The widespread adoption of machine learning (ML) across various industries has raised sustainability concerns due to its substantial energy usage and carbon emissions. This issue becomes more pressing in adversarial ML, which focuses on enhancing model security against different network-based attacks. Implementing defenses in ML systems often necessitates additional computational resources and network security measures, exacerbating their environmental impacts. In this paper, we pioneer the first investigation into adversarial ML's carbon footprint, providing empirical evidence connecting greater model robustness to higher emissions. Addressing the critical need to quantify this trade-off, we introduce the Robustness Carbon Trade-off Index (RCTI). This novel metric, inspired by economic elasticity principles, captures the sensitivity of carbon emissions to changes in adversarial robustness. We demonstrate the RCTI through an experiment involving evasion attacks, analyzing the interplay between robustness against attacks, performance, and carbon emissions.