Calculating radius of Rubidium in unit cellHelp.

[christian0710]

Homework Statement

Calculate the Radius of Rubidium ion (which adopts sodium chloride structure.), if the density of Rubidium chloride is 2.76g*cm^(-3) and if we assume that the ions touch each other along the sides of the edge of the unit cell.


I'm a bit lost here. I assume the density is the density of the whole unit cell. But how can I find a radius without knowing any length at all?

 

[Borek]

How many moles of RbCl per one cubic centimeter of the crystal? How many molecules it is? Unit cells?

 

[christian0710]

In one unit cell there must be 4 moles of sodium and 4 chloride units even thought the cation sodium is much smaller than Cl.

 

[Borek]

In one unit cell there must be 4 moles of sodium

Atoms, not moles. And mole is known number of atoms (molecules, ions, whatever).

 

[christian0710]

Ahh yes, so perhaps if we know the radii ratio? It's not given in the problem, but i could imagine we would have to know how many times one atom is bigger than another?

 

[Borek]

On the second thought, while apparently mole step is necessary to calculate volume of the unit cell, I don't see how to calculate radius. Sum of radii of the cation and the anion is obvious, but separating them is not, unless I am missing something.

It happens that the radii are almost identical, but it is not said in the question.