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Kinetic Energy of the Products of Nuclear Reaction?

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Calculate the total kinetic energy of the products of the reaction d+C-13 --> N-14 + n if the incoming deuteron (d) has 36.3 MeV.


    2. Relevant equations
    Q=(Parent Mass - Daughter Mass - Decay Particle Mass)*c^2
    1u = 931.5 MeV
    C-13 = 13.00335u
    N-14 = 14.003241u
    Neutron = 1.008664u
    deuteron = 2.014101
    KE before = KE after
    3. The attempt at a solution
    Alright I'm kinda lost on this problem though I feel it's easy. Since KE before=KE after I took the energy of the deuteron (36.3 MeV) and added that to the resting energy of C-13, which I got to be 13.00335*931.5= 12112.6MeV
    Now I thought that would be the answer, but it wasn't, so I tried subtracting the mass of the products from the mass of the reactants to get the Q value. So I took (2.014101+13.00335)-(14.003241+1.008664)=.005546u*931.5MeV/c^2= 5.1661MeV,

    ...but that wasn't right either so I'm confused as to what I'm actually trying to find. If someone could tell me what I'm solving for and what equation to use? Or if I have a wrong conversion factor or isotope mass? Thanks!
     
  2. jcsd
  3. Dec 8, 2011 #2
    No, total energy before equals total energy after (not just kinetic). Momentum before equals momentum after, however.
     
  4. Dec 8, 2011 #3
    I understand but can I find momentum for C-13 if there is no velocity? The only thing I can think of is to do KE=p^2/2m, but that doesn't give me the right answer either. I ended up getting 10261.7 MeV.
     
  5. Dec 8, 2011 #4
    You shouldn't need momentum since you have the rest mass energies of the reactants, the KE of the deuteron (the others are assumed to be at rest from the problem description), and the rest masses of the products.
     
  6. Dec 8, 2011 #5
    Ok, so I took;

    36.3+(13.00335*931.5) = 12148.9 MeV and
    (14.003241*931.5)+(1.008664*931.5)= 13983.6 and
    12148.9-133983= 1834.67 (wrong answer)

    so I tired taking out the neutron rest mass because I assume it's moving afterwards...
    through the same process I got 895.098 (wrong answer).

    Am I going through the correct process to get the resting KE?
     
  7. Dec 8, 2011 #6
    Ahh, I just got the right answer, I took
    (13.00335+2.0141)-(14.003241+1.008664) = .005546 and
    .00546* 931.5 = 5.1661 and
    5.1661+36.3 = 41.46, which was the correct answer.

    So for a problem like this I just take the Q value, then add that to the incoming KE value?
     
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