  We study nuclear structure properties for various isotopes of Ytterbium (Yb),
Hafnium(Hf), Tungsten(W), Osmium(Os), Platinum(Pt) and Mercury(Hg) in $Z = 70 -
80$ drip-line region starting from $N =80$ to $N=170$ within the formalism of
relativistic mean field (RMF) theory. The pairing correlation is taken care by
using BCS approach. We compared our results with Finite Range Droplet
Model(FRDM) and experimental data and found that the calculated results are in
good agreement. Neutron shell closure are obtained at $N=82$ and $126$ in this
region. We have also studied probable decay mechanisms of these elements.
