How many nodes would the homo of beta-carotene have

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Question- 1) Beta-carotene is one of the pigments tha cause carrots to look orange. how many nodes would the HOMO OF BETA-CAROTENE HAVE?

2) In acid-catalyzed rearrangements of 2,5-octadiene to 3,5-octadiene would you ecpect the UV maximum to shift to a longer or shorter wavelength?

3) The real benzene molecule is 36 kcal/mole more stable than the imaginary 1,3,5-cyclohexatriee.What de we call this 36 kcal/mole?

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