  Exclusive semileptonic B decays to radially excited charmed mesons and rare
radiative B decay to the orbitally excited tensor K_2^*(1430) meson are
investigated in the framework of the relativistic quark model based on the
quasipotential approach in quantum field theory. The heavy quark expansion is
applied for the semileptonic B\to D^{(*)}'e\nu decays. Both relativistic and
the 1/m_Q corrections are found to play an important role for these decays and
substantially modify results. For rare radiative B -> K_2^*(1430)\gamma decay
such an expansion is not used for the s quark. Instead we apply the expansion
in inverse powers of large recoil momentum of final K_2^*(1430) meson. The
calculated branching fraction BR(B -> K_2^*(1430)\gamma)=(1.7\pm 0.6)\times
10^{-5} as well as the ratio BR(B -> K_2^*(1430)\gamma)/BR(B ->
K^*(892)\gamma)=0.38\pm 0.08 are found to be in a good agreement with recent
experimental data from CLEO.
