Chemistry · General chemistry I · Concept
Photon energy, wavelength and frequency
Light comes in photons, and each photon’s energy is set by its frequency: E = hν, where h is Planck’s constant. Since c = λν, E = hc/λ, so shorter wavelengths carry more energy. Multiplying by Avogadro’s number gives the energy of a mole of photons, the scale of chemical bond energies.
Wavelength and frequency
All electromagnetic radiation travels at c = 2.998 × 10⁸ m/s in a vacuum. Wavelength λ and frequency ν are linked by c = λν, so a shorter wavelength means a higher frequency.
The energy of one photon
Planck’s relation gives the energy of a single photon, with h = 6.626 × 10⁻³⁴ J·s.
Energy per mole of photons
Chemists compare photon energies with bond energies, which are quoted per mole. Multiply the energy of one photon by Avogadro’s number, 6.022 × 10²³ mol⁻¹.
Across the spectrum
Radio waves and microwaves have long wavelengths and tiny photon energies. Visible light spans roughly 400 to 700 nm. Ultraviolet photons, with shorter wavelengths, carry enough energy to break many chemical bonds.
Keep the units in meters
Convert the wavelength to meters before substituting: 1 nm = 10⁻⁹ m. With λ in meters and h in J·s, hc/λ comes out in joules.
Common mistakes
- Leaving the wavelength in nanometers: 425 nm is 4.25 × 10⁻⁷ m.
- Thinking a longer wavelength carries more energy: the energy falls as the wavelength grows.
- Mixing up energy per photon and energy per mole, which differ by a factor of 6.022 × 10²³.
- Using a frequency in MHz or GHz without converting it to hertz, s⁻¹.
Key terms
- Photon
- A packet of light energy, E = hν. A mole of photons carries Avogadro’s number times that energy.
- Wavelength
- The distance between neighboring peaks of a wave, written λ. For light, λ = c ÷ ν, where c is the speed of light and ν the frequency, so shorter wavelengths mean higher frequencies and more energetic photons.
- Frequency
- How many wave cycles pass a point each second, in hertz (Hz = s⁻¹), written ν. For light, c = λν, and a higher frequency means more energy per photon (E = hν).
- Planck constant
- The exact constant h = 6.62607015 × 10⁻³⁴ J·s, which links a photon’s energy to its frequency: E = hν.
- Electromagnetic spectrum
- The full range of electromagnetic radiation arranged by wavelength or frequency, from radio waves through microwaves, infrared, visible, ultraviolet and X-rays to gamma rays.
Work through an example
Find the frequency, the energy of one photon and the energy of a mole of photons for light of wavelength 425 nm.
Find a photon’s energy from its wavelength →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Convert it in Photons & spectrophotometry Check the energy in a Chemistry box Open worked example on a board Chemistry formulas: atomic structureYour existing work stays on this device. Examples open as editable copies.