Question

Regarding hexatriene described in the previous question,  calculate the wavelength of light required to induce a transition from the ground state to the first excited state using the particle in a box model. To calculate the box length, assume that the molecule is linear and use the values 135 and 154 pm for C=C and C–C bonds, ignore the two ends (3 double bonds, 2 single bonds)

Please enter the wavelength in the unit of nm (without entering the unit), with one decimal

Answer 1

. --- The hexatirene molecule is given by eaten at &=&=&=&=&=6 d . The length of the box is the length of c, lo of were iguarings the two ends. I will not Hexatriene contains there double bonds and two single bonds. So, the length of the ID bose in = 3 x 135 + 2x 154) pm = 713pm [The length of the box is calculated by this way because election can move within the molecule .]

state in the W particle in The energy of the with the 10 bone model is, in 8 mp where ne energy a 3 Sanat me mass of particle Celection here) in length of the box 27 13 pm (latcakted) JA

Mc for hexabrience the energy states with electronic Configuration is given by - Yo , fc - Ys;&5 a Vy , Eu 12 Yg , £3 L & , & 4, , fi Here the HOMO is 43 and LUMO is with energies Ez and y respectivelys So, the energy of transition from ground state to first excited state is on A£ 2&4 - f3 mm (48h 8m 8² (3) 4² 8m1²

- 16h2 a ah2 8m (² 8m1² Th2 - 8m 12 ore.co Again, we can write, ak = how where a and & are the frequency and wavelength of light required to induce the transition . From (2) and (ih) we have 762 he be - mp3 to ble

= 28met? Th 8 x 9.1 x 10-31 x 3x108 x (7134161 YX 6.626810-34 W = 239 x 20-9am dowe w = 239 mm So, the wavelength of light required transition is 239 nm (Aus) for the