Difficulty: Intermediate | Prerequisites: Chapter 6 (thermochemistry), basic algebra, comfort with scientific notation.
Quantum theory explains why atoms emit and absorb light at specific wavelengths, and why electrons do not behave like tiny billiard balls. This chapter covers the experimental evidence that forced physics to abandon classical models (blackbody radiation, the photoelectric effect, hydrogen line spectra) and introduces the early quantum models that replaced them. If Chapter 6 taught you to track energy through reactions, Chapter 7 shows you where that energy comes from at the atomic level.
Light behaves as both a wave and a particle, and so do electrons and other matter. Classical physics could not explain blackbody radiation, the photoelectric effect, or hydrogen's line spectrum, so Planck, Einstein, and Bohr introduced the idea that energy is quantised. The Bohr model correctly predicts hydrogen's energy levels but fails for anything more complex, setting the stage for the full quantum mechanical treatment.
Wave-particle duality
The principle that quantum objects (photons, electrons, neutrons, even large molecules) exhibit both wave-like and particle-like behaviour depending on the experiment. In simple terms, light can act like a ripple or like a bullet, and electrons can do the same.
Interference pattern
A series of alternating bright and dark fringes produced when waves overlap. Bright fringes appear where waves are in phase (constructive interference); dark fringes appear where they are out of phase (destructive interference). It is the signature of wave behaviour.
Superposition principle
When two or more waves pass through the same point, the resulting amplitude is the sum of the individual amplitudes. This is what makes constructive and destructive interference possible.
Constructive interference
Waves in phase combine to produce a larger amplitude (a taller wave). Think of two people pushing a swing at the same moment.
Destructive interference
Waves out of phase combine to cancel each other out, producing zero amplitude (a flat line). Think of noise-cancelling headphones.
Electromagnetic spectrum
The full range of electromagnetic radiation, ordered by wavelength or frequency. From longest wavelength to shortest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
Frequency (ν)
The number of wave cycles that pass a point per second, measured in hertz (Hz). Higher frequency means shorter wavelength and higher energy.
Wavelength (λ)
The distance between two consecutive crests (or troughs) of a wave. Measured in metres or nanometres (1 nm = 10⁻⁹ m).
Blackbody radiation
The electromagnetic radiation emitted by an idealised object that absorbs all incoming radiation. Classical physics predicted infinite energy at high frequencies (the "ultraviolet catastrophe"); Planck resolved this by proposing that energy is emitted in discrete packets.
Planck's constant (h)
The fundamental constant relating the energy of a photon to its frequency: h = 6.626 × 10⁻³⁴ J·s. It sets the scale of quantum effects.
Photoelectric effect
The ejection of electrons from a metal surface when light of sufficient frequency strikes it. Classical physics predicted the effect should depend on intensity; experiments showed it depends on frequency. Einstein explained this by treating light as photons.
Work function (Φ)
The minimum energy needed to eject an electron from a metal surface. In simple terms, it is the energy "toll" the electron must pay to escape the metal.
Threshold frequency (ν₀)
The minimum frequency of light needed to eject photoelectrons from a given metal. Below this frequency, no electrons are emitted regardless of intensity. ν₀ = Φ / h.
Rydberg formula
An empirical equation that predicts the wavelengths of light emitted or absorbed by hydrogen atoms based on the quantum numbers of the initial and final energy levels.
Bohr model
An early quantum model of the hydrogen atom in which the electron orbits the nucleus in fixed circular paths with quantised angular momentum. It correctly predicts hydrogen's line spectrum but fails for multi-electron atoms.
Heisenberg uncertainty principle
We cannot simultaneously know both the exact position and exact momentum of a quantum particle. The more precisely one is measured, the less precisely the other can be known. In simple terms, the act of looking changes what you see at the quantum scale.
Fire photons or electrons one at a time through two slits: an interference pattern builds up on the detector, even though each particle goes through individually.
This proves quantum objects behave as waves when not observed (interference appears) and as particles when measured (interference vanishes, particle-like distribution appears).
The experiment also shows the Heisenberg uncertainty principle in action: you cannot track a particle's exact trajectory through the slits without destroying the interference pattern.
Observation (measurement) forces the wavefunction to collapse into a definite state.
Wavelength (λ): distance between consecutive crests. 1 nm = 10⁻⁹ m.
Frequency (ν): cycles per second, in Hz.
