A conjugated carbon chain can be thought of in context of the particle in a box

Question

A conjugated carbon chain can be thought of in context of the particle in a box with energy as En=n2h2/8mL2 . If a carbon-carbon bond is 138 picometers, what is the ground state energy of a 4-carbon chain with only 1 electron? A conjugated carbon chain can be thought of in context of the particle in a box with energy as En=n2h2/8mL2 . If a carbon-carbon bond is 138 picometers, what is the ground state energy of a 4-carbon chain with only 1 electron? A conjugated carbon chain can be thought of in context of the particle in a box with energy as En=n2h2/8mL2 . If a carbon-carbon bond is 138 picometers, what is the ground state energy of a 4-carbon chain with only 1 electron?

Explanation / Answer

since ground state n = 1

since 4 carbon chain , i.e. 3 bonds , therefore L = 138 x 3 x 10-12 m = 414  x 10-12 m

mass of electron m = 9.11 x 10-31 kg

h = 6.63 x 10-34 Js

therefore E1 = {12 x (6.63 x 10-34)2} / {8 x 9.11 x 10-31 x (414 x 10-12)2} = 3.52 x 10-13 J

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