1. Hybridization of Atomic Orbitals.

Consider the hybrid orbitals:

ya = (3)^-0.5s + (2)^-0.5px -(6)^-0.5pz

yb = (3)^-0.5s + (3/2)^-0.5 pz.

a) Show yb is normalized (assuming the atomic orbitals s, px, py, and pz are orthonormal set of orbitals).

b) Show ya and yb are orthogonal to each other.

c) Show that ya is NOT orthogonal to px but is orthogonal to py

d) A third orbital is given by (3)^-0.5s - c px -(6)^-0.5pz

What is the value of c? Explain

e) Draw the shape and orientation of yb on the x,z axes.

2. Consider the hybrid orbitals:

ya = a s + a px

yb = a s - a px.

a) If ya is normalized (assuming the atomic orbitals s, px, py, and pz are orthonormal set of orbitals), calculate the value of a.

b) Show ya and yb are orthogonal to each other.

c) Show that ya is NOT orthogonal to px but is orthogonal to py.

d) Draw the shape and orientation of the s, px, and yb on the x axis. Include in your sketch the sign of the wave amplitude.