No, Planck's derivation of the energy element, often denoted as "hv" or "hf" (where h is Planck's constant and v or f represents the frequency), is not based on a standing wave formed by the motion of an ether composed of matter.
In fact, Planck's derivation of the energy element is closely related to his work on black-body radiation and the quantization of energy. Planck introduced the concept of energy quantization to explain the observed behavior of electromagnetic radiation emitted by a black body. He proposed that the energy of electromagnetic radiation is not continuous but rather quantized into discrete packets or "quanta."
Planck's idea of quantized energy was a departure from the classical wave theory of light, which assumed that energy could be emitted or absorbed in a continuous manner. Instead, Planck postulated that energy could only exist in multiples of a fundamental unit, later known as the Planck constant (h).
Planck's derivation of the energy element involved assuming that energy could only be emitted or absorbed in discrete amounts proportional to the frequency of the radiation. This assumption led to the famous equation E = hv, where E is the energy, h is Planck's constant, and v is the frequency of the radiation.
It's important to note that Planck's work on the quantization of energy was a significant contribution to the development of quantum theory. It played a crucial role in the understanding of various phenomena, including the photoelectric effect, which later led to Albert Einstein's explanation of the particle-like nature of light in terms of photons.