where N ( 0 ) is the initial number of light sources in the excited state, t is the time and Γ Γ rad is the radiative decay rate of the transition. The number of excited states N thus decays exponentially with time, similar to radioactive decay. After one lifetime, the number of excited states decays to 36.8% of its original value ( 1 e -time). The radiative decay rate Γ Γ rad is inversely proportional to the lifetime τ τ 21 :