# Wave mechanics

1. Mar 3, 2006

### mmh37

This is supposed to be an easy question, but I appear to be slightly lost. Can anyone give me a hint on what to do here?

when waves of wavelength lamda are diffracted by a circular disc of diameter D the first minimum in the intensity of the scattered waves occurs at a scattering angle z given by

$$sin(z) = 1.22 * lamda / D$$

First Minima occur (when scattered from Carbon and Oxygen nuclei)...

for Oxygen (16 O) with E = 420 MeV : z= 45°

for Oxygen (16 O) with E = 360 MeV: z= 53 °

for Carbon (12 C) with E= 420 MeV: z = 50.5°

USE THE ABOVE DATA TO ESTIMATE THE RADII OF THE CARBON AND OXYGEN NUCLEI!

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NOTE: ..... that before I had do derive an expression for the momentum of the particle when it's kinetic energy is very much greater than it's rest mass energy mc^2

using the energy momentum invariant and neglecting the m^2c^4 term I said that:

$$E^2 = p^2*c^2 + m^2*c^4$$

$$p = E/c$$

Last edited: Mar 3, 2006
2. Mar 4, 2006

### mmh37

ok...this problem really was easy. I thought there would be much more to it than it actually was ...but yeah, it's simply dumping in numbers into the formula, solving for D, where D = 2r. Oooops!

3. Mar 4, 2006

### dextercioby

You know, people are used to finding something related to Schroedinger's equation when they see "wave mechanics"...

Daniel.

4. Mar 4, 2006

### mmh37

I know...that's why I was so confused. "Wave mechanics" is the heading to this problem on my sheet...I really don't see why!

Anyways...I am very sorry about having confused you!

Last edited: Mar 4, 2006