Wavelength - differences in equations

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    Wavelength
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Discussion Overview

The discussion revolves around the calculation of the wavelength of electrons, particularly in relation to their speed and the equations used for such calculations. Participants explore the differences between using the equations λ = h/mv and λ = hc/E, as well as the implications of relativistic versus non-relativistic momentum. The conversation also touches on electron transitions in hydrogen atoms and their relation to UV light.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions which equation to use for calculating the wavelength of electrons with a given speed, noting that λ = hc/E is often used for transitions between energy states.
  • Another participant explains the historical context of the equations, stating that λ = h/p applies to both photons and electrons, with p being the momentum.
  • A different participant emphasizes that for electrons moving at high speeds, the relativistic momentum should be considered, suggesting that λ = h/p is the appropriate starting point.
  • There is a mention of the need to differentiate between the equations for massless particles and those for particles with mass, indicating that λ = hc/E is specific to photons.
  • One participant shifts the topic to electron transitions in hydrogen atoms and seeks guidance on calculating the wavelengths associated with UV light emissions.

Areas of Agreement / Disagreement

Participants express differing views on which equation is most appropriate for calculating the wavelength of electrons, particularly in the context of relativistic effects. There is no consensus on a single method, as multiple perspectives are presented regarding the applicability of the equations.

Contextual Notes

Participants note the importance of considering relativistic effects when dealing with high-speed electrons, which may influence the choice of equations. The discussion also highlights the distinction between massless and massive particles in the context of wavelength calculations.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in quantum mechanics, wave-particle duality, and atomic transitions.

The_ArtofScience
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Hi

If I wanted to find a wavelength of electrons having an average speed of 1.7e+8, would use lamdba = h/ mv or lamdba = hc/ E? I noticed that the 2nd eq is used mostly for transition states when an electron either falls or jumps from its n shell. What's the major difference?

Thanks in advance
 
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In the beginning of 20th century the interplay of special relativity of Einstein and the photon quantization hypothesis of Planck (that light is emitted or absorbed in parcels of energy E = h nu, called photons) lead to the formula

lambda = h / p

applicable to photons. Around 1922 de Broglie guessed that material particles like electrons may also have a wave associated with them so he postulated the same exact formula applies to electrons and other material particles.

The moment of the mass zero relativistic photons is p = E/c which leads to lamdba = hc/ E.
The moment of non-relativistic electrons is p = mv, leading to lamdba = h/mv.

Your two formulas are just two particular cases of the same master formula.
 
Last edited:
The_ArtofScience said:
If I wanted to find a wavelength of electrons having an average speed of 1.7e+8,

I assume the speed is in m/sec.

would use lamdba = h/ mv or lamdba = hc/ E?

Neither one. The correct starting point for the wavelength is [itex]\lambda = h / p[/itex] where p is the momentum of the particle.

[itex]\lambda = h/mv[/itex] uses the non-relativistic momentum [itex]p=mv[/itex] instead of the relativistic momentum [itex]p = mv / \sqrt {1 - v^2/c^2}[/itex]. Your speed is more than half the speed of light, so it makes a significant difference.

[tex]\lambda = hc/E[/itex] applies only to massless particles like photons, for which [itex]E = pc[/itex], that is, [itex]p = E/c[/itex].[/tex]
 
Thanks guys

I'm also wondering about what electron transitions correspond to a UV light coming out from a hydrogen atom. How do I calculate that? And how do I differentiate that from the visible light?
 

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