Source: The Atom lecture, Purdue University General Chemistry
Difficulty: Beginner to Intermediate | Prerequisites: Basic algebra, comfort with scientific notation
Tags: light, electromagnetic radiation, wavelength, frequency, speed of light, photon energy, Planck's constant, EM spectrum, wave-particle duality, visible light, general chemistry
Light is one of the main tools chemists use to study atoms, because the way atoms absorb and emit light reveals their internal structure. This section covers what light actually is (electromagnetic radiation), how it is measured (wavelength and frequency), how its energy is calculated (Planck's equation), and the key insight that light behaves as both a wave and a particle. You need to be comfortable with these relationships before moving on to the Bohr model and electron energy levels.
Light is electromagnetic radiation that behaves as both a wave and a particle. Its wavelength and frequency are inversely proportional, and their product always equals the speed of light. The energy of a single photon is directly proportional to its frequency, calculated using Planck's constant.
Electromagnetic radiation
Energy that travels through space as waves, differing in the amount of energy carried at different frequencies. In simple terms, it is the broad family of energy that includes radio waves, microwaves, visible light, and X-rays.
Wavelength (lambda, λ)
The distance between two corresponding points on a wave (e.g. crest to crest). Measured in metres (m) or nanometres (nm, where 1 nm = 10^-9 m). Think of it as how "stretched out" each wave cycle is.
Frequency (ν, nu)
The number of wave cycles that pass a given point in one second. Measured in hertz (Hz), which is the same as inverse seconds (s^-1). Think of it as how rapidly the wave oscillates.
Speed of light (c)
The constant speed at which all electromagnetic radiation travels in a vacuum: 3.0 x 10^8 m/s. This value ties wavelength and frequency together.
Photon
A single "packet" or quantum of light energy. Light travels as a stream of these discrete packets, each carrying a specific amount of energy.
Planck's constant (h)
A fundamental physical constant, 6.626 x 10^-34 J·s. It links the energy of a photon to its frequency. In simple terms, it is the conversion factor between how fast a wave oscillates and how much energy each photon carries.
Wave-particle duality
The principle that light has properties of both a wave (wavelength, frequency, interference) and a particle (photons, discrete energy packets) at the same time.
Visible light
The narrow band of the electromagnetic spectrum that human eyes can detect, spanning roughly 400 to 750 nm in wavelength (or 7.5 x 10^14 to 4.0 x 10^14 s^-1 in frequency). The colours run from violet (short wavelength) to red (long wavelength), often remembered as ROY G BIV.
Wavelength and frequency are inversely proportional.
When one increases, the other decreases.
They are linked by the speed of light: c = λ × ν.
Rearranged: frequency = c / λ, and wavelength = c / ν.
From highest energy (shortest wavelength) to lowest energy (longest wavelength): gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves.
Visible light sits in a narrow window of this spectrum, between about 400 nm (violet) and 750 nm (red).
Everything outside that window is invisible to the human eye but still real electromagnetic radiation.
Light behaves as a wave: it has wavelength, frequency, and can interfere with other waves.
Light also behaves as a particle: it comes in discrete packets (photons), each with a definite energy.
Both descriptions are simultaneously true. This was one of the revolutionary insights of early 20th-century physics.
The energy of a single photon is directly proportional to its frequency.
Higher frequency means higher energy per photon.
Because wavelength and frequency are inversely related, higher energy also means shorter wavelength.
Speed of light equation
c = λ × ν
Where c = 3.0 x 10^8 m/s, λ = wavelength in metres, ν = frequency in Hz (s^-1).
Photon energy (frequency form)
E = h × ν
Where E = energy in joules (J), h = 6.626 x 10^-34 J·s, ν = frequency in Hz.
Photon energy (wavelength form)
E = h × c / λ
This is the same equation rearranged by substituting ν = c / λ. Useful when you are given wavelength instead of frequency.
Remote controls use infrared light, and microwave ovens use microwaves, both of which are electromagnetic radiation outside the visible range. Medical X-rays exploit the high energy of short-wavelength radiation to pass through soft tissue but not bone, producing an image of the skeleton.
Students often confuse wavelength and frequency, thinking they increase together. They do not. They are inversely proportional: as one goes up, the other goes down.
Some students assume that all light is visible. Visible light is only a tiny slice of the electromagnetic spectrum. Most electromagnetic radiation is invisible.
A common error is forgetting to convert nanometres to metres before using the speed of light equation. The constant c is in m/s, so wavelength must be in metres.
Students sometimes think that a photon's energy depends on the intensity (brightness) of the light. It does not. Photon energy depends on frequency. Brightness relates to the number of photons, not the energy per photon.
⚠️ You will be asked to calculate wavelength from frequency (and vice versa) using c = λν. Practise rearranging this equation both ways.
⚠️ Photon energy calculations (E = hν or E = hc/λ) are a staple of general chemistry exams. Make sure your units are consistent (metres, not nanometres).
⚠️ Know the order of the electromagnetic spectrum from highest to lowest energy. A common exam question asks you to rank types of radiation.
⚠️ Wave-particle duality is a conceptual favourite. Be ready to explain why light is described as both a wave and a particle.
True or false: wavelength and frequency are directly proportional. (False, they are inversely proportional.)
Fill in the blank: the speed of light is approximately ______ m/s. (3.0 x 10^8.)
True or false: a photon with a higher frequency has less energy. (False, higher frequency means higher energy.)
Fill in the blank: Planck's constant has a value of ______ J·s. (6.626 x 10^-34.)
True or false: visible light spans the entire electromagnetic spectrum. (False, it is only a small portion.)
Q: A photon has a wavelength of 500 nm. What is its frequency?
A: First convert 500 nm to metres: 500 x 10^-9 m = 5.0 x 10^-7 m. Then ν = c / λ = (3.0 x 10^8 m/s) / (5.0 x 10^-7 m) = 6.0 x 10^14 Hz.
Q: Which has more energy per photon: red light or blue light?
A: Blue light, because it has a shorter wavelength and therefore a higher frequency. Since E = hν, higher frequency means higher energy.
Q: What is the energy of a photon with a frequency of 5.0 x 10^14 Hz?
A: E = hν = (6.626 x 10^-34 J·s)(5.0 x 10^14 s^-1) = 3.3 x 10^-19 J.
Q: List the types of electromagnetic radiation in order from highest energy to lowest energy.
A: Gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves.
Q: Why must wavelength be converted to metres before using c = λν?
A: Because the speed of light (c) is expressed in metres per second. If wavelength is left in nanometres, the units will not cancel properly and the answer will be wrong by a factor of 10^9.
This material connects directly to the Bohr model and atomic emission spectra, where the specific wavelengths of light emitted by atoms reveal their electron energy levels. It also underpins spectroscopy techniques used throughout chemistry and physics. Understanding photon energy is essential for later topics such as the photoelectric effect and quantum mechanics.
light, electromagnetic radiation, EM spectrum, wavelength, frequency, speed of light, c equals lambda nu, photon, photon energy, Planck's constant, h nu, E equals hf, wave-particle duality, visible light, ROY G BIV, ultraviolet, infrared, X-ray, gamma ray, microwave, radio wave, hertz, nanometre, general chemistry light, Purdue general chemistry