Calculating Voltage & Velocity of Electrons in an Electron Microscope

[UrbanXrisis]

electrons in an electron microscope are accelerated form rest to a momentum making their wavelength 0.06 nm.

1. what is the voltage Vo needed for this?

2. What is the final electron velocity?

For 1.

$$E=\frac{hc}{\lambda}=\frac{1240eVnm}{0.06 nm}$$
solve for E

For 2.

$$E=.5mv^2$$
Solve for v plugging in E from #1 and m=mass of electron

is this the correct thought process?

 

[phucnv87]

I think that the correct process for classical mechanic.

 

[UrbanXrisis]

i'm not sure I understand what you mean

 

[inha]

This is just a guess but I think he might mean relativistic corrections. I don't think those are absolutely necessary because the electrons energy would be roughly 20keV which is still quite a bit smaller than it's rest energy.

 

[UrbanXrisis]

oh, you mean for part 2, i should use $$E=\sqrt{(pc)^2+(mc^2)^2}$$?