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# Ψ and Ψ² Graphical Representation ## Equations - Ψ = √2/a * sin(nπx/a) - Ψ² = (1/a) * sin²(nπx/a), n = 1, 2, 3 ## Graph The graph shows the wave functions for n = 1, 2, 3. The x-axis represents the distance across the molecule, and the y-axis represents the value of the wave function. - n...

# Ψ and Ψ² Graphical Representation ## Equations - Ψ = √2/a * sin(nπx/a) - Ψ² = (1/a) * sin²(nπx/a), n = 1, 2, 3 ## Graph The graph shows the wave functions for n = 1, 2, 3. The x-axis represents the distance across the molecule, and the y-axis represents the value of the wave function. - n = 1 - The wave function is a single, positive lobe. - n = 2 - The wave function has two lobes, one positive and one negative. - n = 3 - The wave function has three lobes, two positive and one negative. The graph also shows the nodes, which are the points where the wave function is zero. The graph is labeled with the following: - Y axis: Ψ1, Ψ2, Ψ3 - X axis: a/2, a = 0, X = 0 - Nodes: n = 1, n = 2, n = 3 # Conjugate Molecule - C-C ⇒ 154 pm - C=C ⇒ 134 pm ## Definition A molecule that has a conjugated system of electrons and orbitals, which means that three or more of its atoms have overlapping p-orbitals, is called a conjugate molecule. ## Calculation 1. l = (l') = 1 = 1 x 134pm = 134pm 2. (l') = 0 = 0 x 154pm = 0 3. (l') = 0 = (1/2) * 134pm + (1/2) * 134pm = 288pm