Question

In Figure $\mathbf{4}\mathbf{.}\mathbf{6}\mathbf{.}$Rays are shown scattering off atoms that are lined up in columns, with the atoms in one atomic plane exactly above those in the plane below. Actually, the atoms in different planes are usually not aligned this way, they might, for instance, be aligned as in the accompanying figure. Does this affect the validity of the Bragg law $\mathbf{(}\mathbf{4}\mathbf{-}\mathbf{1}\mathbf{)}$? Explain your answer.

Short answer

The atomic locations within the same plane will not impact the interference pattern as long as the crystal planes themselves do not vary their distance or orientation relative to each other, and Bragg's law will still be valid.

Step-by-step solution

Bragg's law.

Bragg's law is a special case of Laue diffraction, which determines the angles of coherent and incoherent scattering from a crystal lattice.

When X-rays strike a certain atom, they cause an electronic cloud to travel in the same way as an electromagnetic wave does.

Bragg's diffraction.

The interference phenomena in Bragg’s diffraction are related with the crystal planes;it has nothing to do with atomic locations.

That is, as long as the distance between the atomic planes and their orientation do not vary, the scattering sources, such as atoms, have a cumulative impact in the crystal, maintaining the same interference pattern.

As a result, the electrons scatter with the same Bragg's law formula regardless of the orientation of the atoms on the same plane. Finally, this is true regardless of whether the plane is on top or bottom in relation to the incident beam.

Hence,the atomic locations within the same plane will not impact the interference pattern as long as the crystal planes themselves do not vary their distance or orientation relative to each other, and Bragg's rule will still apply.