wavelength

Examples of wavelength in the following topics:

• Electromagnetic Spectrum

  • Wavelength is inversely proportional to wave frequency; hence, gamma rays have very short wavelengths that are a fraction of the size of atoms, whereas other wavelengths can be as long as the universe.
  • Wavelengths of electromagnetic radiation, no matter what medium they are traveling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.
  • The behavior of electromagnetic radiation depends on its wavelength.
  • Wave number = 1/wavelength in cm Speed of light = wavelength x frequency Energy = Planck's constant x frequency.
  • The wavelengths of various regions of the electromagnetic spectrum are shown alongside an approximate proxy for size of the wavelength.

• Background

  • Visible wavelengths cover a range from approximately 400 to 800 nm.
  • The longest visible wavelength is red and the shortest is violet.
  • Other common colors of the spectrum, in order of decreasing wavelength, may be remembered by the mnemonic: ROY G BIV.
  • In horizontal diagrams, such as the one on the bottom left, wavelength will increase on moving from left to right.
  • The remaining light will then assume the complementary color to the wavelength(s) absorbed.

• The Electromagnetic Spectrum

  • This electromagnetic spectrum ranges from very short wavelengths (including gamma and x-rays) to very long wavelengths (including microwaves and broadcast radio waves).
  • The following chart displays many of the important regions of this spectrum, and demonstrates the inverse relationship between wavelength and frequency (shown in the top equation below the chart).
  • The bottom equation describes this relationship, which provides the energy carried by a photon of a given wavelength of radiation.

• Planck's Quantum Theory

  • Wavelength is the distance from one wave peak to the next, which can be measured in meters.
  • When the electrons return to the ground state, they emit energy of various wavelengths.
  • A prism can be used to separate the wavelengths, making them easy to identify.
  • Instead, there are discrete lines created by different wavelengths.
  • The distance used to determine the wavelength is shown.

• The de Broglie Wavelength

  • The de Broglie wavelength is inversely proportional to the momentum of a particle.
  • The de Broglie equations relate the wavelength (λ) to the momentum (p), and the frequency (f) to the kinetic energy (E) (excluding its rest energy and any potential energy) of a particle:
  • At these temperatures, the thermal de Broglie wavelengths come into the micrometer range.
  • The researchers calculated a de Broglie wavelength of the most probable C60 velocity as 2.5 pm.
  • Use the de Broglie equations to determine the wavelength, momentum, frequency, or kinetic energy of particles

• UV-Visible Absorption Spectra

  • Ultraviolet radiation having wavelengths less than 200 nm is difficult to handle, and is seldom used as a routine tool for structural analysis.
  • An optical spectrometer records the wavelengths at which absorption occurs, together with the degree of absorption at each wavelength.
  • The resulting spectrum is presented as a graph of absorbance (A) versus wavelength, as in the isoprene spectrum shown below.
  • Fortunately, conjugation generally moves the absorption maxima to longer wavelengths, as in the case of isoprene, so conjugation becomes the major structural feature identified by this technique.
  • The magnitude ofε reflects both the size of the chromophore and the probability that light of a given wavelength will be absorbed when it strikes the chromophore.

• Emission Spectrum of the Hydrogen Atom

  • The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula: $\frac { 1 }{ \lambda_{vac} } =RZ^2( \frac { 1 }{ {n_1 }^{ 2 } } -\frac { 1 }{ { n_2 }^{ 2 } })$,
  • where R is the Rydberg constant (approximately 1.09737 x 107 m-1), $\lambda_{vac}$ is the wavelength of the light emitted in vacuum, Z is the atomic number, and n1 and n2 are integers representing the energy levels involved such that n1 < n2.
  • Lines are named sequentially starting from the longest wavelength/lowest frequency of the series using Greek letters within each series.
  • Lines outside of the visible spectrum typically cannot be seen in observations of sunlight, as the atmosphere absorbs most infrared and ultraviolet wavelengths through the action of water vapor and ozone molecules respectively.

• Properties of Waves and Light

  • There are three measurable properties of wave motion: amplitude, wavelength, and frequency (the number of vibrations per second).
  • The relation between the wavelength λ (Greek lambda) and frequency of a wave ν (Greek nu) is determined by the propagation velocity v, such that
  • When utilizing these equations to determine wavelength, frequency, or velocity by manipulation of the equation, it is important to note that wavelengths are expressed in units of length, such as meters, centimeters, nanometers, etc; and frequency is typically expressed as megahertz or hertz (s–1).
  • What is the wavelength of the musical note A = 440 hz when it is propagated through air in which the velocity of sound is 343 m s–1?
  • This image shows the anatomy of a sine curve: the crest is the peak of each wave, and the trough is the valley; the amplitude is the distance between the crest and the x-axis; and the wavelength is the distance between two crests (or two troughs).

• Introduction

  • The portion of the infrared region most useful for analysis of organic compounds is not immediately adjacent to the visible spectrum, but is that having a wavelength range from 2,500 to 16,000 nm, with a corresponding frequency range from 1.9*1013 to 1.2*1014 Hz.
  • Wavelength units are in micrometers, microns (μ), instead of nanometers for the same reason.
  • Most infrared spectra are displayed on a linear frequency scale, as shown here, but in some older texts a linear wavelength scale is used.

• Color

  • Large energy differences should correspond to smaller wavelengths and purple colors, while small energy differences should result in large wavelengths and colors closer to red.
  • For example, you might expect to see red for a complex with a small energy gap and large wavelength.
  • A decrease in the wavelength of the complimentary color indicates the energy gap is increasing and can be used to make general rankings in the strengths of electric fields given off by ligands.