In the context of classical electromagnetism and wave theory, the energy of a photon is indeed proportional to its frequency. The energy (E) of a photon is given by the Planck-Einstein relation:
E = h * f
where: E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 joule-seconds), f is the frequency of the photon.
However, the amplitude of a photon is not a well-defined concept in the same way it is for classical waves. In classical wave theory, like in water waves or sound waves, amplitude refers to the maximum displacement or intensity of the wave from its equilibrium position. The higher the amplitude, the more energy the wave carries.
Photons, on the other hand, are considered elementary particles of light and other electromagnetic radiation. They exhibit both wave-like and particle-like properties, which is known as wave-particle duality. In the wave-like description, photons are described by electromagnetic waves, and their energy is related to their frequency as mentioned earlier.
However, in the particle-like description, photons are quantized packets of energy, and they do not have a size or a well-defined amplitude in the way classical waves do. In this particle-like picture, the energy of a photon is determined solely by its frequency, and it is localized at a point in space.
So, to summarize, the energy of a photon is proportional to its frequency, but the concept of amplitude does not apply to photons in the same way it does to classical waves. Instead, the particle-like nature of photons is better described by their energy and momentum, which are proportional to the photon's frequency and wave vector, respectively.