▎ 摘　　要

The scaling law of exciton effect in the surface hydrogenated graphene nanoribbon with armchair edge (H-AGNRs) is studied by first principle density function theory (DFT) with quasi-particle corrections and many-body, i.e. electron-hole interactions. Realizing the failure of the traditional family effect in the pristine AGNRs, we introduce an effective width model, which can systematically describe the electronic structures of H-AGNRs by three catalogues. In the model, the relationship between the effective widths and the effective family index can well line up at the ground states of H-AGNRs. We also scale the exciton binding energies with effective width of H-AGNRs. This work provides more general understanding for the surface modification on the electronic properties in ultra-narrow AGNRs and discloses a more universal family effect in the AGNRs systems.