Physics 2 · Unit 7: Quantum, Atomic, and Nuclear Physics · 14 min read · Updated 2026-05-11
Nuclear Mass, Binding Energy and Strong Nuclear Force — AP Physics 2
AP Physics 2 · Unit 7: Quantum, Atomic, and Nuclear Physics · 14 min read
1. Core Concepts Overview★★☆☆☆⏱ 3 min
This topic makes up a significant portion of the 20-25% exam weight assigned to AP Physics 2 Unit 7, with questions appearing in both multiple-choice and free-response sections. It connects mass-energy conversion to nuclear stability, and is required for all further nuclear physics topics on the exam.
2. Mass Defect and Mass-Energy Conversion★★★☆☆⏱ 4 min
The measured mass of any stable bound nucleus is always less than the sum of the masses of its individual free protons and neutrons. This missing mass is called the **mass defect** ($\Delta m$). The difference arises because when nucleons bind, some mass is converted to binding energy that holds the nucleus together, per mass-energy equivalence.
\Delta m = Z m_\text{H} + N m_n - m_\text{atom}
Where $Z$ is atomic number, $N = A-Z$ is neutron number, $m_\text{H}$ is the mass of a neutral hydrogen atom, $m_n$ is the mass of a free neutron, and $m_\text{atom}$ is the mass of the neutral atom. A convenient AP conversion is $1\ \text{u} = 931.5\ \text{MeV}/c^2$, so binding energy is calculated directly as $E_b (\text{MeV}) = \Delta m (\text{u}) \times 931.5$, no extra $c^2$ term needed.
3. Binding Energy Per Nucleon and Nuclear Stability★★★☆☆⏱ 4 min
Total binding energy always increases with the number of nucleons, so it cannot be used to compare stability between different-sized nuclei. To compare stability, we use **binding energy per nucleon**, defined as $\text{BE}/A = E_b/A$. Higher binding energy per nucleon means the nucleus is more tightly bound and more stable.
The binding energy per nucleon curve has a characteristic shape: it rises sharply for light nuclei ($A < 20$), peaks at $A \approx 56$ (iron-56 is one of the most stable nuclei), then slowly decreases for heavier nuclei ($A > 56$). This explains why energy is released in fusion of light nuclei and fission of heavy nuclei: both processes produce nuclei closer to the peak with higher average binding energy per nucleon.
4. Properties of the Strong Nuclear Force★★★☆☆⏱ 3 min
Protons repel each other via the long-range Coulomb force, so an attractive force is needed to hold the nucleus together: the strong nuclear force. AP Physics 2 requires you to remember four key properties:
It is very short-range: it only acts between adjacent nucleons, with a range of ~1-2 femtometers ($1\ \text{fm} = 10^{-15}\ \text{m}$). Beyond 2 fm, it drops to nearly zero.
It is ~100 times stronger than Coulomb repulsion at short (1 fm) distances.
It is repulsive at distances less than ~0.5 fm, which prevents the nucleus from collapsing into a point.
It is charge-independent: it acts the same between any pair of nucleons (proton-proton, proton-neutron, neutron-neutron).
The short-range property explains the shape of the binding energy per nucleon curve: in large nuclei, each nucleon only interacts with immediate neighbors via the strong force, so adding more nucleons does not increase strong attraction per nucleon. Coulomb repulsion is long-range, so cumulative repulsion increases as the nucleus grows, lowering binding energy per nucleon for heavy nuclei. Heavy stable nuclei need more neutrons than protons because neutrons add strong attraction without adding Coulomb repulsion.
Common Pitfalls
Why: Students mix up which mass is larger; free unbound nucleons have more mass than the bound nucleus.
Why: Students confuse total binding energy with binding energy per nucleon; uranium has higher total binding energy than iron but is much less stable.
Why: Students confuse the direction of mass conversion; more tightly bound products have less mass than reactants.
Why: Students mix up strong force properties with Coulomb force properties.
Why: Students confuse the force holding the nucleus together with the force holding the atom together.
Why: Students forget the convenient conversion factor for nuclear calculations.