Atomic Size

Having the following three single crystals available: Sodium Chloride, Potassium Chloride and Rubidium Chloride, we have the possibility to perform XRD scanning for these three crystals and compare the results to obtain information on the atomic dimensions of the different ions.
For this experiment we use the tel-x-ometer diffractometer configured at 30 KV and 80 μA, with the Nikel filter in order to have a monochromatic X beam at the emission of copper.

The results of the scans are presented in the graph below where we see the Bragg peaks for the three compounds, we note that the intensity of the peak is decreasing passing from NaCl to KCl and to RbCl, but this depends on the scattering factor and the phenomenon of self-absorption of the diffracted radiation from the crystal.

From the Bragg law we can calculate the crystal spacing from the following formula :

d = λ / 2sinθ

We insert the data obtained in the following table with the data for the peaks present in the chart for each compound, where λ = 0.154 nm is the wavelength of the Kα copper emission and a = 2d is the size of the crystal cell unit.

 Crystal 2θ (°) θ (°) senθ λ (nm) d (nm) a (nm)  a* (nm)
 NaCl  31.50  15.75  0.271  0.154  0.284  0.568  0.564
 KCl  28.17  14.08  0.243  0.154  0.317  0.634  0.630
 RbCl  26.67  13.33  0.231  0.154  0.333  0.666  0.658

a* : values from scientific literature

Observe that the crystal spacing, a increases with the Atomic Number of the Alkaline metals; Na, in the third period has eleven (11) electrons at K, L and M levels; K in the fourth period has nineteen (19) electrons but in the K, L, M and N states, whereas Rb has thirty seven (37) electrons in the five energy states , K, L, M, N and O. Chlorine is common to the three compounds and thus the evidence suggests that the size of individual atoms increases with atomic number.

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