Friday, April 4, 2008

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Chapter 15 - Nuclear Physics

Nuclear physics is the study of the nuclei (center) of atoms and associated energy levels that are similar to those of atomic physics (which deals with electron energy levels), but the forces and energies associated with nuclear reactions are about 1000 times greater!

The Constituents and Structure of Nuclei
    Nuclei consist of protons and neutrons, collectively called nucleons.
    Nuclear mass (nearly same as atomic mass since me << mp):  A = N + Z
       Z = Atomic number
       N = Neutron number
       A = Nuclear (~atomic) mass number
    Isotopes are nuclei with the same atomic number (Z) but different neutron number (N).
    Ponderable:  Why are atoms defined by Z instead of N or E?
     Most atoms are stable when N ~ Z or slightly greater, as can be seen in the diagram for half life of various isotopes.
    Atomic mass unit:  1 u = 1/12 mass of one atom of C-12 (common element in all organic matter)
       Energy (E=mc^2):  1 u = 931.5 MeV/c^2  (which is much greater than atomic energies:  ~ eV)
    Neutrons and protons have masses slightly greater than 1 u, with mn > mp
    Nuclei are held together by the strong nuclear force, which is attractive between all nulceons within range of few fermis (fm).
       Nuclear size:  radius of a nucleus is proportional to the cubed root of the number of nucleons:  r = (1.2 fm)A^1/3
       Note: The atomic diameter of the hydrogen atom (~1 angstrom = 0.1 nm), is about 50 000 times bigger than the nucleus (~2 fm).
          This means that if the nucleus of the hydrogen atom were the size of a baseball, the electron would typically be ~4 km away.
       Note:  It just so happens that 1 fermi (fm) = 10-15 m = 1 femtometer = 1 fm.

Radioactivity - one of three types of nuclear reactions (fission and fusion are the other two)
   Radioactivity from uranium was first discovered by Henri Becquerel, and Marie and Pierre Curie discovered radium.
    Every isotope with atomic number greater than 83 (bismuth) is radioactive, and many isotopes of lighter elements are as well.
    Radioactivity refers to emissions observed when a nucleus decays to a lower energy state or changes its composition.
        Alpha decay - radioactivity with lowest energy.  Alpha particle is He nucleus (2 protons + 2 neutrons).  half-thickness ~ paper sheet
        Beta decay - Emission of an electron (B-) or positron (B+).  Can occur when neutron decays into proton, electron, and antineutrino. half-thickness ~ cm Al
        Gamma decay - Occurs when an excited nucleus drops to a lower energy state and emits a photon (Z and N remain same).  half-thickness ~ cm Pb
    Ponderable:  Why is E(alpha) < E(beta) < E(gamma)?
    Activity of a radioactive sample is the number of decays per second:  1 becquerel = 1 Bq = 1 decay/s
        1 curie (Ci) = 3.7e10 decays/s  (~activity of 1 g of radium, which is what Marie Curie studied)
    Example:  What are the daughter elements for: alpha decay of U-238,  beta decay of Th-234, and beta decay of C-14?
    What are some practical uses of radioactive isotopes?

Half-life and Radioactive Dating
    Decay constant (lambda):  N = Noexp(-lambda*t)
    Half life:  T1/2 = ln2/lamda
    Decay rate or activity:  R = dN/dt = lambda*N
    Carbon-14 dating can be used to date organic materials up to ~15,000 y  (Why?)
    t = 1/lamda*ln(Ro/R)   where Ro = 0.231 Bq, lambda = 1.21e-4 /y, T1/2 of C-14 is 5730 y

Nuclear Binding Energy - energy needed to separate a nucleus into its component nucleons

Nuclear Fission is the process where a large nucleus captures a neutron and then divides into two smaller "daughter" nuclei.  When this happens, two or three neutrons are typically released, and this can result in other fission reactions (chain reaction).  This process is used in nuclear power plants and nuclear bombs.

Nuclear Fusion occurs when two small nuclei merge to form a larger nucleus.  Energy is needed to overcome the Coulomb repulsion of the two positive nuclei, but the final product results in a net release of energy (an exothermic reaction).  This is the process that fuels our Sun.

Practical Applications of Nuclear Physics - Nuclear radiation can be useful, but it can have harmful effects as well. 
Radiation dosage can be measured in different ways:
    roentgen:  1 R = 2.58e-4 C/kg  (ionization charge produced by 200-keV X-rays in 1 kg of dry air at STP)
    radiation absorbed dose (rad):  1 rad = 0.01 J/kg  (energy absorbed by any type of radiation)
    Relative Biological Effectiveness (RBE) = (dose of 200-keV X-rays)/(does of particular radiation)
    roentgen equivalent in man (rem) = (dose in rad)*RBE
        A dose of 1 rem causes same biological damage, regardless of radiation type.
    Four sensible ways to reduce radiation exposure:
    1) Use smallest amount of radioactive material necessary
    2) Use appropriate shielding to block radiation
    3) Increase distance from radioactive source (exposure decreases as inverse square of distance)
    4) Minimize exposure time (more damage results from long-term exposure)

Elementary Particles - fundamental building blocks of matter
    There are four fundamental forces in nature.  From strongest to weakest they are:
    1) strong nuclear force - relative strength: 1, range of ~ 1 fm
    2) electromagnetic force - relative strength: 10-2, range: infinite (proportional to 1/r2)
    3) weak nuclear force - relative strength: 10-6, range:  ~0.001 fm
    4) gravitational force - relative strength: 10-43, range: infinite (proportional to 1/r2)
 
    Leptons are elementary particles that experience the weak nuclear force but not the strong nuclear force.
    Hadrons are composite particles that experience both the weak and strong nuclear force.
    Quarks are elementary particles that combine to form hadrons.  Mesons are formed from quark-antiquark pairs; baryons are formed from combinations of three quarks.