What is a photon? How is its energy related to its frequency? To it wavelength?

Imagine light, not as a continuous wave, but as a stream of tiny particles or 'packets' of energy. These packets are known as photons, which can be thought of as the fundamental units, or quanta, of light. Each photon is indivisible, meaning it cannot be split into smaller parts, making it the smallest quantity of electromagnetic radiation that can exist.

Photons exhibit both wave-like and particle-like properties, a duality that is at the heart of quantum mechanics. Despite having no mass, they carry momentum and can exert pressure on objects – a phenomenon exploited in technologies such as solar sails for space exploration. Interestingly, photons are not slowed down by inertial resistance, allowing them to travel at a constant speed – the speed of light – in a vacuum. Furthermore, each photon is characterized by its wavelength or frequency, which determines its color in the visible spectrum and its energy level.

In essence, understanding photons as quanta of light provides the basis for comprehending fundamental interactions in the universe, from the functioning of lasers and LEDs to the mechanisms of photosynthesis in plants.

Electromagnetic radiation encompasses a wide array of phenomena including what we commonly know as light, radio waves, microwaves, X-rays, and gamma rays. It's all part of the electromagnetic spectrum, with each type of radiation differing in wavelength and frequency. Light that we see with our eyes is just a small section of this broad spectrum.

In its essence, electromagnetic radiation is a form of energy that is propagated through space or matter, carrying the energy from one place to another without the need for a medium. It's made up of both electric and magnetic field components, which oscillate perpendicularly to each other and to the direction of propagation.

What's fascinating is that while the speed of electromagnetic radiation remains constant in a vacuum (approximately 3 x 10^8 meters per second), its energy can vary greatly depending on the frequency or wavelength. This variability in energy is what defines the different types of electromagnetic radiation and determines their interactions with matter, from transmitting information through space to causing molecular changes in living organisms.

The connection between the energy of photons and electromagnetic radiation is finely tuned by a fundamental constant in physics known as Planck's constant, symbolized by 'h'. This constant has an incredibly small value of approximately 6.626 x 10^-34 joule seconds (Js), yet its significance is monumental in the realm of quantum mechanics.

Planck's constant provides the scale of quantization that links the energy carried by a photon with its frequency; a higher frequency (or shorter wavelength) means more energy per photon. The relationship is expressed by the formula:
E = h * f

where E is the energy of the photon in joules, f is the frequency in hertz, and h is Planck's constant. This equation signifies that energy is quantized – it can only exist in specific, discrete amounts rather than any arbitrary value. Planck's constant also plays a critical role in the Heisenberg Uncertainty Principle, which states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. Ultimately, Planck's constant is a key player in understanding the microscopic world, influencing the behavior of atoms and subatomic particles and challenging our classical views of physics.