Sombor index is a recently introduced degree based graph topological index. For a graph $G$, it is defined as $$SO(G)=\sum _{uv\in E(G)}\sqrt{d_u^2+d_v^2},$$ where $d_u$ denotes the degree of the vertex $u$ in $G$. Within a short period of time after introduction of this index by Gutman, many aspects of it have been studied by many researchers. Relating the Sombor index $SO(G)$ of a graph $G$ with the energy $\epsilon (G)$ of $G$ is one such instance among the others. In this article, we aim to provide some improved results relating $SO(G)$ and $\epsilon (G)$.