(Solved): The conjugated -electron system of the following compound can be described using a 1-D partic ...

The conjugated $$?$$-electron system of the following compound can be described using a 1-D particle-in-a-box. The energy is given by $$E=\frac{n^2{h}^2}{8m{a}^2}$$, jwhere a is the dimension of the box and $$\mathrm{n}$$ is the quantum number. Given that the average bond distance, $${\mathrm{I}}_c=140\mathrm{pm}$$ and the penetration term, $$p=140\mathrm{pm}$$, determine the wavelength corresponding to the first transition. Given: $$\mathrm{h}=6.626\times 10^{?34}\mathrm{J}\mathrm{s};\mathrm{k}=1.381\times 10^{?23}\mathrm{J}{\mathrm{K}}^{?1};\mathrm{c}=3.0\times 10^8\mathrm{m}{\mathrm{s}}^{?1}$$ mass of electron $$=9.11\times 10^{?31}\mathrm{kg}$$ (10 marks)