The full, readable lecture — the three sub-atomic particles, Rutherford's nuclear atom, isotopes, Bohr's energy levels, the hydrogen spectrum, the quantum picture and electronic configuration. As you scroll, the panel on the right shows each idea through a real-life picture you already know.
1 — Sub-atomic particles & the electron
Dalton thought the atom was a solid, indivisible ball. Discharge-tube experiments proved otherwise — the atom is built from three fundamental sub-atomic particles: the electron, the proton and the neutron.
Cathode rays → the electron
A high voltage across a gas at low pressure in a discharge tube makes rays stream from the cathode (−) to the anode (+). These cathode rays travel in straight lines, are deflected by fields towards the positive plate (so they are negative), and are independent of the gas — a universal part of all matter. The particle is the electron.
- Electron — charge −1.602 × 10⁻¹⁹ C (relative −1), mass 9.11 × 10⁻³¹ kg (≈ 1/1836 a.m.u). Thomson found e/m = 1.76 × 10¹¹ C·kg⁻¹; Millikan fixed the charge.
- Proton — positive (canal) rays; charge +1, mass 1.0073 a.m.u.
- Neutron — Chadwick (1932); no charge, mass 1.0087 a.m.u.
Nucleons = protons + neutrons, packed in the nucleus; electrons occupy the space around it — exactly like planets circling a sun.
2 — Rutherford's nuclear model
Rutherford fired α-particles (He²⁺) at a thin gold foil and recorded where they hit a screen — like rolling marbles at a wall to feel out what is solid inside.
- Most α-particles passed straight through undeflected.
- A few were deflected through large angles.
- About 1 in 20,000 bounced almost straight back.
Conclusions
The atom is mostly empty space; all the positive charge and nearly all the mass sit in a tiny, dense nucleus; electrons revolve around it like planets around the sun.
Defect: a revolving (accelerating) electron must radiate energy and spiral in — so this model predicts the atom would collapse, and it cannot explain the line spectrum.
3 — Atomic number, mass number & isotopes
- Atomic number (Z) — number of protons (= electrons in a neutral atom).
- Mass number (A) — protons + neutrons, so neutrons = A − Z.
Nuclide symbolZ = protons · A = protons + neutrons
neutrons = A − Z (e.g. ²³₁₁Na → 11p, 11e, 12n)
- Isotopes — same Z, different A — like identical twins of slightly different weight (e.g. ³⁵Cl and ³⁷Cl, or ¹H, ²H, ³H).
- Isobars — different elements, same A (⁴⁰Ar, ⁴⁰K, ⁴⁰Ca).
relative atomic mass of chlorine
Chlorine is 75% ³⁵Cl and 25% ³⁷Cl.
A_r = (75×35 + 25×37)/100 = 3550/100 = 35.5 a.m.u
4 — Electromagnetic radiation & Planck's quantum
Light is an electromagnetic wave with wavelength λ and frequency ν, related to the speed of light by c = νλ.
Key relationsc = ν λ (c = 3 × 10⁸ m/s)
E = h ν = h c / λ (h = 6.63 × 10⁻³⁴ J·s)
Max Planck proposed that energy is absorbed or emitted not continuously but in tiny discrete packets — quanta. One quantum of light is a photon. Like coins from a vending machine, energy comes only in whole packets, never half a packet.
energy of a photon
Frequency 5 × 10¹⁴ Hz.
E = hν = (6.63×10⁻³⁴)(5×10¹⁴) = 3.315 × 10⁻¹⁹ J
5 — Bohr's atomic model (hydrogen)
Niels Bohr (1913) fixed Rutherford's stability problem with quantisation: the electron may sit only on certain fixed levels — like the numbered tiers of seats in a stadium, never on the steps between.
- The electron revolves in fixed circular orbits (stationary states) without radiating.
- Angular momentum is quantised: mvr = nh/2π.
- Energy is emitted/absorbed only on a jump: E₂ − E₁ = hν.
Hydrogen orbit nrₙ = 0.529 × n² Å
Eₙ = −1312 / n² kJ·mol⁻¹ (= −13.6/n² eV)
The negative sign means the electron is bound — energy must be supplied to free it. n = 1 (ground state) is lowest and most stable.
6 — The hydrogen emission spectrum
When hydrogen is energised, its electron jumps up, then falls back, emitting a photon of a definite wavelength. Only certain jumps are allowed, so the result is a line spectrum — sharp coloured lines, like a barcode, not a continuous band. It is unique to each element — the very colours you see in fireworks and gas-lamp flames.
| Series | Falls to | Region |
|---|
| Lyman | n = 1 | Ultraviolet |
| Balmer | n = 2 | Visible |
| Paschen | n = 3 | Infrared |
Rydberg equation1/λ = R_H ( 1/n₁² − 1/n₂² ) (R_H = 1.09 × 10⁷ m⁻¹)
7 — Defects of Bohr, the wave picture & quantum numbers
Bohr's model is perfect for hydrogen but fails for many-electron atoms and the fine splitting of lines. Two ideas replaced the fixed orbit with an orbital:
- de Broglie — a moving particle is also a wave: λ = h/mv.
- Heisenberg — position and momentum cannot both be exact: Δx·Δp ≥ h/4π.
- Orbital — a region where the probability of finding the electron is maximum (~95%). A fuzzy cloud, like a swarm of bees around a hive, not a single bee on a fixed track.
| QN | Tells you | Values |
|---|
| n | shell — size & energy | 1, 2, 3, … |
| ℓ | subshell — shape (s p d f) | 0 … n−1 |
| m | orientation | −ℓ … +ℓ |
| s | spin | +½ or −½ |
Shapes: s spherical (2 e⁻), p dumb-bell (6 e⁻), d cloverleaf (10 e⁻). Subshell capacity = 2(2ℓ+1); shell capacity = 2n².
8 — Electronic configuration: Aufbau, Pauli, Hund
Electrons fill orbitals like an audience filling a theatre — everyone takes the cheap front seats (lowest energy) before moving back.
- Aufbau / (n+ℓ) rule — lowest energy first; lower (n+ℓ) fills first, giving 1s 2s 2p 3s 3p 4s 3d 4p…
- Pauli — an orbital holds 2 electrons of opposite spin; no two electrons share all four quantum numbers.
- Hund — within a subshell, fill orbitals singly first (parallel spins), then pair.
Drag the slider in the live panel to choose an element (Z = 1–20) and watch its seats fill, one electron per box first, then pairing.
Exam anomalies: Cr = [Ar] 3d⁵ 4s¹ and Cu = [Ar] 3d¹⁰ 4s¹ — half/fully-filled d is extra stable.