  We derive the relativistic Hamiltonian of hydrogen atom in dynamical
noncommutative spaces (DNCS or {\tau}-space). Using this Hamiltonian we
calculate the energy shift of the ground state and as well the [2P]_(1/2),
[2S]_(1/2) levels. In all cases the energy shift depend on the dynamical
noncommutative parameter {\tau}. Using the accuracy of the energy measurement
we obtain an upper bound for {\tau}. We also study the lamb shift in DNCS. Both
the levels [2P]_(1/2) and [2S]_(1/2) receive corrections due to dynamical
noncommutativity of space which is in contrast to the non-dynamical
noncommutative spaces (NDNCS or {\theta}-space) in which the level [2S]_(1/2)
receives no correction.
