Relativistic Calculations for De-Broglie Wavelength

[IWantToLearn]

Homework Statement

At what energy will a non-relativistic calculation of the De Broglie wavelength of an electron be in error by 5%? What is this energy for a proton? Comment on your results.

Homework Equations

I have two (seemed to be) logical answers for this question, but with different values

how to resolve this, there must be at least one wrong answer

i need a resolution [/B]

The Attempt at a Solution

Solution 1

Solution 2

 

[mfb]

The second approach has the right relativistic de-Broglie wavelength. It depends on the momentum, not on "the energy above the rest energy plugged into the nonrelativistic expression".

 

[IWantToLearn]

As far as i understand, there is nothing in the first approach states that the De-Broglie wavelength depend in anything but the momentum
in the first approach i replaced the momentum by the kinetic energy, and this is a valid replacement

please explain your point

 

[mfb]

You replaced momentum by the kinetic energy in nonrelativistic mechanics. It won't give the right result for relativistic speeds.