Hcp structure. Show that the c/a ratio for an ideal hexagonal closed-packed structure is = 1.633. If c/a is significantly larger than this value, the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked.

At 23° K, the crystal structure transforms from BCC to HCP keeping density same. The 0 cubic face in BCC is a = 3.42 A and in HCP is == 1.53. The lattice constant in HCP a structure is, 0 (a) 2.64 A 0 (b) 3.16 A 0 (c) 2.16 A 0 (d) 2.42 A

p9C.1 Familiarity with the magnitudes of overlap integrals is useful when con- sidering bonding abilities of atoms, and hydrogenic orbitals give an indication of their values. (a) The overlap integral between two hydrogenic 2s orbitals is 1 ( ZR ZR +. 2а, " 12 а, 1 + ZR 240 a, -ZR/Z0 S(2s, 2s)={1+ Plot this expression. (b) For what internuclear distance is S(2s,2s) = 0.50? (c) The side-by-side overlap of two 2p orbitals of atoms of atomic number Z is ZR 1 ( ZR ZR S(2p,2p) ={1+ 10 a, 2a, 120 a. Plot this expression. (d) Evaluate S(2s,2p) at the internuclear distance you calculated in part (b).