**ABSTRACT**

In our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, *e _{n} *= 2.95

*e*and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). In our formula, first term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. In this paper, we make an attempt to estimate the number of free nucleons with two alternative expressions. Proceeding further, we proposed a three term relation associated only with mass number for estimating the maximum possible binding energy. Following this relation, unified atomic mass unit and Avogadro number can be understood very easily. With this kind of approach, theoretically, it seems certain to establish the existence of our proposed electroweak fermion of rest energy 585 GeV in condensed matter physics.

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