The energy of a particle in the Rainbow Rindler metric is derived using Hamilton's variational principle. Saha Ionization equation and Pair production in Rainbow Rindler metric have been investigated. Saha ionization equation and Pair production in Rainbow Rindler metric depend on corrected acceleration which is energy-dependent. This means energy ($E$) and metric tensor ($g_{\mu \nu}(E)$) depends on the inertial observer. The physical implications of energy-dependent acceleration, observer-dependent(inertial) energy and metric tensor are discussed. On comparing the above results with that of Rindler metric we get the result obtained by Sanchari De and Somenath Chakarabarthy by applying the correspondence principle.