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The results of experimental studies of the low-energy isomeric state in the$^{229}$Th nucleus are presented. The work is consisted of several stages.During the first stage $^{229}$Th nuclei were excited with the inverse internalconversion to the low-lying isomeric level in plasma that was formed by laserpulse at the $^{229}$Th-containing target surface. Then thorium ions havingexcited nuclei were extracted from the plasma by an external electrical fieldand implanted into thin SiO$_2$ film grown on a silicon substrate (that is adielectric material with about 9 eV band-gap). Gamma decay of isomeric nucleiwas registered during the second stage by the general methods of the electronspectroscopy after the photon-electron emission from the silicon substrate.Substitution of the photon registration with the electron one allowed us toincrease the desired signal by several orders of magnitude and detect the$^{229}$Th nuclei decay. During the third stage the electron spectra fromstandard Xe VUV source was obtained that allowed determining the energy ofphotons. In order to prove that the detected signal is caused by isomeric$^{229}$Th nuclei decay a series of experiments was carried. The analysis ofelectron spectra gives the following results: the energy of the nucleartransition is $E_{\text{is}}=7.1(^{+0.1}_{-0.2})$~eV, the half-life of theisomeric level in bare nucleus in vacuum is $T_{1/2}=1880\pm170$~s, the reducedprobability of the isomeric nuclear transition is$B_{\text{W.u.}}(M1;3/2^+\rightarrow 5/2^+)=(3.3\pm0.3)\times10^{-2}$.

Excitation of $^{229}$Th nuclei in laser plasma: the energy and half-life of the low-lying isomeric state