azatkgz
Oct25-07, 07:54 AM
1. The problem statement, all variables and given/known data
Nucleus A has rest mass m_A,collides with nucleus B which has rest mass m_B.In the laboratory frame,nucleus A has energy E>m_Ac^2 and nucleus B is stationery.After the collision,a nuclear reaction takes place:
A+B\rightarrow C+D
where nucleus C has rest mass m_C and nucleus D has rest mass m_D.Suppose that m_A+m_B+Q=m_C+m_D,where Q>0.Find the minimum value of E required for this reaction to occur.Give answer in terms of m_A,m_B,Q
2. Relevant equations
E^2-P^2c^2=const
3. The attempt at a solution
(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
E=\frac{2m_Am_Bc^4+Q^2}{2m_Ac^2}
Nucleus A has rest mass m_A,collides with nucleus B which has rest mass m_B.In the laboratory frame,nucleus A has energy E>m_Ac^2 and nucleus B is stationery.After the collision,a nuclear reaction takes place:
A+B\rightarrow C+D
where nucleus C has rest mass m_C and nucleus D has rest mass m_D.Suppose that m_A+m_B+Q=m_C+m_D,where Q>0.Find the minimum value of E required for this reaction to occur.Give answer in terms of m_A,m_B,Q
2. Relevant equations
E^2-P^2c^2=const
3. The attempt at a solution
(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
E=\frac{2m_Am_Bc^4+Q^2}{2m_Ac^2}