Final answer:
To calculate the mean ionic polarizability and the dielectric constant at optical frequencies for KCl, we sum the polarizabilities of the ions per unit cell and then find per ion pair value. We then apply the Clausius-Mossotti relation using the unit cell volume to find the optical dielectric constant, noting that the low-frequency dielectric constant differs due to ionic movement.
Step-by-step explanation:
To calculate the mean ionic polarizability per ion pair αi and the dielectric constant εrop at optical frequencies for KCl, we first need to find the total polarizability αtotal of the unit cell. The total polarizability of the unit cell is the sum of the polarizability of all the ions in the unit cell.
Since KCl has the same structure as NaCl, which is face-centered cubic (FCC), there are 4 K+ and 4 Cl- ions per unit cell. Therefore, αtotal = 4(ΰ.92 × 10-40 + 4.0 × 10-40) Fm2. To find αi, we divide αtotal by 4, since there are 4 ion pairs in the unit cell.
Next, to find the dielectric constant at optical frequencies εrop, we use the Clausius-Mossotti relation which relates the dielectric constant to the polarizability and the volume of the unit cell. The lattice parameter given as 0.629 nm is the edge length of the unit cell. For FCC, the volume V = a3, where a is the lattice parameter. Using the Clausius-Mossotti relation, εrop can be calculated knowing αi and V. T
he low frequency dielectric constant εr is provided as 4.80, but due to ion contributions at low frequencies, this is not the same as εrop which ignores ionic movement.