Nuclei

Lesson

Part 1 — what a nucleus is made of, how big and dense it is, what holds it together, and where nuclear energy comes from.

In this lesson you will

Describe the composition and size of nuclei and the properties of the nuclear force
Use E = mc² to relate mass defect to binding energy
Interpret the binding energy per nucleon curve

Concept

Composition of the nucleus

A nucleus contains protons (charge $+e$ ) and neutrons (no charge), together called nucleons.

Atomic number $Z$ = number of protons; mass number $A$ = number of nucleons; neutron number $N = A - Z$ . Notation: ${}^{A}_{Z}\text{X}$ .
Atomic masses are measured in unified atomic mass units: $1\ \text{u} = \tfrac{1}{12}$ of the mass of a ¹²C atom $= 1.6605 \times 10^{-27}$ kg.
$m_p = 1.007276$ u, $m_n = 1.008665$ u (the neutron, discovered by Chadwick in 1932, is slightly heavier).

Table defining isotopes, isobars and isotones with an example of each
Term	Meaning	Example
Isotopes	Same Z, different A	¹²C and ¹⁴C
Isobars	Same A, different Z	³H and ³He
Isotones	Same N = A − Z, different Z	¹⁹⁸Hg and ¹⁹⁷Au (N = 118)

Diagram

Size of the nucleus

Scattering experiments show that the nuclear radius grows with mass number as $R = R_0 A^{1/3},\qquad R_0 \approx 1.2\ \text{fm} = 1.2 \times 10^{-15}\ \text{m}$

So the volume $\propto R^3 \propto A$ : each nucleon occupies about the same volume.
Uranium-238 has 60 times as many nucleons as helium-4 but is only about 3.9 times wider.

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