Define the frequency of electromagnetic radiation. How is frequency related to wavelength?

Wave-particle duality is a fundamental concept of quantum mechanics that tells us that every particle or quantum entity exhibits both wave-like and particle-like properties. This means that entities such as photons, the basic units of light, can behave like a wave when propagating through space, and like a particle when interacting with matter, such as being detected by a camera or absorbed by an atom.

For instance, light can be diffracted and interfered like a wave, which is evident when passing light through slits, resulting in a pattern of dark and light areas—yet it can also be counted as photons, acting like discrete packets of energy. This dual nature was first proposed by physicist Louis de Broglie and was instrumental in the development of quantum mechanics. This concept also ties into the relationship between frequency and wavelength of electromagnetic radiation through the equation \(E = hf\), where \(E\) stands for energy, \(h\) is Planck's constant, and \(f\) is the frequency of the wave.
Understanding this duality is essential in fields such as quantum optics, and quantum information technology, and helps explain phenomena that classical physics cannot.

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ from one another in terms of wavelength (or frequency). It ranges from very long wavelengths, like those used in radio communication, to extremely short wavelengths, such as those seen in gamma rays.

The spectrum is usually depicted as a continuous range that includes, from the longest to the shortest wavelength: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each of these categories of electromagnetic waves has specific characteristics and uses. For example, visible light enables us to see the world around us and is essential for photosynthesis in plants, while X-rays can penetrate soft tissues of the body and are used in medical imaging.
The frequency of electromagnetic radiation plays a critical role in determining its position on the spectrum and its interactions with matter. For instance, higher frequencies, such as those of X-rays, carry more energy and have the power to ionize atoms and may pose a health risk, while lower frequencies like radio waves are typically non-ionizing and are used for broadcasting and communication purposes.

The speed of light in a vacuum is a fundamental physical constant that plays a vital role in the understanding of the universe. It is denoted by the symbol \(c\) and has a value of approximately 3 x \(10^8\) meters per second.

Light speed is crucial because it sets the maximum speed at which all energy, matter, and information in the universe can travel. According to Einstein's theory of relativity, nothing can travel faster than the speed of light. It is also an essential component of the equation \(c = f\lambda\), which relates the speed of light (\(c\)), frequency (\(f\)), and wavelength (\(\lambda\)) of electromagnetic waves.
The constancy of the speed of light leads to profound consequences in physics, including time dilation and length contraction as predicted by special relativity. It also means that we are looking back in time when we observe distant celestial objects, because their light has taken years to travel across space to reach us. Thus, the speed of light is not just a measure of velocity; it is a bridge between space and time, profoundly affecting our understanding of the structure and evolution of the universe.