Population of high quantum number states can differ from their LTE values at high densities (Ne ~106 − 108 cm−3) and temperatures of the order of 104 K. In this case, the intensity of recombination lines can be strongly amplified. The amount of amplification depends on density and temperature, and it is different for different quantum numbers, allowing the determination of the physical and kinematic conditions of the emitting region through the observation of recombination lines of different quantum numbers. This was the case of the massive binary system η Carinae. This system was observed with ALMA in the recombination lines H21α, H28α, H30α, H40α and H42α and the continuum at the frequencies of the corresponding lines. The continuum spectrum was characteristic of a compact HII region, becoming optically thin at around 300 GHz. From the intensity and width of the recombination lines we concluded that the not-resolved emission region, assumed spherically symmetric, is a shell of 40 AU radius and 4 AU width, expanding at velocities between 20 and 60 km s−1, with density of 107 cm−3 and temperature of 17000 K.