= Ammonia inversion transition
{title2=$h\nu_0$}
In <ammonia>, the <nitrogen> <chemical atom> can lie on either side of the plane of the three <hydrogen> <chemical atoms>. <Quantum tunnelling> couples these configurations; the resulting pair of <energy levels> permits an <electric dipole> transition. This geometrical inversion is distinct from <population inversion>, which concerns how many <molecules> occupy each level.<Chapter 9: The Ammonia Maser>[§9–1, ammonia configurations and inversion doublet]{ref}
For an idealized pair of <energy levels> with equal <quantum degeneracy>, the <Boltzmann distribution> gives $N_u/N_l=\exp[-h\nu_0/(k_{\mathrm B}T)]<1$ at positive <temperature> $T$. A warm source therefore supplies upper-state <molecules> together with an unwanted lower-state population. Selecting the former can produce <population inversion> in the transmitted beam without exciting each transmitted <molecule> during selection. The <energy> per net downward transition is
$$
\epsilon=h\nu_0.
$$
Here $h$ is the <Planck constant>. Taking the reported $\nu_0=23.87\,\mathrm{GHz}$ as a rounded input gives $\epsilon\approx1.582\times10^{-23}\,\mathrm J$. This calculation is a conversion of the reported <frequency>, not a new measurement of the <ammonia inversion transition>.
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