The growth and analysis of the optical properties of isotopically enriched ZnO nanorods is presented. ZnO nanorods were grown on silicon substrates by chemical bath deposition on a drop-coated ZnO seed layer followed by carbothermal-reduction vapour phase transport (VPT). Zn-isotopically enriched samples were grown using very small amounts of Zn-enriched ZnO source powders in the VPT phase. Oxygen-enriched ZnO nanorods were grown by two modified novel vapour-solid (VS) and vapour-liquid-solid (VLS) methods. Characterisation by scanning electron microscopy and x-ray diffraction confirm the growth of high quality, dense, c-axis aligned nanorods over a large surface area in Zn-enriched and VS O-enriched nanorods, and non-aligned nanorods for VLS O-enriched samples. Zn isotopic enrichment was confirmed by secondary ion mass spectroscopy and Raman. Optical studies by low temperature photoluminescence (PL) show shifts in the band edge exciton recombination energy with changing isotopic masses, again confirming enrichment. The optical quality of the nanorods was excellent. The well-known Cu-related emission at 2.86 eV was studied by PL in order to investigate possible involvement of intrinsic, native defects such as interstitials and vacancies in this deep centre. Shifts in this zero phonon line (ZPL) energy were measured and compared to changes in the band edge energies. No relative shift was observed in these Zn-enriched samples, indicating only O atoms in the vicinity of the Cu atom, and no involvement of Zn interstitials or O vacancies in this Cu defect. PL and Raman shifts in the O-enriched samples were less than those previously reported for the same nominal enrichment levels, indicating possible lower enrichment than anticipated. Band edge and ZPL emissions in samples with O-enrichment displayed a relative shift and the ZPL line widths showed a substantial increase, which could indicate O interstitials or Zn vacancies complexing with Cu, however we attribute these effects instead to the multiple local configurations possible for O atoms in these mixed isotope environments in such lesser enriched samples.