Speed: c = νλ (for light in a vacuum, c = 3.00 × 10⁸ m/s).
Amplitude: height of the wave, related to intensity.
Frequency and wavelength are inversely related: as one increases, the other decreases.
Increasing wavelength (decreasing frequency and energy): gamma rays → X-rays → ultraviolet → visible → infrared → microwaves → radio waves.
Know the approximate order. Visible light sits in the middle; infrared has longer wavelengths and lower frequencies than visible.
When waves overlap, their amplitudes add (superposition principle).
Constructive interference: waves in phase, amplitudes add to a larger wave.
Destructive interference: waves out of phase, amplitudes cancel to zero.
Interference patterns (alternating bright and dark fringes) are the hallmark of wave behaviour.
A blackbody emits radiation across all wavelengths. As temperature increases, the peak shifts to higher frequency and the total radiated energy increases.
Classical physics predicted infinite energy at short wavelengths (the ultraviolet catastrophe).
Planck's resolution: the oscillators in the blackbody can only have quantised energies. He introduced Planck's constant (h) and fitted it to experimental data.
Experiment: shine light on a metal surface in vacuum, measure kinetic energies of ejected electrons as a function of light frequency and intensity.
Classical prediction (wrong): electron kinetic energy should increase with light intensity and should not depend on frequency.
Experimental result: electron kinetic energy increases linearly with frequency and does not depend on intensity. Below a threshold frequency (ν₀), no electrons are emitted at all.
Einstein's explanation: light consists of photons, each carrying energy E = hν. A photon's energy must exceed the work function (Φ) to eject an electron. Excess energy becomes the electron's kinetic energy.
The slope of a graph of electron KE vs. frequency gives Planck's constant, h, matching the value from blackbody data.
Hydrogen emits light at discrete wavelengths (a line spectrum, not a continuous spectrum).
These wavelengths follow the Rydberg formula, which relates them to integer quantum numbers.
Given n_initial and n_final, you can calculate the wavelength, frequency, or photon energy of the light emitted or absorbed.
Electron orbits the nucleus in circular paths with quantised angular momentum: m·u·r = n·h / 2π.
Orbital radius is proportional to n² (larger n means the electron is further from the nucleus).
The model correctly predicts the wavelengths of hydrogen's emission lines (agrees with the Rydberg formula).
E_n = –2.18 × 10⁻¹⁸ J × (1/n²), where n = 1, 2, 3, ...
All energies are negative, meaning the electron is bound to the nucleus. Zero energy is defined as the electron at infinite distance (n = ∞), completely free.
Emission: electron drops from higher n to lower n; the atom releases a photon whose energy equals the difference between the two levels.
Absorption: electron jumps from lower n to higher n; the atom absorbs a photon of exactly that energy.
The Bohr frequency condition: E_photon = hν = |E_final – E_initial|.
Cannot predict effects of external magnetic fields on the hydrogen atom.
Fails for atoms with more than one electron.
Treats the electron as a particle in a defined orbit, which is incompatible with the Heisenberg uncertainty principle.
The Schrödinger equation, which treats the electron as a wave, gives the same energy levels for hydrogen but extends successfully to more complex systems.
c = \nu \lambda \quad (c = 3.00 \times 10^8\;\text{m/s})E_{\text{photon}} = h\nu = \frac{hc}{\lambda} \quad (h = 6.626 \times 10^{-34}\;\text{J·s})E_{\text{photon}} = \Phi + \tfrac{1}{2}mu^2 \quad (\text{photoelectric effect})\nu_0 = \frac{\Phi}{h} \quad (\text{threshold frequency})E_n = -2.18 \times 10^{-18}\;\text{J} \times \frac{1}{n^2} \quad (n = 1, 2, 3, \ldots)\Delta E = E_{\text{final}} - E_{\text{initial}} = -2.18 \times 10^{-18}\;\text{J} \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)m \cdot u \cdot r = \frac{n \cdot h}{2\pi} \quad (\text{Bohr quantisation of angular momentum})The photoelectric effect is the principle behind solar panels: photons strike a semiconductor and knock electrons loose, generating current. Emission spectra are how astronomers identify the chemical composition of distant stars, and how neon signs produce their characteristic colours. Planck's constant shows up everywhere quantum mechanics matters, from laser design to MRI machines.
