Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8×10 -5 accuracy level

Abstract

In this article, we describe an experiment performed at the Laboratoire de physique des lasers and dedicated to an optical measurement of the Boltzmann constant k B. With the proposed innovative technique, determining k B comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell-Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to kBT and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO 2 laser with a wavelength λ≈10 μm. The absorption cell is placed in a thermostat, keeping the temperature at 273.15 K within 1.4 mK. We were able to measure k B with a relative uncertainty as small as 3.8×10 -5, which represents an improvement of an order of magnitude for an integration time comparable to our previous measurement published in 2007. To cite this article: K. Djerroud et al., C. R. Physique 10 (2009). © 2009 Académie des sciences.