Question

why is potassium denisty lower than sodium even though the density of alkaline metal increases down the group?

Answer 1

I don't know. Density going down a group is a subtle interplay between increasing Zeff (because the inner electrons are never perfectly shielding), more shells of electrons, and the degree to which valence electrons participate in metallic bonding (the stronger the bonding, the denser the metal).

For what it's worth, if you look at calculations of Zeff for the outermost s electron for the Group 1A metals (cf. webelements.com):

Li 1.28
Na 2.51
K 3.50
Rb 4.98
Cs 6.36

There's a little downward kink in the line at potassium -- Zeff doesn't increase as much for K as you'd think it would. That would tend to make the radius grow a little faster than it might otherwise, which would lead to an unusually low density.

But that doesn't necessarily mean it's K that is out of line. What may be going on is that after potassium Zeff rises a little faster than you'd expect, based on the first four rows. That's a lttle easier to explain -- it comes from the fact that some of the inner electrons in Group 1A elements heavier than K are d electrons, and these are notably less shielding than s or p electrons. Note that in Group 2A the trend is lower density going down the group until Ca, and then, once again, when the inner electrons start being d electrons, the density rises. (When the inner electrons start being f electrons, the effect is really significant, and this is why the center of the bottom of the d block boasts really dense elements.)