1. The problem statement, all variables and given/known data An alpha particle traveling with a kinetic energy of 5.5 MeV and a rest-mass of 3727.8 MeV/c^2 strikes a gold atom with a rest-mass of 183,476 MeV/c^2. -The gold atom is initially at rest -The alpha particle deflects perpendicular to the horizontal in the after state 2. Relevant equations Conservation of Energy: Ebefore=Eafter Conservation of momentum: Pbefore=Pafter E^2=P^2c^2+(mc^2)^2 3. The attempt at a solution Total Energy Before Collison: Ebefore=E(α)+E(Au)=3727.8MeV+5.5MeV+183476MeV=187,209MeV Momentum before (in x-direction): E^2=p^2c^2+(mc^2)^2 ==> (3727.8+5.5)^2=P^2c^2+(3727.8)^2 ==> P=202.6 MeV/c AFTER STATE: Conservation of momentum: in x: P(Au)cosθ=202.6MeV/c (1) in y: P(Au)sinθ-P(α)=0 (2) Conservation of Energy: E(Au)=√(P(Au)^2+183476^2) E(α)=√(P(α)^2+3727.8^2) ==> √(P(Au)^2+183476^2)+√(P(α)^2+3727.8^2)=187,209 MeV (3) Solve the system of equations to find θ, P(Au), and P(α): Solve (3) for P(α): P(α)=√(1.36998E9-P(Au)^2) Plug back into Eq. (2): P(Au)sinθ=√(1.36998E9-P(Au)^2) Solve (1) for θ: θ=arccos(202.6/P(Au)) Plug into (2) and solve for Au: P(Au)sin[arccos(202.6/P(Au))]=√(1.36998E9-P(Au)^2) ==> P(Au)=26,172.7 MeV/c Solve for θ: 26,172.7cosθ=202.6 ==> θ=89.56° Solve for P(α): 26,172.7sin(89.56°)=P(α) ==> P(α)=26,171.9 MeV/c However, when I plug these numbers back into equation (3) the solution doesn't come out right. I have been looking over this for hours and can't figure out where my error might be. Thanks!