E=hf
Quantum and Nuclear | Light Sound and Waves

Frequency and energy

Physics Narrative for 14-16 Supporting Physics Teaching

Frequency and energy shifted by each photon are linked

The frequency of a visible photon is measured in terahertz (400–700 terahertz). The energy of such photons is measured in attojoules (30–50 attojoule).

The energy increases with the frequency, but you're not getting many joules for each hertz. The increase is proportional.

The constant of proportionality is rather famous: Planck's constant. It is a very small number, h is 6.67 × 10-34 joule inverse hertz.

Then the connection between the energy and frequency of a photon is remarkably simple: E = h × f.

Energy related to frequency

The proportionality between the energy shifted by each photon and the frequency of that photon was established in the early years of the 20th century, and was the start of the revolution in our understanding of the universe that is quantum physics. Nothing was ever quite the same again. This was especially traumatic for Planck, a rather conservative thinker, who did such fundamental work in the area that his name is used for the constant that relates energy to frequency. It's now a quantum signature: whenever you meet h, Planck's constant, you are in the realm of the quantum. This is where the physics of the very small rules. And the rules are often counter-intuitive. Think about this for a while and you won't be so surprised: our intuitions are developed over timescales of seconds, and distances of metres – far removed from the time and space where individual photons interact.

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