. The conjugated system of retinal consists of 11 carbon atoms and one oxygen at

Question

. The conjugated system of retinal consists of 11 carbon atoms and one oxygen atom. In the ground state of retinal, each level up to n=6 is occupied by two electrons. Using the particle-in-a-box model and assuming and average inter-nuclear distance of 1.40 x 10-10 m, a. (10 Points) Calculate the separation in energy between the ground state and first excited state in which one electron occupies the state with n=7. b. (6 Points) Calculate the wavelength and frequency of the radiation required to produce a transition between these two states.

Explanation / Answer

Answer (a)

First of all ,The quantized energies of an electron particle "in a box" are:

En = n2h2 / 8mL2

with

n=1,2,......

and L indicating the distance between the two barriers.
If I want to determine the amount of energy needed to "jump" from n=6 to n=7, then I have to calculate:

E67=E7E6

E67 = 13h2 / 8mL2

E67 = {13×(6.626×1034J/s)2 }/ {8 (9.11×1031Kg) (1.4×1010 m)2 }

E67 = ( 5.70 x 10-66 ) / (1.43 x 10-49 )

E67 = 3.98 x 10-17 J

Answer (b)

To calculate the frequency, I simply have to use this formula:

E =h

= E67 / h

v = (3.98 x 10-17 J ) / (6.626×1034 J/s)

v = 0.60 x 10 17 (1/s)

v = 60 x 10 15 Hz

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