We have observed the excitation of the 29.83 keV nuclear level of the radioactive 40K nuclide, which level is not populated by any radioactive source, by synchrotron radiation for the first time. The absolute energy of the level of 29.834+/-0.011 keV and the half-life of 4.13+/-0.12 ns were obtained from our measurements. Our success in observing the nuclear excitation of radioactive 40K in a KCl powder sample shows the possibility for study of the local vibrational states and the electronic states of potassium in various areas of research.