  We present an important contribution to the non-commutative approach to the
hydrogen atom to deal with lamb shift corrections. This can be done by studying
the Klein-Gordon and Dirac equations in a non-commutative space-time up to
first-order of the non-commutativity parameter using the Seiberg-Witten maps.
We thus find the non-commutative modification of the energy levels and by
comparing with the the current experimental results on the Lamb shift of the 2P
level to extract a bound on the parameter of non-commutativity, we show that
the fundamental length ($\sqrt{\Theta}$) is compatible with the value of the
electroweak length scale ($l$). Phenomenologically, this effectively confirms
the presence of gravity at this level.
