# Why do high frequency waves have high energy [duplicate]

It is known that electromagnetic waves with a high frequency possess a greater amount of energy than waves with lower frequencies. Why is this the case? Does it have anything to do with Planck's law?

It is known that electromagnetic waves with a high frequency possess a greater amount of energy than waves with lower frequencies.

This isn't quite true. The energy carried by an electromagnetic wave is the product of two independent factors:

• the energy of each individual photon, which is given by the Planck law $$E_\mathrm{photon}=h\nu,$$ in terms of the light's frequency $\nu$ and the Planck constant $h$, and
• the number $N$ of photons present in the beam.

For light that's far away from the quantum regime, the total quantum-mechanical energy $E=Nh\nu$ transitions over into the classical regime, where it becomes better described by the classical intensity, which is proportional to the amplitude of the electric-field oscillations in the light. In that regime, the light can carry any amount of energy you wish to put into it.

However, that property fails to be true at low energies, where the photon number $N$ is of order $1$. In this regime, quantum mechanics takes over, and the light becomes incapable of carrying less energy than the photon energy $h\nu$: it either has one photon's worth, or none at all. And, because of the Planck law, this minimal energy increases with the frequency.

The reason this is important is that if you have a biological tissue that's absorbing, say, one UV photon's worth of energy spread over a bunch of infrared photons, then the energy absorbed by each individual molecule can be quite small. However, if the light is in the UV, then it's impossible to break that energy down into smaller chunks, and it's a single molecule that needs to take the entire hit, and if the photon energy is big enough then that will take the molecule over its damage threshold.

Quantum mechanics tells you that the energy and frequency of an individual photon are related as $$E = h\nu$$ where $h$ is Planck's constant. This is part of the Quantum Hypothesis of Planck.

I don't think that an electromagnetic wave carries more energy depending of the frequency as the energy of the electromagnetic field (or better, its density) is
$E=\frac{1}{2}\cdot \epsilon_0 \cdot {E_0}^2$
so it depends the maximum value of the electric field $E_0$.
Differently, a single photon has the energy
$E=h\nu$
so a single photon which frequency is higher, carries higher energy.

• Example of a possible misunderstanding: a wave can be composed by 5 photons with high frequency and thus energy, or by 100000 photons with low frequency and energy (each) but in total, adding the single photon ones, the wave "has" more energy. Aug 30, 2018 at 10:24
• A wave does not "carry" photons, instead it carries energy; a wave "exchanges" energy with particles in units of photons. The two are not the same thing. Aug 30, 2018 at 15:25