De Broglie wavelength and atom penetration

[Bakery87]

Homework Statement

Calculate the de broglie wavelength (DBW) of an electron with kinetic energy 60 GeV.

What percentage of an atom's diameter can it penetrate?

Homework Equations

DBW = h/p
p=mv

The Attempt at a Solution

Basically I have an electron traveling at the speed of light. I arrived at this from its kinetic energy (60 GeV) and by using the relativistic K-energy equation. So I get it's de broglie wavelength fairly easily (I have this part done).

The part I don't understand is the penetration. I guess I just need some guidance/equations. Any ideas?

 

[Redbelly98]

Welcome to PF, Barkery87.

For an atom's diameter, they might mean take the diameter of the Bohr model for the hydrogen atom in its ground state. What percentage of that diameter is the deBroglie wavelength?

p.s.
Um, you didn't use the electron's rest mass to calculate p=mv, did you?

 

[Bakery87]

I used 0.511003 MeV/c^2

 

[Redbelly98]

Momentum is calculated differently for relativistic motion. There should be a formula in your textbook or lecture notes, relating E, p, and m (the rest mass, sometimes called m₀)

 

[Bakery87]

I did find something...

p = K/c

I'm still looking through my notes.

 

[Redbelly98]

p = K/c

Actually, that's a valid approximation for extremely relativistic situations (like this one).