(d) mass defect; binding energy; binding energy per nucleon

The idea

The mass defect of a nucleus is the difference between the total mass of its separate protons and neutrons and the actual mass of the nucleus. This missing mass corresponds to the binding energy, the energy needed to separate the nucleus into its individual nucleons, found from E = Δmc². Binding energy per nucleon is the binding energy divided by the nucleon number A, and it measures how tightly each nucleon is held. For helium-4, the mass defect is about 0.0304 u, giving a binding energy near 28.3 MeV and about 7.1 MeV per nucleon. A larger binding energy per nucleon indicates a more stable nucleus.

What earns the marks

• Define mass defect as the difference between the sum of the masses of separate nucleons and the mass of the nucleus.
• Calculate binding energy from the mass defect using E = Δmc², converting u to kg or using 1 u = 931.5 MeV.
• Define binding energy per nucleon as binding energy divided by nucleon number A.
• Interpret a higher binding energy per nucleon as a more stable nucleus.
• Use consistent units, giving binding energy in J or MeV and binding energy per nucleon in J or MeV per nucleon.

Common mistakes and how to put them right

• Confusing mass defect with the mass of the nucleus.

  Put it right: It is the difference between separate-nucleon mass and nuclear mass.

• Dividing binding energy by the number of protons rather than the nucleon number A; the correction is to divide by the total number of protons and neutrons.

• Forgetting to convert the mass defect from u to kg before using E = Δmc².

  Put it right: Convert or to use the MeV equivalent of 1 u.

Exam tips

• Show the mass-defect subtraction explicitly so the examiner can follow your arithmetic.
• Quote binding energy per nucleon with the unit MeV per nucleon or J per nucleon.
• Compare values across nuclei only when they are expressed in the same unit.