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The energy eigenvalues and the wave functions of an $\alpha$ particle in aBohrium $270$ nucleus were calculated by solving Schr\"odinger equation forGeneralized Symmetric Woods-Saxon potential. Using the energy spectrum byexcluding and including the quasi-bound eigenvalues, entropy, internal energy,Helmholtz energy, and specific heat, as functions of reduced temperature werecalculated. Stability and emission characteristics are interpreted in terms ofthe wave and thermodynamic functions. The kinetic energy of a decayed $\alpha$particle was calculated using the quasi-bound states, which is found close tothe experimental value.

Properties of an $\alpha$ particle in a Bohrium $270$ Nucleus under the Generalized Symmetric Woods-Saxon Potential