What is the identity of the edge length in terms of r for a body-centered cubic cell?

Question

A. 2r

B. 4r²

C. 3√2r

D. 2√2r

E. 4r/ √3

Answer 1

Hi Chris J.,

You can figure this one out yourself! Body centered cubic means there's one atom in the middle of the cubic cell. Since there are also atoms on all the corners, the diagonal corner-to-corner is where the atoms come in contact, and that determines the size of the unit cell. The distance corner-to-opposite-corner d = 4r, that is, r + 2r + r. Now express that distance d in terms of the edge e, using 3D Pythagorean Theorem. And solve for e. Piece of cake, IF you remember your Pythagorean Theorem. (Don't ever forget it!). Note that the edge length involves 2 atoms which are NOT touching -- it is the geometry corner-to-opposite-corner that governs!

--Cheers, -- Mr. d.