Chapter 15, Problem 15B.5AE

Interpretation Introduction

Interpretation:

The scattering factor in the forward direction for $B{r}^{-}$ has to be determined.

Concept Introduction:

The atomic scattering factor describes the dependency of the magnitude of an atom’s scattering of X-rays on the scattering angle $\theta$.  Mathematically it can be represented as

  $f=4\pi {\displaystyle \underset{0}{\overset{\infty }{\int }}\rho \left(r\right)}\frac{\sin kr}{kr}{r}^{2}dr$

Where,

  $k=\frac{4\pi }{\lambda }\sin \theta$

It is clear from the expression that the scattering factor depends upon electron density distribution in the atom which implies that heavy atoms give rise to stronger scattering than light atoms.  As there is no angular dependency, the scattering factor is a spherical distribution.  The scattering factor equals to the total number of atomic or ionic, electrons in the forward direction of scattering $\left(\theta =0\right)$.  It is smaller in non-forward directions.  While comparing isoelectronic atoms and ions, the less diffuse species that means greater $\rho \left(r\right)$ exhibits greater scattering.