  In this work we study the decay constants of $B$ and $B_s$ mesons based on
the wave function obtained in the relativistic potential model. Our results are
in good agreement with experimental data which enables us to apply this method
to the investigation of $B$-meson distribution amplitudes. A very compact form
of the distribution amplitude is obtained. We also investigate the one-loop QCD
corrections to the pure leptonic decays of $B$ mesons. We find that, after
subtracting the infrared divergence in the one-loop corrections using the
factorization method, the QCD one-loop corrections to the hard amplitude of
leptonic decay will be zero.
