How Do You Calculate the Speed of a Proton and Alpha Particle from a Decaying Lithium Isotope?

[wildrjetta]

I seem to be stuck on this problem. I thought calculating the velocity of the center of mass of the system would get me somewhere, but I remain confused about where to go next. Here is the problem:
The light isotope, 5^Li is unstable and breaks up spontaneously into a proton (hydrogen nucleus) and an alpha particle(helium nucleus). In this process, a total energy of 2.70E-13 J is released, appearing as the kinetic energy of the two reaction products. Determine the speeds of the proton and the alpha particle that arise from the decay of a 5^Li nucleus at rest. (Note: the two masses of the proton and alpha particle are m(proton)=1.67E-27 kg and m(alpha particle) = 4m(proton) = 6.68E-27kg).
The answer may be more simpler than I am realizing...or way more difficult. Any assitance on this problem would be GREATLY appreciated. THANKS!

 

[geometer]

I seem to be stuck on this problem. I thought calculating the velocity of the center of mass of the system would get me somewhere, but I remain confused about where to go next. Here is the problem:
The light isotope, 5^Li is unstable and breaks up spontaneously into a proton (hydrogen nucleus) and an alpha particle(helium nucleus). In this process, a total energy of 2.70E-13 J is released, appearing as the kinetic energy of the two reaction products. Determine the speeds of the proton and the alpha particle that arise from the decay of a 5^Li nucleus at rest. (Note: the two masses of the proton and alpha particle are m(proton)=1.67E-27 kg and m(alpha particle) = 4m(proton) = 6.68E-27kg).
The answer may be more simpler than I am realizing...or way more difficult. Any assitance on this problem would be GREATLY appreciated. THANKS!

I think what you're missing is conservation of momentum. The momentum of the system before the decay must be the same as after the decay. I think this, along with the fact that you are given the amount of energy released will allow you to calculate the speeds of the reaction products.