DeBroglie Wavelength: Solving for Electrons in Relativity

[gaobo9109]

Homework Statement

An electron of charge e and rest mass m₀ is accelerated to relativistic speeds by a potential V. Show that the deBroglie wavelength is given by the expression

lambda= h(2m₀eV)^-1/2 (1+eV/2m₀c²)^-1/2

The Attempt at a Solution

eV = gamma m₀c² equation one
p = gamma m₀v₀ equation two

From first equation, i get

v₀ = (c² - m₀²c⁴/e²v²)^1/2

However, when i substitute this result into equation two, the expression is nowhere near the proposed expression.

 

[vela]

One of the things about special relativity is that if you take the wrong approach, you can get bogged down in a bunch of algebra. I suspect that is the case here. You could probably eventually get to that final expression, but you'd be better off starting over.

Try using the fact that E²-(pc)² = (m₀c²)², where E is the total energy of the particle.