frequency

Examples of frequency in the following topics:

• Group Frequencies

• Electromagnetic Spectrum

  • The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation.
  • The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation.
  • Frequencies observed in astronomy range from 2.4×1023 Hz (1 GeV gamma rays) down to the local plasma frequency of the ionized interstellar medium (~1 kHz).
  • Wave number = 1/wavelength in cm Speed of light = wavelength x frequency Energy = Planck's constant x frequency.
  • Calculate frequency or photon energy, identify the three physical properties of electromagnetic waves

• Planck's Quantum Theory

  • From the wave perspective, all forms of EM radiation may be described in terms of their wavelength and frequency.
  • Frequency is the number of waves that pass by a given point each second.
  • For each metal, there is a minimum threshold frequency of EM radiation at which the effect will occur.
  • Instead, there is a clear-cut minimum frequency of light that triggers electron ejection.
  • The implication was that frequency is directly proportional to energy, with the higher light frequencies having more energy.

• The Photoelectric Effect

  • It also led to Max Planck's discovery of quanta (E=h$\nu$), which links frequency ($\nu$) with photon energy (E).
  • The photons of a beam of light have a characteristic energy proportional to the frequency of the light.
  • This frequency is called the threshold frequency.
  • where h is the Planck constant (6.626 x 10-34 m2kg/s) and f is the frequency of the incident photon.
  • where f0 is the threshold frequency for the metal.

• The Electromagnetic Spectrum

  • 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 energy associated with a given segment of the spectrum is proportional to its frequency.

• Vibrational Spectroscopy

  • The exact frequency at which a given vibration occurs is determined by the strengths of the bonds involved and the mass of the component atoms.
  • i) Stretching frequencies are higher than corresponding bending frequencies.
  • ii) Bonds to hydrogen have higher stretching frequencies than those to heavier atoms.
  • iii) Triple bonds have higher stretching frequencies than corresponding double bonds, which in turn have higher frequencies than single bonds.
  • Absorption bands in the 4000 to 1450 cm-1 region are usually due to stretching vibrations of diatomic units, and this is sometimes called the group frequency region.

• The Bohr Model

  • In terms of electron emission, this would represent a continuum of frequencies being emitted since, as the electron moved closer to the nucleus, it would move faster and would emit a different frequency than those experimentally observed.
  • According to the Maxwell theory, the frequency (ν) of classical radiation is equal to the rotation frequency (νrot) of the electron in its orbit, with harmonics at integer multiples of this frequency.
  • These jumps reproduce the frequency of the k-th harmonic of orbit n.
  • For sufficiently large values of n (so-called Rydberg states), the two orbits involved in the emission process have nearly the same rotation frequency so that the classical orbital frequency is not ambiguous.
  • But for small n (or large k), the radiation frequency has no unambiguous classical interpretation.

• The Chemical Shift

  • Unlike infrared and uv-visible spectroscopy, where absorption peaks are uniquely located by a frequency or wavelength, the location of different nmr resonance signals is dependent on both the external magnetic field strength and the rf frequency.
  • Since no two magnets will have exactly the same field, resonance frequencies will vary accordingly and an alternative method for characterizing and specifying the location of nmr signals is needed.
  • To correct these frequency differences for their field dependence, we divide them by the spectrometer frequency (100 or 500 MHz in the example), as shown in the diagram above.
  • Note that νref is the resonant frequency of the reference signal and νsamp is the frequency of the sample signal.

• 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.
  • The frequency scale at the bottom of the chart is given in units of reciprocal centimeters (cm-1) rather than Hz, because the numbers are more manageable.
  • The reciprocal centimeter is the number of wave cycles in one centimeter; whereas, frequency in cycles per second or Hz is equal to the number of wave cycles in 3*1010 cm (the distance covered by light in one second).
  • Most infrared spectra are displayed on a linear frequency scale, as shown here, but in some older texts a linear wavelength scale is used.

• Introduction

  • For nmr purposes, this small energy difference (ΔE) is usually given as a frequency in units of MHz (106 Hz), ranging from 20 to 900 Mz, depending on the magnetic field strength and the specific nucleus being studied.
  • Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state.
  • The following diagram displays energy differences for the proton spin states (as frequencies).
  • The following diagram gives the approximate frequencies that correspond to the spin state energy separations for each of these nuclei in an external magnetic field of 2.35 T.
  • The formula in the colored box shows the direct correlation of frequency (energy difference) with magnetic moment (h = Planck's constant = 6.626069•10-34 Js).