## Summarizing Lessons on Electromagnetic Energy

Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, *c*, of 2.998 × 10^{8} m s^{−1}. This radiation shows wavelike behavior, which can be characterized by a frequency, *ν*, and a wavelength, *λ*, such that *c* = *λν*.

Light is an example of a travelling wave. Other important wave phenomena include standing waves, periodic oscillations, and vibrations. Standing waves exhibit quantization, since their wavelengths are limited to discrete integer multiples of some characteristic lengths.

Electromagnetic radiation that passes through two closely spaced narrow slits having dimensions roughly similar to the wavelength will show an interference pattern that is a result of constructive and destructive interference of the waves.

Electromagnetic radiation also demonstrates properties of particles called photons. The energy of a photon is related to the frequency (or alternatively, the wavelength) of the radiation as *E* = *hν* (or \(E = \cfrac{hc}{λ}\)), where *h* is Planck’s constant. That light demonstrates both wavelike and particle-like behavior is known as wave-particle duality.

All forms of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves interact differently with matter and have very different practical applications.

Electromagnetic radiation can be generated by exciting matter to higher energies, such as by heating it. The emitted light can be either continuous (incandescent sources like the sun) or discrete (from specific types of excited atoms).

Continuous spectra often have distributions that can be approximated as blackbody radiation at some appropriate temperature. The line spectrum of hydrogen can be obtained by passing the light from an electrified tube of hydrogen gas through a prism. This line spectrum was simple enough that an empirical formula called the Rydberg formula could be derived from the spectrum.

Three historically important paradoxes from the late 19th and early 20th centuries that could not be explained within the existing framework of classical mechanics and classical electromagnetism were the blackbody problem, the photoelectric effect, and the discrete spectra of atoms. The resolution of these paradoxes ultimately led to quantum theories that superseded the classical theories.

### Key Equations

- \(c = λν\)
- \(E = hν = \frac{hc}{λ},\) where
*h*= 6.626 × 10^{34}J s - \(\frac{1}{λ} = R_∞ \left ( \frac{1}{n_1^2} \; – \;\frac{1}{n_2^2} \right )\)