A highly stable experimental setup was developed for the measurement of shot noise in atomic contacts and molecular junctions to determine the number of atoms or molecules present. The use of a nano-fabricated mechanically controllable break junction (MCBJ) electrode improved the overall stability of the experimental setup. The improved stability of the system and optimization of measurement system enabled us to comprehensively investigate the shot noise as well as charge transport properties in Au atomic contacts and molecular junctions. We present a solid proof that the number of atoms (cross sectional atom) in the Au atomic contacts was exactly one. In the atomic contacts, contribution from the additional channels was under the detection limit. Furthermore, the effect of molecular adsorption on the charge transport in the Au atomic contact was investigated. Additional transport channels were opened by exposing pyrazine molecules to the Au contacts, which gave rise to an increase in the Fano factor in the shot noise.