Suppose That an Atom Has Two Energy Levels Separated by an Energy

Multiple Choice

Suppose that an atom has two energy levels separated by an energy difference $\Delta E$ . When such atoms are in thermal contact with a reservoir at temperature $T$ , there is roughly 1 atom in the higher state for every 4 in the lower state. What is the approximate ratio of $\Delta E$ to $k_{B} T$ ?

A) $\frac{1}{4}$
B) 4
C) In 4
D) $-\ln 4$
E) $e^{-1 / 4}$
F) $e^{-4}$
G) Other (specify)