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In the paper, a unique process of the decay of the $^{229m}$Th($3/2^+,8.28\pm0.17$ eV) low energy nuclear isomer via the internal conversion (IC) channel onRydberg states is considered for the first time. The Rydberg atom$^{229m}$Th$^{+}+e^-_{Ry}$ is a unique object where IC is possible exclusivelyon the Rydberg electron $e^-_{Ry}$. It is shown that in the$^{229m}$Th$^{4+}+e^-_{Ry}$ system a) IC on the electron states with relativelysmall values of the principal quantum number $n$ and the orbital moment $l$ ispractically completely suppressed, b) IC probability, $W_{IC}$, on the$\psi_{ns_{1/2}}({\bf{r}})$ states is proportional to $|\psi_{ns_{1/2}}(0)|^2$and can be related with the energy of the hyperfine interaction of the Rydbergelectron with the nucleus, c) $W_{IC}$ decreases rapidly with the increase of$n$ in the range from 10 to 50, and in the range $n\gtrsim 150$ $W_{IC}$changes as ${\text{Const}}/n^3$ typical for hydrogen-like ions, d) at$n\thickapprox 10$--30, $W_{IC}$ as a function of $l$ has a characteristic"knee" between $l=3$ and $l=4$, i.e. a three order of magnitude decrease of$W_{IC}$ due to the qualitative change in the ratio between the centrifugal andshielding potentials.

Decay of the low-energy nuclear $^{229m}$Th isomer via atomic Rydberg states