Energies of a spherical quantum dot (a) Derive the formula (63) for the charging energy (b) Show that, for d B the result is the same as that obtained using the parallel plate capacitor result C 0 A d (c) For the case of an isolated dot, d Find the ratio of the charging energy to lowest quantized energy level Express your answer m terms of the radius R of the dot and the effective Bohr radius a B

Question: Energies of a spherical quantum dot (a) Derive the formula (63) for the charging energy. (b) Show that, for d < < B. the result

Energies of a spherical quantum dot

(a) Derive the formula (63) for the charging energy.

(b) Show that, for d << B. the result is the same as that obtained using the parallel plate capacitor result. C = εε₀A/d.

(c) For the case of an isolated dot, d → ∞. Find the ratio of’ the charging energy to lowest quantized energy level. Express your answer m terms of the radius R of the dot and the effective Bohr radius a_B.

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