Question

Question: (a) How many π molecular orbitals are present in deca-1,3,5,7,9-pentaene $\mathbf{(}{\mathbf{CH}}_2\mathbf{=}\mathbf{CH}\mathbf{-}\mathbf{CH}\mathbf{=}\mathbf{CH}\mathbf{-}\mathbf{CH}\mathbf{=}\mathbf{CH}\mathbf{-}\mathbf{CH}\mathbf{=}\mathbf{CH}\mathbf{-}\mathbf{CH}\mathbf{=}{\mathbf{CH}}_2\mathbf{)}$? (b) How many are bonding MOs and how many are antibonding MOs ? (c) How many nodes are present in ${\mathbf{\text{ψ}}}_{\mathbf{1}}^{\mathbf{*}}$? (d) How many nodes are present in ${\mathbf{\psi }}_{10}^{*}$?

Short answer

a. 10

b. Number of bonding MOs: 5

Number of antibonding Mos: 5

c. Number of nodes in ${\text{ψ}}_1$: 0

d. Number of nodes in ${\text{ψ}}_{10}^{*}$: 9

Step-by-step solution

Bonding and antibonding molecular orbitals

The combination of two atomic orbitals results in the formation of two molecular orbitals, of which the lower energy one is named the bonding molecular orbital, and the one having higher energy is named the antibonding molecular orbital.

Nodes

The regions where the probability of finding an electron is zero is termed a node.

The decrease in the number of bonding interactions results in an increase in the number of nodes.

π molecular orbitals present in deca-1,3,5,7,9-pentaene

(a) deca-1,3,5,7,9-pentaene consists of five pi bonds, and hence, it will have a total of ten π molecular orbitals.

(b) Bonding and antibonding molecular orbitals are present in equal numbers, and therefore, the compound will have five bonding and five antibonding molecular orbitals.

(c) ${\text{ψ}}_1^{*}$ represents the lowest energy-bonding molecular orbital that has only bonding interactions and, therefore, no nodes.

(d) ${\text{ψ}}_{10}^{*}$represents the highest energy antibonding molecular orbital that has no bonding interactions and, therefore, nine nodes.