Suppose you are given a cube made of magnesium (Mg) metal of edge length 1.0 cm.
(a) Calculate the number of Mg atoms in the cube.
(b) Atoms are spherical in shape. Therefore, the Mg atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Mg atoms, calculate the radius in picometers of a Mg atom. (The density of Mg is 1.74 g/cm3 and the volume of a sphere of radius r is 43πr3.)