(adsbygoogle = window.adsbygoogle || []).push({}); 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]

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# Homework Help: Relativistic Nuclear Reaction.

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