Difficulty: Introductory to Intermediate | Prerequisites: basic algebra, familiarity with scientific notation and SI units.
This material sits at the foundation of modern chemistry and physics. It explains how light behaves, why energy comes in discrete packets rather than continuous streams, and why atoms emit or absorb only specific colours of light. You need this before you can make sense of electron configurations, chemical bonding, or spectroscopy. If you are coming in cold, the core idea is that the classical picture of light as a smooth wave broke down in the early 1900s, and a new framework (quantum mechanics) replaced it.
Light is electromagnetic radiation characterised by wavelength, frequency, and energy. Planck showed energy transfer between light and matter is quantised (comes in chunks of hv). Einstein used this to explain the photoelectric effect, proving light also behaves as particles (photons), while de Broglie showed that matter also has wave properties.
Electromagnetic radiation (EM radiation)
Energy that travels through space as oscillating electric and magnetic fields perpendicular to each other. In simple terms, this is what light, radio waves, X-rays and microwaves all are: the same phenomenon at different wavelengths.
Wavelength (λ, "lambda")
The distance between two consecutive peaks (or troughs) of a wave, measured in metres (often nanometres for visible light). Think of it as the length of one full cycle of the wave.
Frequency (ν, "nu")
The number of wave cycles that pass a given point per second, measured in hertz (Hz = s⁻¹). In simple terms, how rapidly the wave oscillates.
Speed of light (c)
The constant speed at which all electromagnetic radiation travels in a vacuum: 3.00 × 10⁸ m s⁻¹. Wavelength and frequency are inversely related through c.
Quantised / quantisation
A quantity is quantised when it can take only certain discrete values rather than any value in a continuous range. Think of stairs versus a ramp: on stairs you can stand only at fixed heights.
Photon
A single "packet" (quantum) of electromagnetic energy with energy E = hν. In simple terms, the smallest possible chunk of light at a given frequency.
Planck's constant (h)
A fundamental constant, h = 6.626 × 10⁻³⁴ J·s, that relates the energy of a photon to its frequency. It was introduced by Max Planck to fit blackbody radiation data.
Blackbody radiation
The spectrum of light emitted by an idealised object that absorbs all incident radiation. Classical physics could not predict its shape; Planck solved this by assuming energy is quantised.
Photoelectric effect
The ejection of electrons from a metal surface when light of sufficient frequency strikes it. This was the key evidence that light behaves as particles (photons), not just waves.
Work function (Φ)
The minimum energy needed to eject an electron from a particular metal surface. Equal to hν₀, where ν₀ is the threshold frequency for that metal.
Wave-particle duality
The principle that electromagnetic radiation exhibits both wave-like behaviour (diffraction, interference) and particle-like behaviour (quantised energy exchange). Matter has this duality too.
de Broglie wavelength
The wavelength associated with a moving particle, given by λ = h / (mv). In simple terms, everything that moves has a wavelength, but it is only noticeable for very small, light particles like electrons.
All EM radiation travels at speed c in a vacuum.
The spectrum ranges from gamma rays (high frequency, short wavelength, high energy) to long radio waves (low frequency, long wavelength, low energy).
Visible light occupies a narrow band, roughly 400 nm (violet) to 700 nm (red).
Wavelength and frequency are inversely proportional through λ × ν = c.
Energy increases with frequency and decreases with wavelength.
Classical physics predicted that a heated blackbody should emit infinite energy at short wavelengths (the "ultraviolet catastrophe"). This did not match experiment.
Planck resolved this by proposing that energy is exchanged between light and matter only in discrete packets: ΔE = nhν, where n is a positive integer.
The quantity hν is called a photon of energy. A system can absorb or emit n photons at a time.
Planck's constant h = 6.626 × 10⁻³⁴ J·s was introduced solely to fit the experimental data.
When light of sufficient frequency hits a metal surface, electrons are ejected.
Classical prediction: any frequency should work if the amplitude (intensity) is large enough. This is wrong.
What is observed:
Below the threshold frequency ν₀, no electrons are ejected regardless of intensity.
Above ν₀, increasing frequency increases the kinetic energy of ejected electrons, but not their number.
Increasing intensity increases the number of ejected electrons, but not their kinetic energy.
Einstein explained this: each photon delivers energy hν. An electron is ejected only if hν ≥ Φ (the work function). Any leftover energy becomes kinetic energy of the electron.
The equation: KE = hν - Φ, where Φ = hν₀.
Sodium metal irradiated with 400 nm light (Φ_Na = 4.4 × 10⁻¹⁹ J).
First find photon energy: E = hc/λ = (6.626 × 10⁻³⁴)(3 × 10⁸) / (400 × 10⁻⁹) = 4.97 × 10⁻¹⁹ J.
KE = E - Φ = 4.97 × 10⁻¹⁹ - 4.4 × 10⁻¹⁹ = 5.7 × 10⁻²⁰ J.
Velocity: v = √(2 × KE / mₑ) = √(2 × 5.7 × 10⁻²⁰ / 9.1 × 10⁻³¹) = 354,000 m/s = 354 km/s.
Light exhibits both wave and particle behaviour.
Diffraction patterns (constructive and destructive interference) are evidence of wave behaviour.
Quantised energy exchange (photoelectric effect) is evidence of particle behaviour.
Matter also exhibits wave-particle duality. Electrons fired through a crystal produce diffraction patterns, just like X-rays.
Any moving particle has an associated wavelength: λ = h / (mv).
For an electron at 3.00 m/s: λ = 6.63 × 10⁻³⁴ / (9.12 × 10⁻³¹ × 3.00) = 2.42 × 10⁻⁴ m. This is large enough to detect.
