3. The smallest carbon fullerene has 20 carbon atoms. For the divalent cations: C202+, there are 18 electrons. These electrons are freely moving around the sphericallike surface around the C202+ cage. If we treat these electrons at the level of particles-on-a-spherical-surface without electron-electron repulsion, answer the following questions. (a) (8pt) Based on Pauli Exclusion Principle, the HOMO energy level is corresponding to the quantum number in the particles-on-a-spherical- spherical-like C202+ surface. Sketch the energy diagram to show how electrons are placed in the sphere radius =0.156 nm available energy states and mark the HOMO and LUMO energy level. (b) (12pt) Determine the wavelength (in nm ) of the electromagnetic radiation that can be absorbed by the transition from HOMO to LUMO in the spherical-like hollow C202+