Calculation of wavelength of EMW produced due to an accelerated charged particle

[ritesh goel]

if an electron is accelerated by 2eV energy. then what will be the wavelength of emw produced? can we use E=hc/wavelength here? should we use always de broglie hypothesis for this? what will be the difference between wavelength of electron and wavelength of emw? are they same or not?

 

[jpreed]

This is diving into particle/wave duality. Yes, a moving electron has a wavelength. Yes, a photon has a wavelength. Yes, if a moving electron suddenly comes to a halt it will release a photon. The connection between all of these concepts is through the de Broglie relations.

The two universal laws that are the same for both massive particles (electrons, He atoms, etc) and for EM waves are:

$$E = h f \quad \&\quad p = \frac{h}{\lambda}.$$

For EM waves, the relation between energy and momentum goes as:

$$E = h f = \frac{h c}{\lambda} = c\, p.$$

Where for momentum the energy and momentum relation is the more familiar:

$$KE = \frac{p^2}{2 m}$$

So to answer your question:
If an electron is traveling with an *Energy* of 2eV and releases all of it into 1 photon with energy 2eV, then they will have the same wavelength.

 

[astrokreng]

Yes, we can use the equation E=hc/wavelength to calculate the wavelength of electromagnetic waves (EMW) produced by an accelerated charged particle. This equation relates the energy of the EMW (E) to its wavelength (wavelength) and the speed of light (c). Therefore, if we know the energy of the accelerated electron (2 eV in this case), we can use this equation to calculate the corresponding wavelength of the EMW.

It is not necessary to use the de Broglie hypothesis for this calculation. The de Broglie hypothesis states that particles, such as electrons, have wave-like properties and can be described by a wavelength (known as the de Broglie wavelength). This hypothesis is mainly used to describe the behavior of matter at the atomic and subatomic level, but it is not necessary for calculating the wavelength of EMW produced by an accelerated charged particle.

The difference between the wavelength of the electron and the wavelength of the EMW is that the electron's wavelength is a property of the particle itself, while the wavelength of the EMW is a property of the wave it produces. They are not the same, but they are related through the energy of the accelerated electron, as described by the equation E=hc/wavelength.