Present-day x-ray analysis of silicon the element from

Question

Question: Present-day x-ray analysis of silicon (the element from which modern electronic devices are constructed) shows that atoms in the solid state of Si are arranged as shown in Fig. The cubic box shown contains 8 Si atoms, and its side length is 543.1 pm. (1 pm = 10^-12 m)

a. What is the volume of the box in m³?

b. The measured density of Si is 2330 kg/m³. Calculate the mass of a single Si atom.

c. The atomic weight of Si is 28.086 g (=? in kg). From this and your answers to (a) and (b), find Avogadro's number N_A. (This is presently the most accurate way known to find N_A.)

Fig. - Arrangement of Si atoms in a crystal of silicon