describe a simple model for the nuclear atom to include protons, neutrons and orbital electrons

Simple Nuclear Model of the Atom

The modern picture of an atom is a tiny, dense nucleus surrounded by a cloud of orbital electrons. The nucleus contains positively charged protons and electrically neutral neutrons. Electrons occupy regions of space called orbitals, which are described by quantum mechanics but can be represented simply as concentric shells for introductory study.

Key Particles

Particle	Symbol	Charge	Relative Mass
Proton	$p^{+}$	+$e$ (elementary charge)	1 u
Neutron	$n^{0}$	0	1 u (≈ 1.008 u)
Electron	$e^{-}$	-$e$	≈ $1/1836$ u

Structure of the Atom

1. Nucleus
   • Contains $Z$ protons and $N$ neutrons.
   • Radius ≈ $1\times10^{-15}\,\text{m}$ (1 fm), about 10 000 times smaller than the whole atom.
   • Mass number $A = Z + N$.
2. Electron Cloud
   • Electrons are distributed in shells labelled $K$, $L$, $M$, … corresponding to principal quantum numbers $n = 1, 2, 3, …$.
   • Each shell can hold a maximum of $2n^{2}$ electrons (e.g., $K$ holds 2, $L$ holds 8).
   • The overall size of the atom is characterised by the atomic radius, typically $0.1$–$0.3\,\text{nm}$.

Charge Balance

For a neutral atom the total positive charge of the protons equals the total negative charge of the electrons:

$$ Z\,e = N_{e}\,e \quad\Longrightarrow\quad N_{e}=Z $$

where $N_{e}$ is the number of orbital electrons.

Isotopes

Atoms of the same element have the same $Z$ but different numbers of neutrons $N$, giving different mass numbers $A$. These variants are called isotopes.

Isotope	Notation	Protons ($Z$)	Neutrons ($N$)	Mass Number ($A$)
Carbon‑12	$^{12}\text{C}$	6	6	12
Carbon‑14	$^{14}\text{C}$	6	8	14
Uranium‑235	$^{235}\text{U}$	92	143	235

Simple \cdot isual Representation

A useful classroom diagram shows a central sphere (the nucleus) containing $Z$ protons (red dots) and $N$ neutrons (blue dots), surrounded by concentric circles representing electron shells with the appropriate number of electrons placed on each shell.

Key Points to Remember

• The nucleus contains almost all the mass of the atom but occupies a tiny volume.
• Protons determine the chemical identity (atomic number $Z$).
• Neutrons contribute to nuclear stability; varying $N$ leads to isotopes.
• Electrons balance the nuclear charge in a neutral atom and occupy discrete energy levels.
• Atomic mass (in atomic mass units, u) is approximately equal to the mass number $A$.