Tungsten has the body-centred cubic (BCC) unit cell shown in the figure; its atomic radius and atomic mass are given on the figure. Treating atoms as hard spheres that touch along the body diagonal, determine (a) the lattice parameter a (answer in nm), (b) the atomic packing factor (answer as a fraction, dimensionless) and (c) the theoretical density of tungsten (answer in kg/m^{3}).