The hybrid orbital h₁ = s + p_x + p_y + p_z referred to in Exercise 2F.19 is not normalized. Find the normalization factor N , given that all the atomic orbitals are normalized to 1. A wavefunction ψ can be normalized by writing it as Nψ and finding the factor N which ensures that the integral over all space of (Nψ)² is equal to 1.

Exercise 2F.19

Given that the atomic orbitals used to form hybrids are normalized to 1 and mutually orthogonal,

(a) Show that the two tetrahedral hybrids h₁ = s + p_x + p_y + p_z and h₃ = s - p_x = p_y - p_z are orthogonal.

(b) Construct the remaining two tetrahedral hybrids that are orthogonal to these two hybrids.