A very crude model of the buckminsterfullerene molecule $\left(\mathrm{C}_{60}\right)$ is to treat it as a collection of electrons in a cube with sides of length equal to the mean diameter of the molecule $(0.7 \mathrm{~nm})$. Suppose that only the $\pi$ electrons of the carbon atoms contribute, and predict the wavelength of the first excitation of $\mathrm{C}_{60}$. (The actual value is $730 \mathrm{~nm}$.)
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