Magnesium has an HCP crystal structure and an atomic radius of 0.072 nm. Sketch the HCP unit cell and list the positions of the atoms in the unit cell using the Miller-Bravais coordinate system. Calculate the planar density on the (1111) plane. Assume that the critical resolved shear stress for magnesium is 10 MP. If a stress is applied in the [0 0 0 1], on which slip system will slip occur first? What is the value of the applied stress in problem 1c necessary to initiate stress?