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Homework Help: Relativistic Nuclear Reaction.

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Nucleus A has rest mass [tex]m_A[/tex],collides with nucleus B which has rest mass [tex]m_B[/tex].In the laboratory frame,nucleus A has energy [tex]E>m_Ac^2[/tex] and nucleus B is stationery.After the collision,a nuclear reaction takes place:
    [tex]A+B\rightarrow C+D[/tex]

    where nucleus C has rest mass [tex]m_C[/tex] and nucleus D has rest mass [tex]m_D[/tex].Suppose that [tex]m_A+m_B+Q=m_C+m_D[/tex],where Q>0.Find the minimum value of E required for this reaction to occur.Give answer in terms of [tex]m_A,m_B,Q[/tex]


    2. Relevant equations
    [tex]E^2-P^2c^2=const[/tex]


    3. The attempt at a solution

    [tex](E+m_Bc^2)^2-E^2+m_A^2c^4=(m_C+m_D)^2c^4=(m_A+m_B+\frac{Q}{c^2})^2c^4[/tex]

    [tex]E=\frac{2m_Am_Bc^4+Q^2}{2m_Ac^2}[/tex]
     
  2. jcsd
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