SCI 270: On Nuclear Technology Practice Problems  
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4. Radioactivity and Transmutation of Nuclides

  1. The unit curie (= 3.700x1010 Bq (= decay/s)) is defined to be the decay rate of 1.00 g of radium (226Ra), in honour of the Curies who worked on the radium isotope 226Ra. Radium decays according to the equation: 226Ra ® 222Rn + 4He (The a particle) Each decay releases 4.8 MeV of energy as the kinetic energy of the alpha particle. Recall the Avogadro's number NA, and work out the following:

    Number of 226Ra atoms in 1.00 gram of 226Ra NA/226 = 2.66 e21
    The declay constant l Use A = l N; 1.39 e-11 s-1
    The half-life t1/2 of 226Ra 4.99e10 s = 1581 y
    The amount of radium that will give a radioactivity of 1 microcurie 1.00e-6 g
    many ways to evaluate
    The amount of energy released per day by 1.0 curie of 226Ra 2458 J
    The amount of helium in moles produced by 1.00 curie of 226Ra per day 5.3 e-9 mol
    The number of 226Ra atoms remains after one day from 1.00 curie 2.66 e21
    no significant change
    The decay rate at the start of the second day of 1.00 curie of radium 3.70 e10 Bq
    No significant chagne
    The number of 226Ra atoms remains after one year from 1.00 curie __2.66 e21__
    no significant change
    Radium, 226Ra and its decay decendants 222Rn, 218Po ... emit only a, b and g rays. How many a particles and how many b particles are produced when 226Ra has become a stable 206Pb nuclide? 5 a

    4 b

  2. Tritium, 3T, and deuterium, 2D, are isotopes of hydrogen. Nature hydrogen contains 0.015% stable deuterium, but only a trace of tritium, which is radioactive, 3T ® 3He + b (half-life = 12.26 y) A tritium-contaminated water from a nuclear reactor has a radioactivity of 0.10 Bq per gram of water. Evaluate the following:

    The decay constant of tritium 0.0565 y-1 = 1.55 e-4 d-1
    The number of T nuclei in one gram of water 5.58 e7 nuclei or atoms
    Radioactivity in 1.0 L of water, density = 1 g/mL 100 Bq
    The mass of T atoms in one gram of water 2.78 e-16 g
    The number of all hydrogen atoms in one gram of water 2*NA/18 = 6.69e22 H atoms
    Compare to 5.58 e7 T atoms

  3. Describe the following radioactive decay processes: alpha decay, beta decay, gamma emission, proton Decay, double beta decay, and beta delayed emission