Energy of the $^{229}$Th nuclear clock transition

The first nuclear excited state of $^{229}$Th offers the unique opportunity for laser-based optical control of a nucleus. Its exceptional properties allow for the development of a nuclear optical clock which offers a complementary technology and is expected to outperform current electronic-shell based atomic clocks. The development of a nuclear clock was so far impeded by an imprecise knowledge of the energy of the $^{229}$Th nuclear excited state. In this letter we report a direct excitation energy measurement of this elusive state and constrain this to 8.28$\pm$0.17 eV. The energy is determined by spectroscopy of the internal conversion electrons emitted in-flight during the decay of the excited nucleus in neutral $^{229}$Th atoms. The nuclear excitation energy is measured via the valence electronic shell, thereby merging the fields of nuclear- and atomic physics to advance precision metrology. The transition energy between ground and excited state corresponds to a wavelength of 149.7$\pm$3.1 nm. These findings set the starting point for high-resolution nuclear laser spectroscopy and thus the development of a nuclear optical clock of unprecedented accuracy. A nuclear clock is expected to have a large variety of applications, ranging from relativistic geodesy over dark matter research to the observation of potential temporal variation of fundamental constants.