  An ensemble of atoms in steady-state, whether in thermal equilibrium or not,
has a well defined energy distribution. Since the energy of single atoms within
the ensemble cannot be individually measured, energy distributions are
typically inferred from statistical averages. Here, we show how to measure the
energy of a single atom in a single experimental realization (single-shot). The
energy distribution of the atom over many experimental realizations can thus be
readily and directly obtained. We apply this method to a single-ion trapped in
a linear Paul trap for which energy measurement in a single-shot is applicable
from 10 K and above. Our energy measurement agrees within 5% to a different
thermometry method which requires extensive averaging. Apart from the total
energy, we also show that the motion of the ion in different trap modes can be
distinguished. We believe that this method will have profound implications on
single particle chemistry and collision experiments.
