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Using the particle in a box model, the energy of the highest occupied energy level for...

Using the particle in a box model, the energy of the highest occupied energy level for a linear polyene of length 14 angstroms and containing 10 π electrons is (me = 9.11 x 10 31 kg)

(a) 4.52 x 10-5 J (b) 5.68 x 10-10 J (c) 7.32 x 10-17 J (d) 7.68 X 10-19 (e) 1.45 x 10-34 J

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Answer #1

answer: is d) 7.68*10-19

highest occupied energy level means they are talking about the HOMO energy of polyene

since length is 14 angstroms ( 14*10-10m) and 10 electron means number of double bond(n) = 5

formula used is E = (n2h2) / 8meL2

where E is the energy

n is number of double bond

h is Plank's constant = 6.626*10-34Js-1

me is the mass of electron = 9.11*10-31Kg

L is the length of polyene = 14*10-10 m

so putting all value in energy equation we have

E = (52 * (6.626 * 10 -34 )2 ) / ( 8 * 9.11* 10-31 * (14* 10-10) )

= 7.68* 10-19 J

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