[Physics] Why are X rays in X ray crystallography diffracted by the electron clouds rather than nuclei


I am considering the nuclei as solid particles and the electrons as waves creating clouds of electron density around the nuclei. Thinking of it like this, I can't see how X rays are diffracted by the electron clouds and not nuclei. Perhaps I am thinking about this wrong and the wave-like nature of the nucleus comes into play here?

EDIT: I had an idea, but I am not sure it is correct at all. To be honest I haven't yet thought about what it means for any of these quantum particles to be a 'barrier' to the X-rays, which is probably the starting point. I'm I correct in thinking that a region acts as a 'gap' if it doesn't interact significantly with the X–rays, and a region can be thought of as a barrier if it does, e.g. by repeated absorption of X-rays and emission in different direction etc.

I did a quick calculation using some random values for nuclear energy levels and electron energy levels (not sure what elements/isotopes I was looking at, but I don't think it really matters here) and I got that the greatest energy gap for a nuclear energy level (between n=1 and n=2) was about 7×10(-13)J whereas X-ray energy is about 5×10(-15)J, and electron energy level is on the order of 10(-15)J (again looking at the greatest energy gap transition n=1 to n=2). Perhaps the X-rays are diffracted around the electron density because the electrons interact with the X-rays but the interaction of X-rays with nuclei is minimal because of their different energy levels, so it is the elctrons that act as the barrier and the X-rays generally pass trhough the nuclei without interaction?

Best Answer

Contemplate the difference in "size" of electron orbitals to the nucleus that is contained in the center:

Atomic sizes are on the order of 0.1 nm = 1 Angstrom = 10^-10 m

Nuclear sizes are on the order of femtometers which in the nuclear context are usually called fermis:

1 fm = 10^-15m

These go with the corresponding order of magnitude of energies: electron volts for electronic transitions , and Mega electron volts for nuclear transitions.

X-rays for crystallography are of the order of 10 keV, and it is the elastic scattering off the field of the lattice that identifies the location of atoms. In this sense the field an x-ray interacts with is a combination of the electric field of the orbitals of the electrons and the positive field of the nucleus,but that is orders of magnitude smaller than the field of the electron orbitals at the site of the orbitals. On a particle basis, the x-ray scatter elastically off an electron shell, as the electron orbitals shield the nucleus .

It is only with gamma energies that the nucleus can be approached, gamma wavelengths are small enough to penetrate without interacting with the electron orbitals and "see" the nucleus.

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