Final answer:
To derive the electron density from the crystal's structure factor, the correct method is a Fourier transformation. This process turns the reciprocal space data of diffracted waves into a real space representation that shows the distribution of electrons within the crystal.
Thus option b. is correct answer.
Step-by-step explanation:
To go from the structure factor of a crystal to the electron density equation, one needs to perform a Fourier transformation. This mathematical process translates the structure factor, which is expressed in reciprocal space with information about amplitude and phase of diffracted waves, into a real space representation which conveys the electron density within the crystal.
The square of the wavefunction (often represented as Ψ2) is proportional to the probability of finding an electron at a certain point, which when calculated across all points, yields the electron density. The electron density can be visualized graphically with colored dots of varying density, representing the likelihood of electron presence at different locations within the atom or crystal.
In the context of scattering experiments such as the Davisson-Germer experiment, the diffraction pattern obtained from X-rays or electrons scattering provides information about the crystal structure. Fourier transformation uses this data to reconstruct the electron density map, giving insights into the material's atomic arrangement.
Thus option b. is correct answer.