Worked example 1
Using m(H-1) = 1.007825 u, m(n) = 1.008665 u and m(⁴He) = 4.002603 u, find the mass defect of helium-4.
Try it first: Add up two hydrogen atoms and two neutrons before subtracting.
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Nuclear ChemistryBinding EnergyContent level: Core 18 min
Mass Defect and Nuclear Binding Energy
What you'll be able to do: Calculate a mass defect, convert it to binding energy with E = mc², and use binding energy per nucleon to compare nuclear stability.
Best after: Nuclear Fission and Fusion
Introduction
Weigh a helium nucleus and it comes out lighter than its parts. That missing mass is not an error: it is the energy that holds the nucleus together, and converting between the two is the whole of this topic.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Define mass defect and calculate it from nucleon and nuclide masses
- Convert a mass defect to binding energy using 1 u = 931.5 MeV
- Calculate binding energy per nucleon and use it to rank stability
- Interpret the binding-energy-per-nucleon curve and locate its peak
- Connect binding energy to why fission and fusion release energy
Lesson
The missing mass
Add up the masses of 2 protons and 2 neutrons and you get 4.032980 u. An actual ⁴He nucleus has a mass of 4.002603 u. The 0.030377 u difference is the mass defect. It is not lost: it was released as energy when the nucleus formed.
Mass defect to energy
Einstein's relation E = mc² converts the missing mass into energy. Doing this in SI units every time is tedious, so nuclear chemistry uses the shortcut 1 u = 931.5 MeV. Multiply the mass defect in u by 931.5 and you have the binding energy in MeV.
E (MeV) = Δm (u) × 931.5
What binding energy means
The binding energy is the energy released when free nucleons come together to form the nucleus, and equally the energy that would have to be supplied to break the nucleus back into free nucleons. A larger binding energy means a more tightly held nucleus.
Binding energy is always positive when quoted this way. It is an amount of energy, not a signed enthalpy change.
Binding energy per nucleon
A uranium nucleus has a far larger total binding energy than a helium nucleus simply because it has more nucleons, so total binding energy is a poor stability comparison. Divide by the number of nucleons instead. Helium-4 gives 28.3 MeV / 4 = 7.07 MeV per nucleon; ⁵⁶Fe gives about 8.8 MeV per nucleon.
binding energy per nucleon = total binding energy / mass number
The curve and its peak
Plotting binding energy per nucleon against mass number gives a curve that rises steeply from hydrogen, peaks around ⁵⁶Fe and nickel-62 at roughly 8.8 MeV per nucleon, then declines slowly toward uranium. Nuclides near the peak are the most stable. Everything to the left can release energy by fusing, everything to the right by fissioning.
The peak explains both fission and fusion at once, which is why examiners keep returning to this curve.
Key ideas
Definition
Mass defect
The difference between the summed masses of the free nucleons and the actual mass of the nucleus.
Definition
Binding energy
The energy equivalent of the mass defect: released on formation, required for separation.
Rule
Conversion factor
1 u = 931.5 MeV.
Rule
Fair comparison
Compare stability using binding energy per nucleon, not total binding energy.
Key concept
Peak at iron
Binding energy per nucleon is greatest near iron-56, the most stable region of the curve.
Equation
Mass defect
Δm = [Z × m(p) + N × m(n)] − m(nucleus)
- Z = number of protons
- N = number of neutrons
- Δm = mass defect in u
Equation
Mass-energy equivalence
E = mc²
- c = 3.00 × 10⁸ m/s
Equation
Practical conversion
E (MeV) = Δm (u) × 931.5
- 931.5 = MeV equivalent of one atomic mass unit
Equation
Binding energy per nucleon
BE/A = total binding energy / A
- A = mass number, the total nucleon count
Worked examples
Worked example 2
Convert that mass defect into the total binding energy of helium-4, then find the binding energy per nucleon.
0 of 2 steps revealed.
Worked example 3
A fission event converts 0.200 u of mass into energy. How much energy is released?
0 of 2 steps revealed.
Common mistakes
Ranking stability by total binding energy.
Why it's wrong: Big nuclei have big totals simply because they contain more nucleons; uranium beats helium on total but is less stable per nucleon.
Check instead: Always divide by the mass number before comparing.
Forgetting to divide the mass defect by the nucleon count when the question asks for binding energy per nucleon.
Why it's wrong: The two answers differ by a factor equal to the mass number, so the numerical answer is far too large.
Check instead: Underline whether the question says total or per nucleon before starting.
Believing mass is destroyed in nuclear reactions.
Why it's wrong: Mass and energy are two forms of the same quantity; the mass is converted, and the total mass-energy is conserved.
Check instead: State the mass defect as mass converted to energy, never mass lost.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
The mass of any nucleus is slightly less than the sum of the masses of its free protons and neutrons. That difference is the mass defect, and by E = mc² it corresponds to the binding energy, the energy released when the nucleus forms or, equivalently, the energy needed to pull it apart into free nucleons. In nuclear problems the conversion factor 1 u = 931.5 MeV replaces the full calculation. Dividing the total binding energy by the number of nucleons gives the binding energy per nucleon, the fair way to compare nuclei of different sizes. That quantity peaks near iron-56, which is why heavy nuclei release energy by fission and light nuclei release energy by fusion.
- The nucleus weighs less than its separated nucleons; that difference is the mass defect
- E = mc² links the mass defect to the binding energy, packaged as 1 u = 931.5 MeV
- Binding energy is released on formation and required for separation
- Compare stability using binding energy per nucleon, not the total
- The curve peaks near iron-56, which is why heavy nuclei fission and light nuclei fuse
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.