Calculating relativistic mass of neutrons, wrote out my plan please critique

[ronpaulkid]

Homework Statement

I am given an equation, say (239/94)Pu-->(110/53)Fe+(125/41)Nb+4neutrons

I am asked to calculate the relativistic energy so I do that. Q=m(left)-m(right)c^2

I know that m(left)=m(Pu)

I know that m(right)=m(110Fe)+m(125Nb)+4m(neutron)
(i put the answer into MeV for convenience)

so I have Q now. I am now asked to find the mass of the neutrons.
I can't use m=mo/sqrt(1-v^2/c^2) because I am not given the velocity. I have to use E=KE+moc^2

KE=Q/4 (4 neutrons, each gets a quarter of the energy)
mo(rest mass)=4m(neutron) maybe 4(1.008665u)? I am unsure if I use the rest mass of just 1 neutron or 4 neutrons.

so I have Q solved from above. I now solve for m=[(Q/4)+mo(c^2)]/(c^2)

Is this the correct way to find the relativistic mass of the neutrons? My professor said divide Q by 4 because each gets a quarter of the energy. I don't know what to do then with the rest mass. And I don't know if I should multiply the rest mass by 4 to find the total rest mass of the 4 neutrons.

Relevant equations and attempt are above^^
Thanks for your help!

 

[ideasrule]

Q is not the kinetic energy; it's the total energy. The relationship between total energy and relativistic mass is just E=mc^2--which is partially why relativistic mass is sometimes a useful concept--so you just have to divide Q/4 by c^2 to get the answer.