# Easy question on 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 lambda 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

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

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 and 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:

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

leads to

$$p = E/c$$

2. Mar 3, 2006

### mmh37

I think the key problem is that I do not know D. Does anyone see how I can calculate this from the given data?

3. Mar 3, 2006

### Kurdt

Staff Emeritus
Find the debroglie wavelength of the concerened atoms and plug it into your diffraction formula rearranged for D.

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