Nuclear Transmutations: (induced radioactivity):

Using Charged Particles:
 Nuclear transmutations occur by collisions between
        nuclei.
 For example, using high velocity a-particles,
         ¹⁴₇N   + ⁴₂a -----> ¹⁷₈O + ¹₁p
1919 Ernest Rutherford did this experiment!

 To overcome electrostatic forces, charged particles need
        to be accelerated before they react.
 A cyclotron consists of D-shaped electrodes (dees) with a
        large, circular magnet above and below the chamber.
 Particles enter the vacuum chamber and are accelerated by
        making the dees alternatively positive and negative.
 The magnets above and below the dees keep the particles
        moving in a circular path.
 When the particles are moving at sufficient velocity, they
        are allowed to escape the cyclotron and strike the
        target.
 The circumference of the ring at the Fermi National
        Accelerator Laboratory in Chicago is 6.3 km.
 

Synthesis of Transuranium Elements:

           ²³⁸₉₂U + ¹₀n -----> ²³⁹₉₂U

    This is followed by decay: ²³⁹₉₂U   ----->  ²³⁹₉₃Np  + ⁰_-1e

                                                                    ²³⁹₉₃Np    -----> ²³⁹₉₄Pu   + ⁰_-1e

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

           ²³⁹₉₄Pu +   2 ¹₀n -----> ²⁴¹₉₄Pu

    This is followed by decay: ²⁴¹₉₄Pu   ----->  ²⁴¹₉₅Am  + ⁰_-1e

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 

            ²³⁹₉₄Pu +   ⁴₂He -----> ²⁴²₉₆Cm + ¹₀n
 
 

            ²⁴²₉₆Cm +    ⁴₂He -----> ²⁴⁵₉₈Cf + ¹₀n
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Rates of Radioactive Decay:
 Radioactive decay is a first-order process.
 Using the integrated rate law for a first order process,
        if the activity of a sample at time t is N_t and the activity at
        time 0 is N_o, then

 Sr-90 has a half life of 28.8 yr.  If 10.0 g of sample are present
     at t = 0, then 5.00 g is present after 28.8 years, 2.50 g
     after 57.6 years, etc.  Sr-90 decays as follows

  Since we know t_1/2 = 0.693/k, we can find k.  Now we can
    find how many g are left after 133.4 yrs, etc.
 

Each isotope has a characteristic half-life.
     Half-lives are not affected by temperature, pressure,
        or chemical composition.
 Natural radioisotopes tend to have longer half-lives than
        synthetic (or man-made) radioisotopes.
 Half-lives can range from fractions of a second to billions
    of years.
 Naturally occurring radioisotopes can be used to determine
        how old a sample is.
 This process is called radioactive dating.

        t_1/2 = 5720 yr = 0.693/k

Plants take in CO₂ in the ratio ¹²₆C/¹⁴₆C = 10¹² atoms/1 atom.
Animals ear the plants.  When the animal dies, no new ¹⁴₆C
coming into the system.  However, ¹⁴₆C decaying to ¹⁴₇N
continues and therefore ¹⁴₆C/¹²₆C  drops.  If we find the ratio
is 0.371/1, how old is the fossil?
    k = 0.693/5720 yr = 1.21 x 10^-4 yr^-1

And, ln(A/A_o) = -kt;     ln(0.371/1) = (-1.21x 10^-4 yr^-1)t
            -0.9916/-1.21 x 10^-4 yr^-1 = t
                8195 years = t
 

_{Detection of Radioactivity:
 Matter is ionized by radiation.
 A Geiger counter determines the amount of ionization by
       detecting an electric current.
A thin window is penetrated by the radiation and causes
        the ionization of Ar gas.
 The ionized gas carries a charge and so current is produced.
 The current pulse generated when the radiation enters is
    amplified and counted.}

_{Energy Changes in Nuclear Reactions:
Einstein showed that energy and mass are related:}

                            _{E = mc}² _{;         DE = Dmc}²
_{since c is the speed of light (3 x 10}⁸ _m.s^-1_{), c}²_{is very large;
thus... small mass changes lead to large energy changes.
Nuclear reactions involve much larger energies than chemical
reactions.}

_Consider         ²³⁸₉₂U _----> ²³⁴₉₀Th   ₊  ⁴₂He

for 1 mole of U-238, the mass changes are as follows.

