Various ground state properties are explored for full isotonic(isotopic) chain of neutron number N(proton number Z)$=$40 using different families of Relativistic Mean-Field theory. Several properties such as nucleon separation energies, pairing energies, deformation, radii and nucleon density distributions are evaluated and compared with the experimental data as well as those from other microscopic and macroscopic models. N$=$40 isotonic chain presents ample of support for the neutron magicity and articulates double magicity in recently discovered $^{60}$Ca and $^{68}$Ni. Our results are in close conformity with recently measured value of charge radius of $^{68}$Ni [S. Kaufmann textit{et al.}, Phys. Rev. Lett. 124, 132502 (2020)] which supports the N$=$40 magicity. Contrarily, Zr isotopes (Z$=$40) display variety of shapes leading to the phenomenon of shape transitions and shape co-existence. The role of 3s$_{1/2}$ state, which leads to central depletion if unoccupied, is also investigated. $^{56}_{16}$S and $^{122}_{40}$Zr are found to be doubly bubble nuclei.
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