Answer in units of y. 012 10.0 points A particle is a bound state of three funda

Question

Answer in units of y. 012 10.0 points A particle is a bound state of three fundamen- tal point particles, each of which has a mass of 500 Mev. The total energy of the system. de that is, the sum of the kinetic and potential energies of all three particles, is -800 MeV. Remember that a bound system always has negative total energy. The usual nomencla- ture is that the "binding energy is 800 MeV, meaning that the work to take the system cise apart and leave the three constituents at rest a great distance apart is 800 MeV.] Given these facts and background, what would be The the observed total mass of the composite par- tion ticle? 1.300 MeV. the s if pla 2.700 MeV on ea

Explanation / Answer

According to the theory of special relativity, the rest energy of a particle is related to its mass by the well-known relation E = mc2. Hence binding energies are in principle measurable by determining the difference between the mass M of the bound state, and the sum of the masses mi of its free constituents: E = mic2 Mc2

800 = m1c2 + m2c2 + m3c2 - Mc2 = {(500+500+500) – M}*(3*10^8)2 = (1500-M)*(3*10^8)2

800/c2 = (1500-M)

Total mass of the composite particle, M = 1500 - 800/c2 = (1500c2 – 800)/c2 = 1500MeV

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