# wavelength to energy factor

ω There are two common definitions of wave vector, which differ by a factor of 2π in their magnitudes. In a multidimensional system, the scalar The direction in which the wave vector points must be distinguished from the "direction of wave propagation". = . In this one-dimensional example, the direction of the wave vector is trivial: this wave travels in the +x direction with speed (more specifically, phase velocity) The kinetic energy of an electron is related to its momentum by: p = (2mT)1/2 = (2 x 9.1 x 10-31 x In both definitions below, the magnitude of the wave vector is represented by The energy of a single photon is a small number because the Planck constant is ridiculously tiny. k A perfect one-dimensional traveling wave follows the equation: k k = k When written out explicitly its contravariant and covariant forms are: In general, the Lorentz scalar magnitude of the wave four-vector is: The four-wavevector is null for massless (photonic) particles, where the rest mass If the medium is anisotropic, the wave vector in general points in directions other than that of the wave propagation. [1] For this article, they will be called the "physics definition" and the "crystallography definition", respectively. θ m ⁡ {\displaystyle \mu =0} ), this becomes: To apply this to a situation where the source is moving transversely with respect to the observer ( . , = 6.625 x 10-34 x 3 x 0 0 The parameters frequency, wavelength, and speed are quantities that can be used to describe a wave. [3][4], In solid-state physics, the "wavevector" (also called k-vector) of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction. is the direction cosine of can be written as the angular frequency = In other words, the wave vector points in the normal direction to the surfaces of constant phase, also called wavefronts. {\displaystyle k} Wavelength of a sine wave, λ, can be measured between any two consecutive points with the same phase, such as between adjacent crests, or troughs, or adjacent zero crossings with the same direction of transit, as shown. where the photon energy was multiplied with the electronic charge to convert 1 On the other hand, the wave vector points in the direction of phase velocity. where the photon energy was multiplied with the electronic charge to convert the energy in Joule rather than electron Volt. ω is the magnitude of the wave vector. {\displaystyle v_{p}} Alternately, the wavenumber The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates, as: where the angular frequency This variable X is a scalar function of position in spacetime. {\displaystyle {\mathbf {k} }\cdot {\mathbf {r} }} In the context of special relativity the wave vector can also be defined as a four-vector. {\displaystyle kx} c 0 T The wave vector is always perpendicular to surfaces of constant phase. For example, when a wave travels through an anisotropic medium, such as light waves through an asymmetric crystal or sound waves through a sedimentary rock, the wave vector may not point exactly in the direction of wave propagation. {\displaystyle \theta =\pi } = 108/(1.6 x 10-19 x 2) = 621 nm. In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. The derivative of this scalar is a vector that characterizes the wave, the four-wavevector.[6]. There are two common definitions of wave vector, which differ by a … Frequency / Wavelength / Energy Calculator To convert wavelength to frequency enter the wavelength in microns (μm) and press "Calculate f and E". {\displaystyle k^{0},k^{1}=k^{0}\cos \theta .}. The wavelength of a 2 eV photon is given by: l = h c / Eph = θ p π Conversion factors for energy equivalents For your convenience, you may convert energies online below. {\displaystyle \lambda } Wavelength refers to a periodic wave’s spatial period. These electron waves are not ordinary sinusoidal waves, but they do have a kind of envelope function which is sinusoidal, and the wavevector is defined via that envelope wave, usually using the "physics definition". cos μ . is the temporal component, and the wavenumber vector and inverse wavelength k In other words, it’s the distance over which the shape of the wave repeats. 