The three sp2 hybridized orbitals in carbon atom may be written as linear combinations of 2s, 2px, and 2py orbitals:

\(h_{1} = s+ \sqrt{2p_{y}}\)

\(h_{2} = s+ \sqrt{\frac{3}{2}p_{x}}-\sqrt{\frac{1}{2}p_{y}}\)

\(h_{3} = s - \sqrt{\frac{3}{2}p_{x}}-\sqrt{\frac{1}{2}p_{y}}\)

Normalize the three hybrid orbitals assuming s, px, and py are normalized and orthogonal to each other.

Also show that the three hybrid orbitals are orthogonal to each other.