_{Nuclear Binding Energies:
 The mass of a nucleus is less than the mass of their nucleons.
 Mass defect is the difference in mass between the nucleus
    and the masses of nucleons.
 Binding energy is the energy required to separate a nucleus
    into its nucleons.
 Since E = mc}²_{, the binding energy is related to the mass
    defect.
 The larger the binding energy, the more likely a nucleus
    will decompose.
 Average binding energy per nucleon increases to a maximum
    at mass number 50 - 60, and decreases afterwards.}
 

_{Fusion: (bringing together nuclei) is exothermic for low
        mass numbers}

_{and fission (splitting of nuclei) is exothermic for high
        mass numbers.}

_{Nuclear Fission:
 The splitting of heavy nuclei is exothermic for large mass
        numbers.
 Consider a neutron bombarding a} ²³⁵_{U nucleus:
 the neutron must move slowly because it is absorbed by the
    U nucleus; the heavy} ²³⁵_{U nucleus can split into many
    different daughter nuclei, e.g.}
 
 

 _{This reaction releases 3.5 x 10}^-11 _{J per} ²³⁵_{U nucleus.
 For every} ²³⁵_{U fission, 2.4 neutrons are produced.
 Each neutron produced can cause the fission of another}
    ²³⁵_{U nucleus.
 Both the energy and the number of fissions increase rapidly.
 Eventually, a chain reaction forms which, without control,
    gives an explosion.
Why? Because each neutron can cause another fission.
 A minimum mass of fissionable material is required for a
    chain reaction (or neutrons escape before they cause
    another fission).
 When enough material is present for a chain reaction, we
    have critical mass.}

_{Below critical mass = subcritical mass, the neutrons escape
    and no chain reaction occurs.
 At critical mass, the chain reaction accelerates.
 Anything over critical mass is called supercritical mass.
 Critical mass for} ²³⁵_{U is about 1 kg. (This is not a large
    volume, because U is dense!)}

_{Nuclear bombs:
Two subcritical wedges of} ²³⁵_{U are separated by a gun
    barrel.
Conventional explosives are used to bring the two subcritical
    masses together to form one supercritical mass.
The supercritical mass leads to uncontrolled nuclear fission
    and a violent explosion.}

_{Nuclear Reactors:
 Use fission as a power source.
 Use a subcritical mass of} ²³⁵_{U (enriched} ²³⁸_{U with about
        3%} ²³⁵_{U).
 Enriched} ²³⁵UO_{2 pellets are encased in Zr or stainless
        steel rods.
 Control rods are composed of Cd or B, which absorb
        neutrons.
 Moderators are inserted to slow down the neutrons.
 Heat produced in the reactor core is removed by a cooling
        fluid to a steam generator.
 The steam is used to drive an electric generator.}

_{Nuclear Fusion:
Occurs in the sun and H-bombs.  Joining together of small
        nuclei to form larger ones, e.g.,}

Fusion products are NOT radioactive...less pollution,
    reactants are plentiful (get from sea water).  Problem...
    high temperatures needed...Thermonuclear reactions.
    No substance known can stand the temperatures, so use a
    magnetic container.  In progress...(TOKAMAK at Princeton)
    hopefully in our lifetime it will happen....and lead to an
    almost endless supply of energy!

Biological Effects of Radiation:
 The penetrating power of radiation is a function of mass.
 Therefore, gamma-radiation (zero mass) penetrates much
    further than beta radiation which penetrates much further
    than alpha radiation.
 Radiation absorbed by tissue causes excitation (non-ionizing
    radiation) or ionization (ionizing radiation).
 Ionizing radiation is much more harmful than non-ionizing
    radiation.
 Most ionizing radiation interacts with water in tissues to
    form H₂O⁺.
 The H₂O⁺ ions react with water to produce H₃O⁺ and OH^.
 OH^. has one unpaired electron.  It is called the
    hydroxy radical.
 Free radicals generally undergo chain reactions.

Radiation Doses:
 The SI unit for radiation is the becquerel (Bq).
 1 Bq is one disintegration per second.
 The Curie (Ci) is 3.7 x 10¹⁰ disintegrations per second.
    (Rate of decay of 1 g of Ra.)
 Absorbed radiation is measured in the gray
    (1 Gy is the absorption of 1 J of energy per kg of tissue)
    or the radiation absorbed dose (1 rad is the absorption of
    10^-2 J of radiation per kg of tissue).
 Since not all forms of radiation have the same effect, we
    correct for the differences using RBE (relative biological
    effectiveness, about 1 for beta- and gamma-radiation
    and about 10 for alpha radiation).
 rem (roentgen equivalent for man) = rads.RBE
 SI unit for effective dosage is the Sievert
    (1Sv = RBE.1Gy = 100 rem).
 

BACK HOME