All the alkali metals crystallize with bcc structures.

(a) Find a general equation relating the metallic radius to the density of a bcc solid of an element in terms of its molar mass and use it to deduce the atomic radius of each of the following elements, given the density of each (in g · cm^–3): Li, 0.53; Na, 0.97; K, 0.86; Rb, 1.53; Cs, 1.87.

(b) Find a factor for converting the density of a bcc element into the density that it would have if it crystallized in a ccp structure.

(c) Calculate what the densities of the alkali metals would be if they were ccp.

(d) Which, if any, would float on water while reacting with it?