# De Broglie wavelength and atom penetration

1. Sep 19, 2008

### Bakery87

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

DBW = h/p
p=mv

3. 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?

2. Sep 19, 2008

### Redbelly98

Staff Emeritus
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?

3. Sep 19, 2008

### Bakery87

I used 0.511003 MeV/c^2

4. Sep 19, 2008

### Redbelly98

Staff Emeritus
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)

5. Sep 19, 2008

### Bakery87

I did find something...

p = K/c

I'm still looking through my notes.

6. Sep 19, 2008

### Redbelly98

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