This paper explores the phenomena of chiral tunneling and the Klein paradox in graphene, a two-dimensional material composed of a single layer of carbon atoms. The Klein paradox, a relativistic quantum phenomenon, involves the unimpeded penetration of relativistic particles through high and wide potential barriers. While this effect has been theoretically discussed in particle and nuclear physics, experimental verification has been challenging. However, the paper demonstrates that these phenomena can be tested in graphene using electrostatic barriers. Graphene's unique electronic properties, described by the Dirac equation, allow it to mimic relativistic particles. The quasiparticles in graphene exhibit linear dispersion relations, similar to massless relativistic particles, and possess chiral properties. This chiral nature leads to highly anisotropic quantum tunneling, distinct from conventional electrons. The paper compares single-layer and bilayer graphene, showing that single-layer graphene behaves like massless Dirac fermions, while bilayer graphene exhibits massive chiral fermions. The Klein paradox in graphene is analyzed through tunneling experiments, where the transmission probability through a potential barrier is studied. For single-layer graphene, the transmission probability approaches unity for certain angles, a feature unique to massless Dirac fermions. In contrast, bilayer graphene exhibits perfect reflection for angles close to normal incidence, demonstrating a different behavior due to its chiral properties. The paper also discusses the implications of these findings for experimental studies. The unique transport properties of graphene, particularly its resistance to backscattering due to the conservation of pseudospin, make it an ideal system for studying relativistic quantum effects. The results suggest that graphene can be used to test the Klein paradox and other QED phenomena experimentally, offering insights into both fundamental physics and potential applications in electronics. The study highlights the importance of chiral and pseudospin properties in determining the transport behavior of graphene, distinguishing it from conventional materials.This paper explores the phenomena of chiral tunneling and the Klein paradox in graphene, a two-dimensional material composed of a single layer of carbon atoms. The Klein paradox, a relativistic quantum phenomenon, involves the unimpeded penetration of relativistic particles through high and wide potential barriers. While this effect has been theoretically discussed in particle and nuclear physics, experimental verification has been challenging. However, the paper demonstrates that these phenomena can be tested in graphene using electrostatic barriers. Graphene's unique electronic properties, described by the Dirac equation, allow it to mimic relativistic particles. The quasiparticles in graphene exhibit linear dispersion relations, similar to massless relativistic particles, and possess chiral properties. This chiral nature leads to highly anisotropic quantum tunneling, distinct from conventional electrons. The paper compares single-layer and bilayer graphene, showing that single-layer graphene behaves like massless Dirac fermions, while bilayer graphene exhibits massive chiral fermions. The Klein paradox in graphene is analyzed through tunneling experiments, where the transmission probability through a potential barrier is studied. For single-layer graphene, the transmission probability approaches unity for certain angles, a feature unique to massless Dirac fermions. In contrast, bilayer graphene exhibits perfect reflection for angles close to normal incidence, demonstrating a different behavior due to its chiral properties. The paper also discusses the implications of these findings for experimental studies. The unique transport properties of graphene, particularly its resistance to backscattering due to the conservation of pseudospin, make it an ideal system for studying relativistic quantum effects. The results suggest that graphene can be used to test the Klein paradox and other QED phenomena experimentally, offering insights into both fundamental physics and potential applications in electronics. The study highlights the importance of chiral and pseudospin properties in determining the transport behavior of graphene, distinguishing it from conventional materials.