The Material Science in modern times seem to be incomplete without nano-materials⁹. The distinction of nano materials with other bulk materials lies in dimensionality of the systems. For instance, we cite the field of carbon nano tubes and other nano materials have in recent days been a promising and emerging area of research due to its dimensionality. In fact, when the particular dimension of a three dimensional system becomes comparable to the de-Broglie wave length, the energy level associated with the dimension become quantized. This quantized energy is found to be fruitful stating point to account for other quantized electrical quantities in composite nano structures and other similar systems. With the help of the quantized energy, a semi classical approach has been adopted to investigate the quantized nature of the drift velocity of electrons and finally an expression of current density in ideal one dimensional carbon nano tubes has been proposed.