  In this theoretical study, we establish a correlation between the neutron
skin thickness and the nuclear symmetry energy for the even$-$even isotopes of
Fe, Ni, Zn, Ge, Se and Kr within the framework of the axially deformed
self-consistent relativistic mean field for the non-linear NL3$^*$ and
density-dependent DD-ME1 interactions. The coherent density functional method
is used to formulate the symmetry energy, the neutron pressure and the
curvature of finite nuclei as a function of the nuclear radius. We have
performed broad studies for the mass dependence on the symmetry energy in terms
of the neutron-proton asymmetry for mass 70 $\leq$ A $\leq$ 96. From this
analysis, we found a notable signature of a shell closure at $N$ = 50 in the
isotopic chains of Fe, Ni, Zn, Ge, Se and Kr nuclei. The present study reveals
an interrelationship between the characteristics of infinite nuclear matter and
the neutron skin thickness of finite nuclei
