[daveyavey]

Barium metal crystallizes in a body-centred cubic lattice. The density of the metal is 3.50gcm^-3. Calculate the radius(in pm) of a barium atom.

M(Ba)=137.3g/mol , NA = 6.022x10^23/mol

(My Attempt)
For 1 unit cell: m=2x137.3/6.022x10^23
=4.56x10^-22g

V=m/p
=4.56x10^-22/3.5
=1.303x10^8pm^3

Cell side length a=v^(1/3)=506.9pm

From here I am confused, the answer is that the cell diagonal length =4r=√3a
Atomic radius r=√3/4a=219.5pm

Can anyone please explain to me how the cell diagonal length varies with different structures, or anything that can help me, thanks.

[AWK]

Calculation of radius depends on type of packing:
see simple cubic, bcc and fcc:
http://stokes.byu.edu/sc.htm - edge of cell = 2r
http://stokes.byu.edu/bcc.htm - body diagonal  = 4r
http://stokes.byu.edu/fcc.htm - face diagonal = 4r