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How does photon energy depend on the frequency of electromagnetic radiation?

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Diagram of a tree leaf illustrating photosynthesis, with arrows showing sunlight, water, and carbon dioxide entering the leaf and sugars and oxygen being produced. A person is shown beside the tree to demonstrate the exchange of oxygen and carbon dioxide between plants and animals. — electromagnetic radiation Diagram of photosynthesis showing how water, light, and carbon dioxide are absorbed by a plant to produce oxygen, sugars, and more carbon dioxide.

In quantum theory, the energy of a photon—the discrete packet of energy that constitutes electromagnetic radiation—is directly proportional to the frequency of the radiation.

This relationship is expressed by the equation:

$E = h ν$

In this formula:
* $E$ represents the energy of the photon.
* $h$ is Planck’s constant, a fundamental physical constant approximately equal to $6.626 \times 10^{- 34}$ joule-seconds.
* $ν$ (the Greek letter nu) represents the frequency of the electromagnetic wave.

Because $h$ is a constant, the energy of a photon increases linearly as the frequency of the radiation increases. This principle, established by Max Planck and further developed by Albert Einstein, demonstrates that higher-frequency radiation—such as ultraviolet light, X-rays, and gamma rays—consists of more energetic photons than lower-frequency radiation, such as radio waves or microwaves.123