Atomic Nucleus
The atomic nucleus is the small, dense, positively charged core at the center of an atom, containing protons and neutrons (collectively called nucleons) held together by the strong nuclear force. Although the nucleus is approximately 10⁻¹⁵ m (1 femtometre) in diameter — about 100,000 times smaller than the atom itself — it contains nearly all the atom's mass. Nuclear reactions, such as fission and fusion, involve changes to the nucleus and release enormous amounts of energy.
Key Formula
r = r₀ × A^(1/3) — nuclear radius approximation
LaTeX: r = r_0 A^{1/3}
| Symbol | Meaning | Unit |
|---|---|---|
| r | Radius of the nucleus | femtometres (fm) |
| r₀ | Empirical constant ≈ 1.2 fm | fm |
| A | Mass number (total nucleons) | dimensionless |
Worked Example
Problem
Estimate the radius of a carbon-12 nucleus (A = 12) using r₀ = 1.2 fm.
Solution
Step 1: Use r = r₀ × A^(1/3). Step 2: r = 1.2 × 12^(1/3). Step 3: 12^(1/3) = 2.289. Step 4: r = 1.2 × 2.289 = 2.747 fm.
Answer
The radius of the carbon-12 nucleus is approximately 2.75 fm (femtometres).
Comparison of Atomic Nucleus and Full Atom
| Feature | Nucleus | Full Atom |
|---|---|---|
| Size | ~10⁻¹⁵ m (1 fm) | ~10⁻¹⁰ m (1 Å) |
| Contains | Protons + Neutrons | Nucleus + Electrons |
| Charge | Positive | Neutral (in neutral atom) |
| Mass | ~99.97% of total mass | Total atomic mass |
| Density | ~2.3 × 10¹⁷ kg/m³ | Very low (mostly empty space) |
Interactive Tools
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Related Terms
Proton
A proton is a positively charged subatomic particle found in the nucleus of every atom, with a charge of +1 elementary charge and a mass of approximately 1.673 × 10⁻²⁷ kg (about 1 atomic mass unit). The number of protons in an atom's nucleus defines the element and is called the atomic number, which determines the chemical identity of the atom. Protons are composed of two up quarks and one down quark held together by the strong nuclear force.
Neutron
A neutron is an electrically neutral subatomic particle found in the nucleus of all atoms except ordinary hydrogen, with a mass of approximately 1.675 × 10⁻²⁷ kg, slightly greater than the proton. Neutrons contribute to the mass of the nucleus and play a crucial role in nuclear stability by reducing electrostatic repulsion between protons through the strong nuclear force. Atoms with the same number of protons but different numbers of neutrons are called isotopes.
Mass Number
The mass number (symbol A) is the total number of nucleons — protons and neutrons — in the nucleus of an atom, and is always a whole number. It is used to distinguish between different isotopes of the same element, as isotopes have the same atomic number (Z) but different mass numbers (A) due to differing neutron counts. The mass number is approximately equal to the atomic mass in atomic mass units (u), though not exactly because of binding energy effects.
From Latin "nucleus" meaning "kernel" or "inner part of a nut". The nucleus was discovered by Ernest Rutherford in 1911 through his gold foil experiment, in which he observed that alpha particles were deflected by a dense central core, disproving the earlier "plum pudding" model of the atom.