Composition of the Atomic Nucleus: MDCAT Physics notes
Composition of the Atomic Nucleus MDCAT notes: protons, neutrons, mass number, isotopes, quarks, strong nuclear force, E = mc², binding energy.
Nucleons and notation
The nucleus contains protons (charge $+e$) and neutrons (no charge), together called nucleons. A nuclide is written $^{A}_{Z}X$:
- Atomic number $Z$ = number of protons.
- Mass number $A$ = number of nucleons (protons + neutrons).
- Number of neutrons $N=A-Z$.
Isotopes
Isotopes have the same $Z$ but different $A$ (different numbers of neutrons). They have the same chemical properties but different masses. Hydrogen has three isotopes:
| Isotope | Symbol | Protons | Neutrons |
|---|---|---|---|
| Protium | $^1_1$H | 1 | 0 |
| Deuterium | $^2_1$H | 1 | 1 |
| Tritium | $^3_1$H | 1 | 2 |
Together, protium + deuterium + tritium contain 3 neutrons more than three protium atoms.
Quarks
Protons and neutrons are not fundamental; each is made of three quarks.
| Particle | Quarks | Total charge |
|---|---|---|
| Proton | u u d | $\tfrac23+\tfrac23-\tfrac13=+1$ |
| Neutron | u d d | $\tfrac23-\tfrac13-\tfrac13=0$ |
Up quark charge $+\tfrac23e$, down quark $-\tfrac13e$. So two down quarks have a total charge of $-\tfrac23e$.
What holds the nucleus together
Protons repel each other electrically, and gravity between them is far too weak to matter. The nucleons are held by the strong nuclear force: very strong, attractive, short range (about $10^{-15}$ m), and independent of charge (acts equally between p-p, n-n and p-n).
| Force | Role in the nucleus |
|---|---|
| Strong nuclear | Binds nucleons |
| Electromagnetic | Repulsion between protons |
| Weak nuclear | Responsible for beta decay |
| Gravitational | Negligible |
Mass defect and binding energy
Einstein's relation $E=mc^2$ shows that mass and energy are directly proportional and interconvertible. The mass of a nucleus is less than the total mass of its separate nucleons; the difference is the mass defect $\Delta m$. The energy released when a nucleus is formed from its nucleons (equal to the energy needed to break it apart) is the binding energy, $E_b=\Delta m\,c^2$.
Binding energy per nucleon measures stability; it is highest near iron. Heavy nuclei undergo fission and light nuclei undergo fusion so that the products have a higher binding energy per nucleon, releasing energy. Fusion of hydrogen into helium powers the Sun.
Key formulas
- $N=A-Z$
- $\Delta m=Zm_p+Nm_n-m_{nucleus}$
- $E_b=\Delta m\,c^2$; 1 u $\approx$ 931 MeV
Common MDCAT traps
- Mass number counts nucleons, not just neutrons or protons.
- Proton is uud (two up, one down); neutron is udd.
- Gravity plays no role in nuclear stability.
- Fission increases binding energy per nucleon; it does not "absorb" energy.
Quick revision
- Neutron has no charge.
- Isotopes: same $Z$, different $N$.
- Strong force: short range, attractive, charge independent.
- $E=mc^2$ links mass and energy.
- The Sun is a natural fusion reactor.