Students often think that increasing light intensity should increase the kinetic energy of ejected electrons. It does not. Intensity increases the number of photoelectrons, not their energy. Only frequency determines kinetic energy.
"Wave-particle duality" does not mean an electron is sometimes a wave and sometimes a particle. It means every quantum object has both wave-like and particle-like properties; which you observe depends on the experiment.
The Bohr model's circular orbits are not the same as the orbitals in the full quantum mechanical picture. Orbits are fixed paths; orbitals are probability distributions. Do not use the two words interchangeably on an exam.
Students sometimes assume negative energy means the electron has lost all its energy. Negative energy simply means the electron is bound to the nucleus. Zero energy means the electron is free (ionised).
⚠️ Be able to convert between wavelength, frequency, and photon energy using c = νλ and E = hν. Unit conversions (nm to m) trip people up under time pressure.
⚠️ Know the order of the electromagnetic spectrum in both directions (by wavelength and by frequency).
⚠️ For the photoelectric effect, be ready to explain why classical predictions fail and how Einstein's photon model fixes each failure.
⚠️ Given two values of n, be able to calculate the energy difference, determine whether the transition is absorption or emission, and find the wavelength of the photon involved.
⚠️ Know the three limitations of the Bohr model (magnetic fields, multi-electron atoms, uncertainty principle). This is a common short-answer or multiple-choice target.
True or false: Increasing the intensity of light increases the kinetic energy of photoelectrons.
False. Only increasing the frequency increases kinetic energy.
Fill in the blank: In the electromagnetic spectrum, ______ have the longest wavelength.
Radio waves.
True or false: The Bohr model correctly predicts the emission spectrum of helium.
False. It works only for hydrogen (one-electron systems).
Fill in the blank: When an electron drops from n = 4 to n = 2, the atom ______ (absorbs/emits) a photon.
Emits.
True or false: A negative energy value for an electron in the hydrogen atom means the electron is bound to the nucleus.
True.
Q: Calculate the energy of a photon with a wavelength of 450 nm.
A: First convert: 450 nm = 4.50 × 10⁻⁷ m. Then E = hc/λ = (6.626 × 10⁻³⁴ J·s)(3.00 × 10⁸ m/s) / (4.50 × 10⁻⁷ m) = 4.42 × 10⁻¹⁹ J.
Q: The work function of sodium is 3.65 × 10⁻¹⁹ J. What is the threshold frequency?
A: ν₀ = Φ/h = (3.65 × 10⁻¹⁹ J) / (6.626 × 10⁻³⁴ J·s) = 5.51 × 10¹⁴ Hz.
Q: An electron in a hydrogen atom drops from n = 5 to n = 2. Is a photon absorbed or emitted, and what is the energy of that photon?
A: Emitted (n decreases). ΔE = –2.18 × 10⁻¹⁸ J × (1/2² – 1/5²) = –2.18 × 10⁻¹⁸ × (0.25 – 0.04) = –2.18 × 10⁻¹⁸ × 0.21 = –4.58 × 10⁻¹⁹ J. The photon carries 4.58 × 10⁻¹⁹ J of energy.
Q: In the two-slit experiment, what happens to the interference pattern when you place a detector at one of the slits to determine which slit the electron passes through?
A: The interference pattern disappears. Observation forces the electron into a particle-like state, and you see two bands instead of fringes.
Q: Name three limitations of the Bohr model.
A: It cannot predict effects of magnetic fields on hydrogen, it fails for atoms with more than one electron, and it is incompatible with the Heisenberg uncertainty principle (it assumes defined orbits).
This connects to thermochemistry (Chapter 6) because quantised energy levels are the atomic-scale reason reactions release or absorb specific amounts of energy. It also sets up the rest of quantum mechanics: the Schrödinger equation, electron configurations, and periodic trends all build on the idea that electrons occupy discrete energy levels, not continuous orbits.
Quantum theory, wave-particle duality, two-slit experiment, double-slit experiment, interference pattern, superposition, constructive interference, destructive interference, electromagnetic spectrum, EM spectrum, blackbody radiation, ultraviolet catastrophe, Planck's constant, photoelectric effect, work function, threshold frequency, photon energy, Rydberg formula, Bohr model, hydrogen emission spectrum, energy levels, Heisenberg uncertainty principle, wavefunction collapse, quantisation, general chemistry, UMN, University of Minnesota