If the lattice constant of silicon is 5.43 å, calculate (a) the distance from the center of one silicon atom to the center of its nearest neighbor, (b) the number density of silicon atoms (#/cm"), and (c) the mass density (g/cm) of silicon.

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)