[neon flash!]

i'm really struggling with this whole "atoms touching" concept.
here is an example question.

Given an a value 3.841 angstroms, where TlCl takes the CsCl structure
a) derive the limiting value for the radius ratio for 8-fold coordination, assuming Cl atoms touch each other.
so i thought it would be r=1/2 x a
because its body centred cubic thus on 1 front face there are only the 2 Cl atoms to consider. if they touch it'd be like this:

this gave an answer of 1.92angstrams

b)Tl has radius 1.59Å, Cl has radius 1.81Å. Is the assumption that Cl atoms touch correct? Give your reasoning.
i'm not sure if my answer above is correct?
if it is would the atoms not be touching because 1.81 is smaller than 1.92, and the radius has to be 1.92 for the Cl's to be touching?

i'm really confused.

[fledarmus]

I don't think you've answered the first part of the question yet - "derive the limiting value for the radius ratio" - I think you are supposed to find a general expression for the ratio of the anion radius to the cation radius which would allow the anions to touch in a body-centred cubic structure.

Assume the radius of the anion is r_a and the radius of the cation is r_c - what would the length of a diagonal through the cube look like? Can you use these terms to generate a general expression for r_a/r_c?

Once you have that answer, the second half just seems to be plugging in your given radii and seeing if they match the expression you just generated.

[neon flash!]

well body diagonal = a x Squareroot 3

for bcc bd=4r = (2ra + 2rc)

so a x squareroot 3 = 2ra + 2rc7

but it says assuming the Cl atoms touch, so why am i looking at the body diagonal? because they cant touch that way since the Tl has to be between them at the body  centre.

[fledarmus]

If all eight chlorine atoms on the corners of your unit cell are touching, then the cation in the middle can be no larger than the space that they would leave. If the cation was any larger than that space, than the chlorines would have to separate slightly to allow it room. By taking a diagonal through the cube, you can calculate how large a cation you can have without forcing the chlorine atoms to separate.

For this calculation, you are not concerned with the value they gave you for a - that is the actual measurement of the unit cell rather than the theoretical measurement of a cell with the anions touching.