  We study an excited atom-polar molecular ion chemical reaction (Ca$^*$ +
BaCl$^+$) at low temperature by utilizing a hybrid atom-ion trapping system.
The reaction rate and product branching fractions are measured and compared to
model calculations as a function of both atomic quantum state and collision
energy. At the lowest collision energy we find that the chemical dynamics
dramatically differ from capture theory predictions and are primarily dictated
by the radiative lifetime of the atomic quantum state instead of the underlying
excited-state interaction potential. We provide a simple rule for calculating
at what temperature this regime, where the collision complex lifetime is longer
than the radiative lifetime of the quantum state, is reached. This effect,
which greatly suppresses the reactivity of short-lived excited states, provides
a means for directly probing reaction range. It also naturally suppresses
unwanted chemical reactions in hybrid trapping experiments, allowing longer
molecular ion coherence and interrogation times.
