Nonrelativistic de Broglie energy Threshold of 1%

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Homework Help Overview

The discussion revolves around determining the energy threshold at which the nonrelativistic expression for the de Broglie wavelength of an electron becomes inaccurate by 1%. Participants are exploring the implications of classical versus relativistic wavelengths in this context.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are examining the relationship between classical and relativistic de Broglie wavelengths, questioning how the factor of gamma relates to the error threshold. There is discussion about the implications of mass increase and momentum on wavelength.

Discussion Status

The conversation is ongoing, with participants offering insights and clarifications regarding the terminology and concepts involved. There is an exploration of different interpretations of mass in the context of relativistic physics, and some guidance has been provided regarding standard terminology.

Contextual Notes

Participants reference a FAQ regarding the concept of relativistic mass, indicating a potential point of confusion in the discussion. The nature of the 1% error is also being scrutinized, with attention to how it can be interpreted in terms of higher or lower values.

Feynman.12
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Homework Statement



Determine at what energy, in electron volts, the Nonrelativistic expression for the de Broglie wavelength will be in error of 1% for an electron.
2. The attempt at a solution

For the error to be 1%, that means that the classical wavelength/relativistic wavelength will be 99% or 0.99. Whe you divide the formula for classical de Broglie wavelength and relativistic de Broglie wavelength, it equals gamma, however, gamma cannot ever be below 1. Thus gamma=0.99 is a contradiction.

I appreciate your help,
Thanks.
 
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One percent can be one percent higher or one percent lower ...
 
Orodruin said:
One percent can be one percent higher or one percent lower ...
That is true. And it makes sense that the classical wavelength will be higher than the relativistic wavelength. This would be because the mass of the electron will increase and thus the momentum, and as the wavelength is inversely proportional to the momentum, then the relativistic wavelength will be slightly smaller.
 
Feynman.12 said:
This would be because the mass of the electron will increase and thus the momentum,

Please see the FAQ https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/
Generally, physicists do not talk about increasing mass.
 
Last edited by a moderator:
Orodruin said:
Please see the FAQ https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/
Generally, physicists do not talk about increasing mass.
Will it be more correct to say that the addition of gamma in the relativistic momentum will cause the momentum to increase as v, and thus the relativistic de Broglie wavelength to decrease?
 
Last edited by a moderator:
Orodruin said:
Please see the FAQ https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/
Generally, physicists do not talk about increasing mass.
Sorry ignore the "as v" in my above reply.
 
Last edited by a moderator:
Neither is "more correct" as long as you know what you mean, but you should be aware of what is the standard way of referring to things in the physics literature or you risk getting confused.
 
Orodruin said:
Neither is "more correct" as long as you know what you mean, but you should be aware of what is the standard way of referring to things in the physics literature or you risk getting confused.
Thank you for your help!
 

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