# DeBroglie wavelength considering relativistic effects

"Electrons are accelerated by a potential of 350kV in an electron microscope. Calculate the de Broglie wavelength of those electrons taling relativistic effects into account"

I attempted the following:

W = W(kin) = 350keV

now

$$W(kin)= (1-gamma)mc^2$$

so, now one could solve for gamma and find the velocity of the particle.

afterwards $$p=m*v=h/lambda$$

HOWEVER: I get a negative result in a root when I try to solve for v. Therefore I think that my energy formula must be wrong (I already excluded calculation errors). Can anyone see it?

## Answers and Replies

nrqed
Homework Helper
Gold Member
*Alice* said:
"Electrons are accelerated by a potential of 350kV in an electron microscope. Calculate the de Broglie wavelength of those electrons taling relativistic effects into account"

I attempted the following:

W = W(kin) = 350keV

now

$$W(kin)= (1-gamma)mc^2$$

It's $(\gamma -1) m c^2$ (the gamma factor is always larger or equal to 1)

Patrick