1 The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. = 2 ; the direction of the wave vector is discussed in the following section. In a lossless isotropic medium such as air, any gas, any liquid, amorphous solids (such as glass), and cubic crystals the direction of the wavevector is exactly the same as the direction of wave propagation. k {\displaystyle \omega /k} = 7.63 x 10-25 kg m/s. [2] In one and three dimensions respectively: The differences between the above two definitions are: The direction of k is discussed in the next section. Applying the Lorentz transformation to the wave vector, and choosing just to look at the It is defined as the ratio of the peak energy stored in the resonator in a cycle of oscillation to the energy lost per radian of the cycle. v divided by the phase-velocity In crystallography, the same waves are described using slightly different equations. is the spatial component. λ The Lorentz matrix is defined as, In the situation where light is being emitted by a fast moving source and one would like to know the frequency of light detected in an earth (lab) frame, we would apply the Lorentz transformation as follows. {\displaystyle {\frac {\omega }{c}}} , or in terms of inverse period {\displaystyle \theta =0} r the direction of the group velocity. v Therefore, it refers to the inverse of spatial frequency. The wavelength of a 2 eV photon is given by: l = h c / E ph = 6.625 x 10 -34 x 3 x 10 8 /(1.6 x 10 -19 x 2) = 621 nm. k The de Broglie wavelength of the electron is then obtained from: l = h/p = [5], A moving wave surface in special relativity may be regarded as a hypersurface (a 3D subspace) in spacetime, formed by all the events passed by the wave surface. , representing the wave vector and the position vector, respectively. {\displaystyle {\vec {k}}} θ The corresponding frequency will be in the "frequency" field in GHz. p {\displaystyle k^{1}} 1.6 x 10-19 x 2)1/2 ω which would have the following relation between the frequency and the magnitude of the spatial part of the four-wavevector: The four-wavevector is related to the four-momentum as follows: The four-wavevector is related to the four-frequency as follows: The four-wavevector is related to the four-velocity as follows: Taking the Lorentz transformation of the four-wavevector is one way to derive the relativistic Doppler effect. ⁡ {\displaystyle \cos \theta \,} x Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinarily the direction of wave propagation (but not always, see below). ⋅ "This effect has been explained by Musgrave (1959) who has shown that the energy of an elastic wave in an anisotropic medium will not, in general, travel along the same path as the normal to the plane wavefront...", light waves through an asymmetric crystal, https://en.wikipedia.org/w/index.php?title=Wave_vector&oldid=985826900, All Wikipedia articles written in American English, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 28 October 2020, at 05:01. {\displaystyle m_{o}=0}, An example of a null four-wavevector would be a beam of coherent, monochromatic light, which has phase-velocity 6.625 x 10-34 / 7.63 x 10-25 = 0 The speed, {eq}v {/eq}, of the wave, corresponds to the speed at which the wave is propagating. You can use the photon energy calculator to further explore the relationship between the photon energy and its frequency or wavelength. {\displaystyle \theta =\pi /2} 0.87 nm. {\displaystyle k} / Note that the source is in a frame Ss and earth is in the observing frame, Sobs. the energy in Joule rather than electron Volt. The condition for the wave vector to point in the same direction in which the wave propagates is that the wave has to be homogeneous, which isn't necessarily satisfied when the medium is anisotropic. k A wavetrain (denoted by some variable X) can be regarded as a one-parameter family of such hypersurfaces in spacetime. ), this becomes: Vector describing a wave; often its propagation direction, Source moving tangentially (transverse Doppler effect), CS1 maint: multiple names: authors list (. The differential form is: dE = - h * c / Lambda^2 * dLambda You transform the x-axis from wavelength to energy using the first above formula. = In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave. In case of heterogeneous waves, these two species of surfaces differ in orientation. One definition is preferred in physics and related fields, while the other definition is preferred in crystallography and related fields. k o Like any vector, it has a magnitude and direction, both of which are important. {\displaystyle \omega } π As an example, to apply this to a situation where the source is moving directly away from the observer ( c See Bloch's theorem for further details. OR enter the would be replaced by the vector dot product In a homogeneous wave, the surfaces of constant phase are also surfaces of constant amplitude. cos 0 / {\displaystyle v_{p}=c}. → wrt θ k θ ), this becomes: To apply this to a situation where the source is moving straight towards the observer ( The energy of a single photon of green light of a wavelength of 520 nm has an energy of 2.38 eV. component results in, where {\displaystyle k} {\displaystyle T} For light waves, this is also the direction of the Poynting vector. k

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