To introduce the spherical harmonics, we discussed the rather contrived model sy

Question

To introduce the spherical harmonics, we discussed the rather contrived model system in which an otherwise free particle was confined to the surface of a sphere. Although this might sound like a silly example, it can be a very useful starting point for many interesting systems with high symmetry. For this problem, assume that the Hamiltonian for pi-type orbitals of C_60 can be approximated by, H = -h^2/2I A^2 (a) The eigenfunctions of this Hamiltonian are the states for a single electron. In chemistry we call these atomic orbitals, or molecular orbitals, and can accommodate 0, 1, or 2 electrons, and each carbon atom adds one electron to the pi orbital space. What is the degeneracy of the highest occupied state? (b) What energy gap must be surmounted in order to excite to the next energy level?

Explanation / Answer

A) degeneracy for the highest occupied orbital is 2l+1 as l=1 for p orbital by subsituting the value we get degeneracy as 2*1+1=3

BAND ENERGY GAP MUST

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