# De Borglie's wavelength equation

1. Mar 1, 2013

### athymy

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

A molecule is 3 nanometers wide and weighs 5 x 10^-15kg. It is fired through a slit that is 5 nanometers wide. Approximately how slow does the molecule have to go so that it diffracts?

2. Relevant equations

I'm thinking that I could use De Borglie's wavelength equation: λ=h/m=h/mv and then solve for v but since I don't know that lambda is I don't see how I can use it.

Does anyone have a clue on how to solve this?

2. Mar 1, 2013

### voko

Re: Diffraction

What is "diffraction'?

3. Mar 1, 2013

### athymy

Re: Diffraction

Quote from Wiki: "Diffraction refers to various phenomena which occur when a wave encounters an obstacle. In classical physics, the diffraction phenomenon is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings"

4. Mar 1, 2013

### voko

Re: Diffraction

The question is, is there any relation between the size of the obstacle and some characteristic of the wave for diffraction to become significant?

5. Mar 1, 2013

### athymy

Re: Diffraction

If I remember correctly, doesn't the wavelength have to be pretty small in order for the particle to diffract? So could I try different values for v and see what my λ turns out to be?

I still don't understand what the slit width has to do with the question. Is it just there to show that the particle is able to go through it?

6. Mar 1, 2013

### voko

Re: Diffraction

You quoted Wiki: "spreading out of waves past small openings". How "small" must the opening be for spreading to become significant?

7. Mar 1, 2013

### athymy

Re: Diffraction

Ahh, so the wavelength should be approximately the size of the slit right?

8. Mar 1, 2013

### voko

Re: Diffraction

Correct.

9. Mar 1, 2013

### athymy

Re: Diffraction

Alright so since the width length 5nm, λ≈5nm or 5x10^-6m

So v=h/(5*10^(-15)*5x10^-6m)≈2.65*10^-14m/s

Is that reasonable? It seems like that is an extremely slow speed...

10. Mar 1, 2013

### voko

Re: Diffraction

Yes, it has to be slow, but not quite as slow. 1 nm is 10^-9 m, not 10^-6 m.

11. Mar 1, 2013

### athymy

Re: Diffraction

Oh yeah, sorry about that. And thank you so much for the help, it was very informative.

12. Mar 1, 2013

### ehild

Re: Diffraction

Well, it was an extremely big molecule.

Think: water molecule, for example has molar mass of M=0.018 kg. The mass of one molecule is M/A (A is the Avogadro number, 6x1023) So the mass of a water molecule is about 3x10-26 kg.

ehild