Speed of Light and Behaviour of Waves
Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, c, of 2.998 × 108 m s−1. This radiation behaves like a wave, 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 periodic oscillations and vibrations. Standing waves exhibit quantization because their wavelengths fit only to discrete integer multiples of certain characteristic lengths. What does this mean? Well, standing waves have specific sizes that are exact multiples of a basic length.
When electromagnetic radiation that passes through two closely spaced narrow slits having dimensions roughly similar to the wavelength will show an interference pattern. This results in patterns from the waves overlapping that either amplify (constructive) or cancel (destructive) each other out.
Electromagnetic radiation also behaves like particles called photons. The energy of a photon is related to the frequency (or alternatively, the wavelength) of the radiation as $E=hν$ (or $E=\frac{hc}{λ}$), where h is Planck’s constant. That light shows behaviour, both wavelike and particle-like, is known as wave-particle duality.
All types of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves. However, they interact differently with matter and have very different practical applications. Electromagnetic radiation are generated by exciting matter to higher energies, such heating. The light emitted can be either continuous, like sunlight we see, or discrete, coming from specific types of excited atoms.
Spectral Analysis and Paradoxes in History
Often times, continuous spectra distributions to black body radiation at a suitable temperature for approximation. To obtain the line spectrum of hydrogen, light passes from an electrified hydrogen gas tube 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 could not explain within the existing framework of classical mechanics and classical electromagnetism. These three 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 The resolution of these paradoxes ultimately led to quantum theories that superseded the classical theories.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 $h=6.626×10^{−34}\;J\;s$ |
| $\frac{1}{λ}=R_∞(\frac{1}{n_1^2}−\frac{1}{n_2^2})$ |