Imagine a system made of 4 pieces, each of mass m. Einstein pointed out that the total mass of the system should be Mc2 = ℰ + 4mc2

Here ℰ is the total internal energy of the system, the sum of the kinetic and potential energies of the 4 particles. But for systems in nature, the size of an atomic nucleus or larger, the total internal energy of a bound system is negative. Notice that this means that M is less than 4m! Physicists define the binding energy of a system as B = -ℰ, so that B is the work it would take to disassemble the system completely.    Example: suppose each particle has a mass of 10 MeV/c2, and the mass of the system is measured to be 30 MeV/c2.  What is the binding energy of the system? ℰ = Mc2 - 4mc2 = 30 MeV - 40 MeV = -10 MeV.  It would take 10 MeV of work to pull the system apart.



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