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# How would I determine wavelength, given only width and thickness?

If I have a doorway that is 62 cm across and 12 cm thick, what would the door's wavelength be? And, more importantly, how would I find the answer?

I'm sorry, I meant the doorway's wavelength.

Here's the actual question:

A 73.5 kg student who has just studied matter waves is concerned that he may be diffracted as he walks through a doorway that is 62 cm across and 12 cm thick.

(a) If the wavelength of the student must be about the same size as the doorway to exhibit diffraction, what is the fastest the student can walk through the doorway to exhibit diffraction?

I took that to mean that the student has the same wavelength as the doorway, but if that's not what it's asking then I'd really appreciate it if you'd be willing to explain it to me.

### 1 Answer

- Randy PLv 71 decade agoFavorite Answer
The door doesn't have a wavelength. I think some of this question is missing.

Edit: It doesn't say his wavelength is the same as the doorway's WAVELENGTH, it says his wavelength is the same as the DOORWAY. 62 cm, in other words. I don't see that the 12 cm makes a difference.

It's talking about the doorway as a single slit, like you use for single slit diffraction of light. The width is what matters.

The student's wavelength is his de Broglie wavelength, h/mv. The faster the speed v, the smaller the wavelength. Set this equal to 62 cm (expressed in meters), plug in the values of h and m and solve for v.