Atomic Structure

Atomic constituents

Particle	Charge	Mass (kg)	Mass (u)	Location
Proton (p)	+e	1.673 × 10⁻²⁷	1.0073	Nucleus
Neutron (n)	0	1.675 × 10⁻²⁷	1.0087	Nucleus
Electron (e)	-e	9.11 × 10⁻³¹	5.486 × 10⁻⁴	Electron cloud

1 atomic mass unit (u) = 1.661 × 10⁻²⁷ kg. Proton and neutron have nearly identical mass; electron is ~1836× lighter.

Size scales

Scale	Size
Atom (typical)	~10⁻¹⁰ m = 1 Å
Nucleus	~10⁻¹⁵ m = 1 fm
Bohr radius (H atom)	0.529 × 10⁻¹⁰ m
Hydrogen nucleus (proton)	~0.84 × 10⁻¹⁵ m
Atom : Nucleus ratio	~100,000:1
Volume ratio (atom/nucleus)	~10¹⁵

If a hydrogen atom were the size of a football stadium, its nucleus would be a marble at center field.

Atomic number Z, mass number A

• Atomic number Z = number of protons. Defines the element. Hydrogen has Z=1, helium Z=2, ..., uranium Z=92.
• Mass number A = total nucleons (protons + neutrons). For ¹²C, Z=6, A=12, so 6 neutrons.
• Isotopes — same Z, different A.
• Atomic mass — average mass weighted by isotope abundance. ¹²C is exactly 12 u (definition); ¹³C is 13.003 u; natural carbon mass is ~12.011.

Electron orbitals

Shell n	Subshells	Max electrons
1	1s	2
2	2s, 2p	2 + 6 = 8
3	3s, 3p, 3d	2 + 6 + 10 = 18
4	4s, 4p, 4d, 4f	2 + 6 + 10 + 14 = 32

Filling rule (Aufbau): orbitals fill in order of increasing energy. Pauli exclusion: max 2 electrons per orbital. Hund's rule: electrons fill empty orbitals first within a subshell.

JavaScript — atomic structure

// Bohr radius for hydrogen-like atom (Z protons)
function bohrRadius(Z = 1, n = 1) {
  // a_n = n²·a_0/Z (a_0 = 5.29e-11 m)
  return n * n * 5.29e-11 / Z;
}

console.log(`H ground state: ${(bohrRadius(1, 1) * 1e10).toFixed(2)} Å`);  // 0.53
console.log(`H n=2: ${(bohrRadius(1, 2) * 1e10).toFixed(2)} Å`);            // 2.12
console.log(`Helium+ ground: ${(bohrRadius(2, 1) * 1e10).toFixed(3)} Å`);   // 0.265

// Bohr energy levels for hydrogen-like atom
function bohrEnergy(Z, n) {
  // E_n = -13.6 · Z²/n² eV
  return -13.6 * Z * Z / (n * n);
}

console.log(`H ground state: ${bohrEnergy(1, 1).toFixed(2)} eV`);    // -13.6
console.log(`H n=2: ${bohrEnergy(1, 2).toFixed(2)} eV`);              // -3.4
console.log(`Helium+ n=1: ${bohrEnergy(2, 1).toFixed(1)} eV`);        // -54.4

// Photon energy from transition
function transitionEnergy(Z, n_initial, n_final) {
  return bohrEnergy(Z, n_initial) - bohrEnergy(Z, n_final);
}

// Hydrogen 3 → 2 (Balmer) → 656.3 nm (red, "Hα")
const E_3to2 = -transitionEnergy(1, 3, 2);  // emitted (positive)
const lambda_3to2 = 1240 / E_3to2;  // hc/E in eV·nm = 1240
console.log(`Hα: ${E_3to2.toFixed(2)} eV = ${lambda_3to2.toFixed(0)} nm`);

// Atomic number and mass for common isotopes
const isotopes = {
  'H': {Z: 1, A: 1},
  'D': {Z: 1, A: 2},
  'He': {Z: 2, A: 4},
  'C12': {Z: 6, A: 12},
  'C14': {Z: 6, A: 14},
  'O16': {Z: 8, A: 16},
  'U235': {Z: 92, A: 235},
  'U238': {Z: 92, A: 238}
};

for (const [name, {Z, A}] of Object.entries(isotopes)) {
  console.log(`${name}: ${Z}p, ${A-Z}n, ${Z}e, mass ≈ ${A}u`);
}

// Pauli exclusion: max electrons in shell n
function maxElectrons(n) { return 2 * n * n; }
console.log(`Shell n=4 max: ${maxElectrons(4)}`);  // 32

// Element from electron count (highly simplified)
function predictElement(Z) {
  const elements = ['H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne'];
  return elements[Z - 1] || `Z=${Z}`;
}

Where atomic structure matters

• Chemistry. Atom-level understanding drives all chemical bonding, reactions, materials.
• Materials science. Crystal structures, defects, doping, electronic properties.
• Spectroscopy. Each element has unique spectrum from electronic transitions.
• Nuclear technology. Reactors, weapons, medicine — all rely on nuclear structure.
• Astronomy. Stellar spectra reveal composition; nucleosynthesis in stars makes elements.
• Quantum computing. Atoms (or atom-like systems) used as qubits in some implementations.
• Medicine. Radioactive isotopes for imaging, treatment.

Common mistakes

• Picturing electrons as planets. Bohr model (1913) was a useful picture but quantum mechanics replaced it. Electrons in orbitals (probability distributions), not orbits.
• Confusing isotope and ion. Isotope — different number of neutrons (same Z). Ion — different number of electrons (charged atom).
• Treating atomic mass as integer. Atomic mass on periodic table is weighted average (e.g., chlorine 35.45). Individual atoms have integer mass numbers, not 35.45.
• Forgetting electron mass in nucleon counting. Most of atom's mass is in nucleus. But total nuclear binding energy contributes; mass of carbon-12 atom is exactly 12 u (by definition).
• Drawing realistic atoms. Most diagrams aren't to scale — nucleus is far smaller than shown. If true scale, nucleus invisible.
• Treating quantum numbers as classical. n, ℓ, m, m_s describe quantized states. Not corresponding to classical orbits or angular momentum directions.