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If we observe the formula $E=hf$ which solved the ultraviolet catastrophe. We know that before Planck proposed the solution to the ultraviolet catastrophe, light was considered as continuous stream of energy.

But Planck discovered that light is made of individual packets of energy, at the rate of $hf$, which can only be absorbed, or emitted, in quite discrete amounts.

But my question is that if light is made up of quanta, one quantum of electromagnetic energy is called a photon. Then how can photons have a frequency since photon is a particle. So how can the formula $E=hf$ be used?

Kyle Kanos
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avito009
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2 Answers2

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A photon isn't just a particle. It's an object that can be represented as either a wave or a particle, and each representation reveals different facets of its dynamics (and becomes more or less appropriate depending on wavelength). The frequency descriptor applies to the wave representation rather than to the particle representation. If you're thinking of light as a particle, frequency is only important in that it tells you the energy of the photon.

probably_someone
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But my question is that if light is made up of quanta, one quantum of electromagnetic energy is called a photon.

Frequency is a well defined number in the classical electromagnetic wave. It is defined by the change in the amplitude of the electric and magnetic field in space and time.

Then how can photons have a frequency since photon is a particle. So how can the formula E=hf be used

The classical wave emerges from zillions of photons, not in an additive way like water molecules in a stream, but in a superposition of the quantum mechanical wave function of the individual photon that build up the classical wave of frequency nu.

The wave function of the photon in its complex amplitude

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carries the information of the frequency which will be seen in the varying electric and magnetic fields of the emergent classical beam.

Measurement of the photon itself can only give the energy and the spin orientation. It is through the formula E=h*nu that the energy of the photon defines the frequency that would manifest a classical wave of frequency nu, for a large ensemble of photons with energy E.

This link might help get an indtuition of how photons build up the classical wave.

anna v
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