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Nuclear Reactions, Can anyone check my solution?

  1. Mar 30, 2013 #1
    1. The problem statement, all variables and given/known data
    A nuclear power station reactor using 235 U (Uranium) as fuel has an output of 107 W. How much uranium is consumed per hour if the overall efficiency is 10%. The 235 U decays by the following reaction:

    n + 235 U → 144 Nd + 89 Y + (3)(n) + (7)(e-)


    2. Relevant equations
    P = E / time
    E = mc2


    3. The attempt at a solution
    I started out by finding the change in mass in the reactants and products:
    mass of reactants = 236.05258 amu
    mass of products = 235.845131 amu
    Δ mass = 0.207449 amu

    I then used E = mc2 to find the energy released from one uranium nuclei:
    E = (0.207449amu)(1.66054 x 10^-27 kg)(2.9979 x 10^8 m/s)^2
    E = 3.096 x 10^-11 J/atom

    I then found the efficiency of the reactor:
    efficiency = output/input x 100%
    0.10 = output / input
    input = 10^8 Joules

    P = E/t
    E = (10^8 W)(3600s)
    E = 3.60 x 10^11 J

    I now know how much energy is inputed into the generator each hour and I know how much energy is released per atom of Uranium. I can find the total number of atoms that undergo this reaction in one hour:

    3.60 x 10^11 J / 3.096 x 10^-11 J/atom = 1.16x10^22 atoms

    I used avogadro's number to find the number of moles

    (1.16x10^22 atoms) * (1 mol / 6.022x10^23 atoms) = 0.0193 moles

    I use n = m / M to find the mass in grams:

    0.0193 mol * 235.043915 amu = 4.54g

    It would be great if anyone could check my steps in my solution. The answer is 4.54 g but I just want to make sure my process is correct and maybe if there is another way to get to the same answer. Thanks, I appreciate it!
     
    Last edited: Mar 30, 2013
  2. jcsd
  3. Mar 31, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I would directly divide the released energy per reaction by the mass of an uranium atom to get J/kg, but your method is fine, too.
     
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