  We report a photoacoustic spectroscopy setup with a high-power mid-infrared
frequency comb as the light source. The setup is used in broadband spectroscopy
of radiocarbon methane. Due to the high sensitivity of a cantilever-enhanced
photoacoustic cell and the high power light source, we can reach a detection
limit below 100 ppb in a broadband measurement with a sample volume of only a
few milliliters. The first infrared spectrum of $^{14}\text{CH}_4$ is reported
and given a preliminary assignment. The results lay a foundation for the
development of optical detection systems for radiocarbon methane.
