Final answer:
To find the edge length of the titanium cube, we determine its volume using the formula density = mass/volume. The mass is calculated using Avogadro's number and the molar mass of titanium. The edge length is then found by taking the cubic root of the volume.
Step-by-step explanation:
To find the edge length of the titanium cube, we need to first determine the volume of the cube. Since the density of titanium is given in grams per cubic centimeter (g/cm³) and the volume of a cube is expressed as V=l³, we can use the formula density = mass/volume to find the volume. Rearranging the formula, we have volume = mass/density. The atomic mass of titanium is approximately 47.867 g/mol, so the mass of the titanium cube can be calculated using Avogadro's number (6.022×10²³ atoms/mol) and the molar mass of titanium. Substituting the given values into the formula, we get:
Volume = mass/density = (2.86×10²³ atoms x 47.867 g/mol)/(450 g/cm³) = 3.02×10¹⁹ cm³
Since the volume of a cube is V=l³, we can solve for 'l' by taking the cubic root of the volume:
Edge length (l) = V^(1/3) = (3.02×10¹⁹ cm³)^(1/3) = 1.57×10⁶ cm
Therefore, the edge length of the titanium cube is approximately 1.57×10⁶ cm, expressed to three significant figures.