Titanium metal has a body-centered cubic unit cell. The density of Titanium is 4.50 g/cm^3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium.

Question

Ok, I know how to find the density using the atomic radius, but I'm having trouble working backwards using the density to find the atomic radius). I'm not really sure how to find the volume. And I know that the pythagorean theorem will help me find the radius but I'm missing some steps in between.

Answer 1

I would be willing to bet you are stuck on just one step. Here it is,
1 mol Ti atoms = 47.88 g (check that on your periodic table)and that mass contains 6.022 x 10^23 atoms. Use that to calculate the mass of 1 atom of Ti, from that you have m =volume x density which allows you to calculate the volume. Take the cube root of V to obtain a, the length of the edge of the cube. Can you take it from here. The radius, if you need help there, is (1/4)*(sqrt 3)*a. I hope this helps.

Answer 2

Thank you so much!