Nonrelativistic de Broglie energy Threshold of 1%

[Feynman.12]

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.

 

[Orodruin]

One percent can be one percent higher or one percent lower ...

 

[Feynman.12]

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.

 

[Orodruin]

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.

 

[Feynman.12]

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?

 

[Feynman.12]

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.

 

[Orodruin]

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.

 

[Feynman.12]

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!