Mass defect and binding energy

Key ideas

• Einstein's mass–energy relationship states that mass is a form of energy:

$E = mc^2$

• Each variable, with sub-bullets:
  • $E$ — energy (J)
  • $m$ — mass (kg)
  • $c$ — the speed of light, $3.00\times10^8$ m s⁻¹
• A useful alternative mass unit is the atomic mass unit, $u$, where $1$ u $= 1.66\times10^{-27}$ kg. This is convenient because nuclear masses are usually given in u or in MeV/c² ($1$ u $= 931.5$ MeV/c²).
• The mass of a nucleus is always LESS than the sum of the masses of its separate, unbound protons and neutrons. This missing mass is the mass defect, $\Delta m$:

$\Delta m = (\text{sum of masses of separate nucleons}) - (\text{mass of the nucleus})$

• The mass defect exists because energy must be released to assemble the nucleus from separate nucleons (the strong nuclear force pulls them together, doing work) — and by $E = mc^2$, that released energy corresponds to a loss of mass.
• The energy equivalent to the mass defect is the binding energy, $E_B$ — the energy that would be needed to completely separate the nucleus back into individual protons and neutrons:

$E_B = \Delta m \, c^2$

• Binding energy per nucleon, $E_B/A$ (where $A$ is the mass/nucleon number), measures how tightly bound, on average, each nucleon is. A higher binding energy per nucleon means a more stable nucleus.

Tips

• Mass defect is always calculated as (separate nucleons) − (actual nucleus), never the other way round — the actual nucleus is always the lighter one. A negative mass defect is a sign of a subtraction done backwards, not a real result.
• Keep at least 4 decimal places when subtracting nuclear masses in u — the mass defect is a small difference between two much larger numbers, so rounding early destroys the answer's accuracy.