The mass defect Δm is converted into binding energy via E = Δm c^2. What does this imply about the mass of a bound nucleus relative to the sum of its constituent nucleons?

The mass defect Δm is converted into binding energy via E = Δm c^2. What does this imply about the mass of a bound nucleus relative to the sum of its constituent nucleons?

• A. The bound nucleus has more mass than the sum of its parts.
• B. The bound nucleus has less mass than the sum of its parts.
• C. The masses are equal.
• D. The bound nucleus mass is unpredictable.

Answer: (B)

Mass-energy equivalence means that binding energy has a mass counterpart. When nucleons bind to form a nucleus, energy is released equal to the binding energy, and that energy comes from a slight decrease in the total mass. So the mass of the bound nucleus is smaller than the sum of the masses of the individual nucleons if they were free. The difference in mass, the mass defect, multiplied by c^2 gives the binding energy. If you tried to separate the nucleus into free nucleons, you’d have to supply that energy, which corresponds to adding the mass back. In short, binding makes the system lighter overall.

Mass-energy equivalence means that binding energy has a mass counterpart. When nucleons bind to form a nucleus, energy is released equal to the binding energy, and that energy comes from a slight decrease in the total mass. So the mass of the bound nucleus is smaller than the sum of the masses of the individual nucleons if they were free. The difference in mass, the mass defect, multiplied by c^2 gives the binding energy. If you tried to separate the nucleus into free nucleons, you’d have to supply that energy, which corresponds to adding the mass back. In short, binding makes the system lighter overall.