De Borglie's wavelength equation

[athymy]

Homework Statement

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?

Homework 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?

 

[voko]

What is "diffraction'?

 

[athymy]

What is "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"

 

[voko]

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

 

[athymy]

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

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?

 

[voko]

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

 

[athymy]

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

 

[voko]

Correct.

 

[athymy]

Correct.

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...

 

[voko]

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

 

[athymy]

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

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

 

[ehild]

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...

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