We perform coincidence measurements between α particles and γ rays from a ^233U source to determine the half-lives of the excited state in a ^229Th nucleus. We first prove that the half-lives of 42.43- and 164.53-keV states are consistent with literature values, whereas that of the 97.14-keV state (93(7) ps) deviates from a previously measured value (147(12) ps). The half-lives of 71.83- and 163.25-keV states are determined for the first time. Based on the obtained half-lives and the Alaga

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... we estimate the radiative half-life of the low-energy isomeric state (^229mTh) to be 5.0(11)×10^3 s, which is one of the key parameters for the frequency standard based on ^229Th.