  In this paper we endeavour to determine the energy levels of an atom by
virtue of the modified Dirac equation. It has been found that the energy levels
contain an extra term in the expression which accounts for the {\it
zitterbewegung} effects in the Compton scale. Applying our perspective to the
hydrogen atom we have been able to find the {\it Lamb shift} for the
$2S_{\frac{1}{2}}$ and $2P_{\frac{1}{2}}$ states. This result substantiates
that a slight modification of the Dirac equation suffices to explain the
phenomenon, where the modification of the Dirac equation arises due to the
non-commutative nature of space-time. Besides, several other unexplained
phenomena can emerge as a natural consequence of this modification
