# Small question about atomic form factor calculation

1. Oct 12, 2014

### skate_nerd

1. The problem statement, all variables and given/known data

This problem just has me find an atomic form factor for some arbitrary basis atom in a bravais lattice where the electron wave function is given (it has a dependence on the Bohr radius in an exponential). I calculated the form factor (a very long, nasty integral that actually simplified nicely in the end), and then I am asked to find the limiting values of the form factor when the wavelength of light used is much larger than the Bohr radius, and when the wavelength is much smaller than the Bohr radius.

2. Relevant equations
The form factor I calculated:
16/((4+(a*G)2)2) where G is the magnitude of the arbitrary reciprocal lattice vector (RLV) and a is the Bohr radius.
I plugged in the formula relating the scattering angle, the wavelength of light, and the RLV magnitude:
G=sin(theta)*4pi/(lambda).

3. The attempt at a solution
I originally worked through these two parts pretty fast; I thought as lambda gets much larger than the Bohr radius, then a/lambda will just be approximately zero and the form factor would end up being 1.
Similarly, when lambda is much smaller than the Bohr radius, a/lambda would get really large making the denominator of the form factor really large and then it would be approximately zero.

Now I'm second guessing myself because the problem statement asks if the form factor limiting values have any dependence on the scattering angle. I feel like she wouldn't have asked that unless one of the limiting values did.
So I'm just gonna ask for some opinions, do you guys think that a problem like this would warrant a taylor expansion on the form factor formula I have? For both cases, or just one of them, and why?
To be clear, the problem just only said "as a>>lambda" and "as a<<lambda". That always seems really vague to me....

2. Oct 17, 2014