Red, green, blue denote group 1, 2, 3 elements respectively. The crosses represent the free electron density, n, and the the circles represent the radius of the atom wrt the Bohr radius, rs/a0.
The free electron density is defined as the number of free electrons per cubic centimetres. One would suspect that for bigger atoms, the free electron density would decrease, i.e. inverse correlation between atom size and free electron density.
So consider the groups of elements, so 1, 2, 3 free electrons for red, green, blue in plot above.
If we look at the free electron densities (crosses), then we see a general trend of moving down the group (following ----), the free electron density decreases. This would be expected since we have the same number of free electrons, but our atoms would be getting bigger to hold the rest of the electrons and the protons.
We can confirm this by looking at the radius of the atom (circles). Moving down the groups (following ....), we see that the radius does indeed increase.
Now consider the periods of the elements, so points with close atomic number.
We see that the atom size decreases (red -> green -> blue), so the greatest radii (circles) are for the group 1 elements. In agreement, considering moving to the right with the period (red-> green->blue), the free electron density (crosses) does indeed increase.
Trend seems intuitive, but thought it'd be nice to see a plot of it, just to check :)
Nice graph. I think rs is not equal to the radius of the atom. It is defined as the radius of a sphere whose volume is equal to the volume per electron. It is another way of expressing the how packed the electrons are to each other like n. Larger n means smaller rs. rs~1/n^1/3. Its 15 minutes till midnight and here I am trolling on this blog. ><
ReplyDeleteMakes sense.
ReplyDeleteI thought it was interesting considering how the magnitudes of the free electron density and resistivities varied so much between elements; for example, the density of free electrons in beryllium is pretty large(24.7x10^22 e/cmcmcm) compared with the usual for transition metals of between around 5 to 15 (same units).
ReplyDeleteAlso, the resistivity of bismuth is way larger than that of anything else on the table.
Finally, it is interesting to look at the trends in resistivity with temperature; I suspect this is something that physicists have been interested in already.....
Python plots for your enjoyment....
ReplyDelete