Do the properties of the waves (wavelength,frequency) emitted by a particle or object depend upon the velocity, or as to say its kinetic energy? Is the De Broglie equation $E = h \nu $ applicable to matter waves as well?


These are two different questions.

Does the properties of the waves(wavelenth,frequency) emitted by a particle or an object depend upon the velocity

Yes, according to relativity, the emission lines of atoms depend on their velocity; it is the relativistic Doppler effect Here the wavelength is the wavelength of the electromagnetic wave emitted by an electron falling on a lower-energy orbital, for example.

is the de-broglie equation E = h(v) applicable to matter waves

The relation is $E=h\nu$ and also applies to the matter waves, that are described by Schroedinger equation. But the corresponding $\nu$ has little to do with the wavelength of an emitted radiation.

  • $\begingroup$ As ν = c / λ, this means that the energy of an object is inversely related to its wavelenth,how correct is it? $\endgroup$ – Fardeen Khan May 31 at 13:28
  • $\begingroup$ This is true only for electromagnetic waves. For matter waves, ruled by Schroedinger equation, $\lambda$ is connected with $p$. Basically, this is because matter cannot move at the speed of light, moreover it has a mass, which must enter in the relation. $\endgroup$ – Doriano Brogioli May 31 at 13:30
  • $\begingroup$ λ is related with velocity as λ = h/mv , wavelenth is still inverse to the velocity of the object (even for matter waves)? $\endgroup$ – Fardeen Khan May 31 at 13:34
  • 1
    $\begingroup$ Yes, this is correct. However, I would not say that the relation between $\lambda$ and $\nu$ is the same for electromagnetic waves and matter waves. In the first case, the involved speed is $c$, which is a physical constant and not a property of the wave, while in the second case there is a dependence on mass. Moreover, the relations between $\nu$ and $k=1/\lambda$ are different (linear in one case, square in the second). $\endgroup$ – Doriano Brogioli May 31 at 13:42
  • $\begingroup$ Okay,does it hold any physical significance,assume this that, the velocity of an object is increased as such that it's wavelenth becomes equal to that of radio waves, is it doable? $\endgroup$ – Fardeen Khan May 31 at 14:01

1- Matter wave is not emitted by the particle, but it is a probability density wave-function. If you calculated the amplitude of this function, squared it, and integrated the result over a certain volume, it will give you the probability to find the particle within this volume

2- Yes, Total Energy (rest energy + kinetic energy)= $hf$, where $\lambda f = u $, and $u$ is the speed of the matter wave $u$ is higher than light speed as it is the speed on a mathematical function, not a physical object, energy or information.

The relation between $u$ and $v$ is:

$C^2= uv$, where $v$, is the particle speed, and C is the speed of light in free space.

  • $\begingroup$ So ,matter waves are nothing but visualation tool to understand phenomenon like electron diffraction,and these waves doesn't really exist in ordinary space. ? $\endgroup$ – Fardeen Khan May 31 at 13:53
  • $\begingroup$ It is not only about diffraction, but something like that. Personally I consider it existing, but mathematically with some physical aspects like speed and distribution through space. $\endgroup$ – Ahmed Kamal Kassem Jun 1 at 15:56

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