An advertising sign gives off red and green light. \begin{equation} \begin{array}{l}{\text { a. Which light has higher energy? }} \\ {\text { b. One of the colors has a wavelength of }} \\ {680 \mathrm{nm} \text { and the other has a wavelength of }} \\ {500 . \text { Which color has which wavelength? }}\end{array} \end{equation}

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ from one another based on their wavelength. Electromagnetic radiation includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

The visible part of the spectrum, which concerns us when discussing colors like red and green, only constitutes a small portion but is crucial for the human experience. Red light, located towards one end of the visible spectrum, has a longer wavelength, while green light, positioned closer to the middle, has a shorter wavelength.

To remember the order of colors in the visible spectrum, think of the acronym ROYGBIV which stands for Red, Orange, Yellow, Green, Blue, Indigo, Violet. As we move from red to violet in this sequence, the wavelength decreases, which typically increases energy.

Planck's constant (\( h \) ) is a fundamental figure in quantum mechanics commanding the relationship between energy and frequency for photons, the particles that constitute light. The constant is approximately equal to 6.626 x 10^-34 joule seconds.

Understanding Planck's constant allows scientists to more accurately describe the quantum behavior of light and atoms. Its application is not only foundational in the formulation of quantum theory but also useful in various realms of physics and chemistry, including understanding the energy levels of electrons in an atom.

It's Planck's constant that directly links the concept of light as both wave and particle, setting the stage for modern quantum physics where such dual properties are the norm, not the exception.

The relationship between the frequency of light and its energy is imperative to understanding its behavior. As explained by the equation \( E = h * f \), the energy (\( E \) ) of a photon is directly proportional to its frequency (\( f \) ).

Frequency is the number of waves that pass a point per second, and since energy increases with frequency, it means that as we observe light with a shorter wavelength (like green compared to red), we are looking at light with a higher frequency and consequently, higher energy.

The exercise that asks to differentiate between the energy levels of red and green light, and assign the wavelengths accordingly, uses this fundamental relationship. As a result, it's not just a question of color perception but a deeper inquiry into the intrinsic properties of light defined by its frequency and energy.