decay, an excited-state
  nucleus decays to a lower energy
  state via photon emission.

• Such nuclear transitions are
  analogous to atomic transitions, but
  with higher energy photons.
  l = 1240 eV nm / Mev = 10–3 nm.

•   g-ray emission usually follows beta
    decay or alpha decay (see figure).

• Mean lifetimes are very short.
  t = hbar / DE = 10–10 s

Phys 320 - Baski              Nuclear Physics (Topic 8)   Page 20
     Radiation Processes: Decay Energy Problem
        80Br can undergo all three types of b decay. In each case,
        (a) write down the decay equation and (b) find the decay energy Q.
        b– Decay Process: 80Br  80Kr + e– + ne
         Q(b–) = M( 80Br)c2 – M( 80Kr)c2
                = 79.918528 uc2 – 79.916377 uc2
         Q(b–) = (0.002151 uc2) (931.5 MeV/uc2) = 2.00 MeV

        b+ Decay Process: 80Br  80Se + e+ + ne
         Q(b+) = M( 80Br)c2 – M( 80Se)c2 – 2mec2
               = 79.918528 uc2 – 79.916519 uc2 – 2(5.4858×10–4)uc2
         Q(b+) = (0.00091184 uc2) (931.5 MeV/uc2) = 0.85 MeV

        e– capture Decay Process: 80Br + e–  80Se + ne
         Q(ec) = M( 80Br)c2 – M( 80Se)c2
               = 79.918528 uc2 – 79.916519 uc2
         Q(ec) = (0.002009 uc2) (931.5 MeV/uc2) = 1.87 MeV
Phys 320 - Baski                 Nuclear Physics (Topic 8)           Page 21
        Radiation Processes: Natural Radioactivity

• Three series of naturally occurring radioactive nuclei.
   – Start with radioactive isotope (U, Th) and end with isotope of Pb.
• Fourth series starts with an element not found in nature (237Np).
• A few other naturally occurring radioactive isotopes occur (14C, 40K).




Phys 320 - Baski              Nuclear Physics (Topic 8)          Page 22
                                              Fusion and Fission: Why?
•Plot Mass Difference DM (= M– Zmp – Nmn) vs. Nucleon Number A.
 –Equals “Inverse” of graph for Binding Energy vs. A.
•Elements with high DM have unstable nuclei.
 –Decay via fusion (low A) or fission (high A) to form more stable nuclei.
 –Total mass decreases and energy is released!
                   DMass / nucleon (MeV/c2)




                                                                                          Why??
                                                                               Fission
                                               Fusion
                                                                              (A ~ 200)
                                                                                          E = mc2




                                                        Nucleon Number A
Phys 320 - Baski                                          Nuclear Physics (Topic 8)           Page 23
                             Fission: Process
• Neutron collides with a 235U nucleus to form an excited state that
  decays into two smaller nuclei (plus neutrons) plus ENERGY!
• Example:         235U   +n    92Kr   + 142Ba + 2n + 180 MeV
      – (238U does not work!)




                                                                 235U  will not
                                                                fission without
                                                                being “kicked”
                                                                  by neutron.




Phys 320 - Baski                    Nuclear Physics (Topic 8)                Page 24
                   Fission: Chain Reaction
• Use neutrons from fission process to initiate other fissions!
• 1942: Fermi achieved first self-sustaining chain reaction.


• For nuclear bomb, need
  more than one neutron
  from first fission event
  causing a second event.
• For nuclear power plant,
  need less than one
  neutron causing a
  second event.



Phys 320 - Baski              Nuclear Physics (Topic 8)           Page 25

								
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