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Describing Very Low Frequency Radio Waves

A hectometre (hm) is a unit of length equal to 100 metres, and it is used to describe very long wavelengths in the Very Low Frequency (VLF) and Low Frequency (LF) bands of the electromagnetic spectrum. Wavelengths in the hectometre range correspond to frequencies between approximately 3 kHz and 3 MHz. These long wavelengths are typically used for maritime navigation, military submarine communication, AM radio broadcasting, and time signal transmissions.

For example, a signal at 300 kHz has a wavelength of 1 kilometre, or 10 hectometres, and a signal at 1 MHz corresponds to 3 hectometres. These long wavelengths have the unique ability to travel long distances and penetrate water and the ground, which is why they are used in submarine communications and emergency broadcast systems.

Using hectometres to express wavelength offers a practical scale for understanding wave propagation over great distances. It also aids in antenna design, where very large antennas—often hundreds of metres long—are needed to efficiently transmit or receive these frequencies. Understanding wavelength in hectometres is important in geophysics, radio astronomy, and large-scale communications infrastructure.

A Quantum Limit of the Electron

The electron Compton wavelength is a fundamental constant in quantum physics that represents the limit at which the wave-like nature of an electron becomes significant in high-energy interactions. It is defined by the equation λ = h / (mₑ c), where h is Planck’s constant, mₑ is the mass of the electron, and c is the speed of light. The value of the electron Compton wavelength is approximately 2.426 × 10⁻¹² meters (or 2.426 picometers). This is significantly larger than the Compton wavelengths of heavier particles like the proton or neutron, reflecting the electron's much smaller mass.

The Compton wavelength is important because it sets a quantum limit on how precisely a particle's position can be defined without introducing enough energy to create particle-antiparticle pairs (like an electron and a positron). It plays a key role in quantum electrodynamics (QED), high-energy physics, and particle interactions involving photons and electrons. For instance, Compton scattering, a process where X-rays scatter off electrons, directly involves this wavelength. Understanding the electron’s Compton wavelength helps physicists analyze the structure of matter, radiation–matter interactions, and the behavior of particles at quantum scales.