Special Relativity: Photoproduction of Mesons?

[mintsnapple]

Homework Statement

12-16 K + mesons can be photoproduced by the reaction γ + p → K⁺ + Λ where the initial proton is at rest in the lab. From the conservation laws, discover if it is possible for either the K⁺ or the Λ to be at rest in the lab, and for what photon energy (in terms of the particle masses) this could happen.

Homework Equations

E^2 = p^2c^2 + m^2c^4
p = mv
E = mc^2

The Attempt at a Solution

I'm really stuck on this problem. It's probably more of an algebraic answer, because I believe I'm supposed to somehow get the two equations of energy and momentum conservation to have like terms and then combine them somehow, but I'm at a loss as to what to do. Any help is appreciated.

 

[Stealth95]

I think you already have the equations.
Conservation of Momentum: \displaystyle{p_\gamma =p_\Lambda \Rightarrow E_\gamma =p_\Lambda c\Rightarrow E_\gamma ^2=E_\Lambda ^2-m_\Lambda ^2c^4}
If you combine this with the conservation of energy you have two equations and two uknowns, \displaystyle{E_\gamma } and \displaystyle{E_\Lambda}.

Another way to solve such problems without algebraic difficulties is by using the momentum 4-vector (also known as 4-momentum). In this problem the calculations are not so tough, because there are only two momenta, so the 4-momentum solution is not much different. But I think it's worth reading about this method, because sometimes it's really helpful.