For an 80.00 kg person at 3.00 m/s: λ = 6.63 × 10⁻³⁴ / (80.00 × 3.00) = 2.76 × 10⁻³⁶ m. This is far too small to observe, which is why we do not notice quantum effects in daily life.
\lambda \times \nu = c = 3.00 \times 10^{8} \; \text{m s}^{-1}Relates wavelength and frequency. If you know one, solve for the other.
E_{\text{photon}} = h\nu = \frac{hc}{\lambda}Energy of a single photon. Use hc/λ when you are given wavelength instead of frequency.
\Delta E = n h \nu \quad (n = 1, 2, 3, \ldots)Planck's quantisation condition. Energy is exchanged in integer multiples of hν.
KE = \frac{1}{2} m_e v^2 = h\nu - \PhiPhotoelectric effect equation. KE of the ejected electron equals photon energy minus the work function.
\Phi = h\nu_0Work function: the minimum photon energy that can eject an electron. ν₀ is the threshold frequency.
\lambda = \frac{h}{mv}de Broglie wavelength of a particle with mass m and velocity v.
Key constants:
h = 6.626 × 10⁻³⁴ J·s
c = 2.998 × 10⁸ m/s
mₑ = 9.109 × 10⁻³¹ kg
1 eV = 1.602 × 10⁻¹⁹ J
1 J = 1 kg·m²·s⁻²
The photoelectric effect is the operating principle behind solar cells (photovoltaics): photons knock electrons loose in a semiconductor, generating electric current. X-ray crystallography uses diffraction of EM radiation to determine the three-dimensional structure of molecules, which is how the structure of DNA was discovered. The de Broglie wavelength of electrons is what makes electron microscopes possible: electrons have wavelengths far shorter than visible light, allowing imaging of objects too small for optical microscopes.
Students often think that increasing the intensity (brightness) of light will increase the kinetic energy of ejected electrons. It does not. Intensity controls only the number of photons, and therefore the number of electrons ejected. Each electron's KE depends on frequency alone.
Students often confuse wavelength and frequency as independent quantities. They are not: once you fix one, the other is determined (since c is constant).
Students often think the de Broglie wavelength is only a theoretical curiosity. It is not. Electron diffraction has been experimentally demonstrated and is the basis of electron microscopy.
Students sometimes assume that quantisation applies only to light. It does not. Energy levels in atoms, vibrational modes, and angular momentum are all quantised.
⚠️ Calculating photon energy from wavelength (E = hc/λ) is a near-certain exam question. Watch your unit conversions: nm to m.
⚠️ Photoelectric effect problems: know how to find the KE of ejected electrons and rearrange for velocity using KE = ½mₑv².
⚠️ Be able to determine whether a given wavelength of light will eject electrons from a metal, given its work function.
⚠️ de Broglie wavelength calculations: be comfortable rearranging λ = h/(mv) and know the units (1 J = 1 kg·m²·s⁻²).
True or false: increasing the intensity of light below the threshold frequency will eventually eject electrons if you make it bright enough.
Fill in the blank: the energy of a photon is ______ proportional to its frequency.
True or false: a 500 nm photon has more energy than a 600 nm photon.
Fill in the blank: the de Broglie wavelength of a particle ______ as its mass increases.
True or false: in hydrogen, wavelength and frequency are independent properties of light.
Answers: 1. False (frequency must exceed ν₀). 2. Directly. 3. True (shorter λ means higher ν and higher E). 4. Decreases. 5. False (they are inversely related through c = λν).
Q: What is the energy of a 500 nm photon?
A: First find frequency: ν = c/λ = (3.00 × 10⁸) / (500 × 10⁻⁹) = 6.00 × 10¹⁴ Hz. Then E = hν = (6.626 × 10⁻³⁴)(6.00 × 10¹⁴) = 3.98 × 10⁻¹⁹ J ≈ 4.0 × 10⁻¹⁹ J.
Q: Electrons are ejected from sodium (Φ = 4.4 × 10⁻¹⁹ J) by 400 nm light. What is their velocity?
A: E_photon = hc/λ = (6.626 × 10⁻³⁴)(3 × 10⁸)/(400 × 10⁻⁹) = 4.97 × 10⁻¹⁹ J. KE = 4.97 × 10⁻¹⁹ - 4.4 × 10⁻¹⁹ = 5.7 × 10⁻²⁰ J. v = √(2 × KE / mₑ) = √(2 × 5.7 × 10⁻²⁰ / 9.1 × 10⁻³¹) ≈ 354 km/s.
Q: What is the de Broglie wavelength of an electron travelling at 3.00 m/s?
A: λ = h/(mv) = (6.63 × 10⁻³⁴) / (9.12 × 10⁻³¹ × 3.00) = 2.42 × 10⁻⁴ m.
Q: Rank the following in order of increasing photon energy: infrared, ultraviolet, visible green, X-ray.
A: Infrared < visible green < ultraviolet < X-ray. Energy increases with frequency (decreases with wavelength).
This connects directly to the Bohr model and the Schrodinger equation (Part 2 of these notes), because quantised photon energies are what produce the discrete line spectra of atoms. It also connects to electron configurations and the periodic table (Part 3), since the quantum mechanical description of electrons underpins how orbitals are filled and why elements in the same group share chemical properties.
electromagnetic spectrum, EM radiation, wavelength, frequency, speed of light, Planck, quantisation, quantization, photon, blackbody radiation, ultraviolet catastrophe, photoelectric effect, work function, threshold frequency, Einstein photon, wave-particle duality, diffraction, interference, constructive interference, destructive interference, de Broglie, matter waves, electron diffraction, electron wavelength, E = hv, E = hc/lambda, KE = hv minus phi, lambda = h/mv, General Physics Ch 12, quantum mechanics intro