Physics
Energy and Frequency Relationship
The energy and frequency relationship in physics refers to the direct proportionality between the energy of a photon and its frequency. This relationship is described by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency. As frequency increases, so does the energy of the photon, and vice versa.
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3 Key excerpts on "Energy and Frequency Relationship"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
Frequency is inversely proportional to wavelength, according to the equation: where v is the speed of the wave ( c in a vacuum, or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant. ____________________ WORLD TECHNOLOGIES ____________________ Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. The energy in electromagnetic waves is sometimes called radiant energy. Particle model Because energy of an EM wave is quantized, in the particle model of EM radiation, a wave consists of discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation: where E is the energy, h is Planck's constant, and f is frequency. It is commonly expressed in the unit of electronvolt (eV). This photon-energy expression is a particular case of the energy levels of the more general electromagnetic oscillator , whose average energy, which is used to obtain Planck's radiation law, can be shown to differ sharply from that predicted by the equipartition principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature. As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level. If the energy is great enough, so that the electron jumps to a high enough energy level, it may escape the positive pull of the nucleus and be liberated from the atom in a process called photoionisation.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Different frequencies undergo different angles of refraction. A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation: where v is the speed of the wave ( c in a vacuum, or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant. ________________________ WORLD TECHNOLOGIES ________________________ Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. The energy in electromagnetic waves is sometimes called radiant energy. Particle model Because energy of an EM wave is quantized, in the particle model of EM radiation, a wave consists of discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation: where E is the energy, h is Planck's constant, and f is frequency. It is commonly expressed in the unit of electronvolt (eV). This photon-energy expression is a particular case of the energy levels of the more general electromagnetic oscillator , whose average energy, which is used to obtain Planck's radiation law, can be shown to differ sharply from that predicted by the equipartition principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature.
eBook - PDF- R. A. Lewis(Author)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
(5.29) Given these energies, it is now a simple matter of writing down the frequency of photons with equivalent energy through the relation E = h f . Dividing the expressions for E by h yields f n = n 2 h 8mL 2 = n 2 f 1 . (5.30) For numerical calculations, it is convenient to express the frequency in terms of tera- hertz, masses in terms of electron masses and lengths in terms of nanometres. In these units the equation reads f n [in terahertz] = n 2 90.92 m [in electron masses](L [in nanometres]) 2 . (5.31) Likewise, for frequency differences, Δ f n→m = (m 2 − n 2 ) f 1 = (m 2 − n 2 ) h 8mL 2 , (5.32) and for numerical calculations, Δ f n→m [in terahertz] = (m 2 − n 2 ) 90.92 m [in electron masses](L [in nanometres]) 2 . (5.33) 5.4 Infinitely high, square potential well 83 Example 5.2 Confined electron What is the characteristic fundamental frequency of an electron confined to a length of the order of the size of the atom, 0.1 nm? Solution We use Equation (5.31) with m, in electron masses, being 1, and L, in nanometres, being 0.1. Then f 1 is 9092 THz. Inside the well, the particle moves as a free particle, so the wavefunction is given by Equation (5.18). The particle cannot get out of the well; the probability of finding it outside the well is zero, and so the wavefunction outside the well is zero. Thus ψ( x) = 0 x < 0, (5.34) ψ n ( x) = √ 2 L sin(k n x) = √ 2 L sin ( nπ L x) 0 < x < L, (5.35) ψ( x) = 0 x > L. (5.36) The importance of the infinite well to terahertz physics is that structures can be fab- ricated in which the energy spacings are in the range of terahertz-frequency photons. The example and the exercises illustrate this. Typically, such structures are made by sandwiching a few atomic layers of one semiconductor, which serves as the bottom of the well, between another semiconductor, which serves as the sides of the well. In one dimension, normal to the layers, electrons are confined.
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