Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 2 / A10 / d / Solution

Relative electron–hole motion uses the exciton reduced mass, rather than either band mass alone:In a screened hydrogenic Wannier-Mott exciton, replace $m_e$ by ${\mu }^{\ast }$ and ${\epsilon }_0$ by ${\epsilon }_r{\epsilon }_0$ in the hydrogen binding-energy scale. ThereforeThe effective Rydberg is an energy here, not a spectroscopic inverse length. Its scale is reduced both by dielectric screening and by the small band reduced mass. The associated radius is about ${\epsilon }_r(m_e/{\mu }^{\ast })a_0=23.5$ Å, several lattice spacings, consistent with using an extended-pair model as a first approximation rather than a tightly localized molecular exciton.